Wavelets, vibrations and scalings
Meyer, Yves
1997-01-01
Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilations. This book discusses the relevance of wavelet analysis to problems in which self-similarities are important. Among the conclusions drawn are the following: 1) A weak form of self-similarity can be given a simple characterization through size estimates on wavelet coefficients, and 2) Wavelet bases can be tuned in order to provide a sharper characterization of this self-similarity. A pioneer of the wavelet "saga", Meye...
Daubechies wavelets for linear scaling density functional theory
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Mohr, Stephan [Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland); Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Ratcliff, Laura E.; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry [Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Boulanger, Paul [Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Institut Néel, CNRS and Université Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 09 (France); Goedecker, Stefan [Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland)
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
Institute of Scientific and Technical Information of China (English)
XIONG Lei; LI haijiao; ZHANG Lewen
2008-01-01
The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions, 4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.
THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION
Institute of Scientific and Technical Information of China (English)
刘海峰; 周炜星; 王辅臣; 龚欣; 于遵宏
2002-01-01
Some properties of the wavelet transform of trigonometric function, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.
A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions
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Seyed Hossein Mahdavi
2015-01-01
Full Text Available Wavelet solution techniques have become the focus of interest among researchers in different disciplines of science and technology. In this paper, implementation of two different wavelet basis functions has been comparatively considered for dynamic analysis of structures. For this aim, computational technique is developed by using free scale of simple Haar wavelet, initially. Later, complex and continuous Chebyshev wavelet basis functions are presented to improve the time history analysis of structures. Free-scaled Chebyshev coefficient matrix and operation of integration are derived to directly approximate displacements of the corresponding system. In addition, stability of responses has been investigated for the proposed algorithm of discrete Haar wavelet compared against continuous Chebyshev wavelet. To demonstrate the validity of the wavelet-based algorithms, aforesaid schemes have been extended to the linear and nonlinear structural dynamics. The effectiveness of free-scaled Chebyshev wavelet has been compared with simple Haar wavelet and two common integration methods. It is deduced that either indirect method proposed for discrete Haar wavelet or direct approach for continuous Chebyshev wavelet is unconditionally stable. Finally, it is concluded that numerical solution is highly benefited by the least computation time involved and high accuracy of response, particularly using low scale of complex Chebyshev wavelet.
Local Extrema of Periodic Function's Wavelet Transform
Institute of Scientific and Technical Information of China (English)
FAN Qi-bin; SONG Xiao-yan
2005-01-01
The theory of detecting ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges. To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal's instantaneous amplitude and period.
Inversion of receiver function by wavelet transformation
Institute of Scientific and Technical Information of China (English)
吴庆举; 田小波; 张乃铃; 李桂银; 曾融生
2003-01-01
A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low tohigh scale, with the inversion result for low order receiver function as the initial model for high order. Aneighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on theinitial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal andupper mantle velocity with high resolution.
Gaussian Functions, Γ-Functions and Wavelets
Institute of Scientific and Technical Information of China (English)
蔡涛; 许天周
2003-01-01
The relations between Gaussian function and Γ-function is revealed first at one-dimensional situation. Then, the Fourier transformation of n-dimensional Gaussian function is deduced by a lemma. Following the train of thought in one-dimensional situation, the relation between n-dimensional Gaussian function and Γ-function is given. By these, the possibility of arbitrary derivative of an n-dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ-function as well as in finding high-dimensional mother wavelets.
Quantization Audio Watermarking with Optimal Scaling on Wavelet Coefficients
Chen, S -T; Tu, S -Y
2011-01-01
In recent years, discrete wavelet transform (DWT) provides an useful platform for digital information hiding and copyright protection. Many DWT-based algorithms for this aim are proposed. The performance of these algorithms is in term of signal-to-noise ratio (SNR) and bit-error-rate (BER) which are used to measure the quality and the robustness of an embedded audio. However, there is a tradeoff relationship between the embedded-audio quality and robustness. The tradeoff relationship is a signal processing problem in the wavelet domain. To solve this problem, this study presents an optimization-based scaling scheme using optimal multi-coefficients quantization in the wavelet domain. Firstly, the multi-coefficients quantization technique is rewritten as an equation with arbitrary scaling on DWT coefficients and set SNR to be a performance index. Then, a functional connecting the equation and the performance index is derived. Secondly, Lagrange Principle is used to obtain the optimal solution. Thirdly, the scal...
MULTI-RESOLUTION WAVELET ANALYSES OF TWO DIFFERENT PERFECTİONİSM SCALES: A UNIVERSITY SAMPLE
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Y. KARACA
2013-01-01
Full Text Available Our prior studies indicated that statistical and wavelet analyses of perfectionism inventories were evaluated by SPSS and Wavelet packets. The main aim of the present study is to investigate different scale affects on perfectionism. We proposed that changes of low-frequency Meyer wavelets reflect students' perfectionism levels. We used Wavelet 1D and continuous 1D Wavelet analyses to measure their time dependence. We studied students' questionnaires. Multi-resolution analysis was obtained from continuous and discrete data as a function of cases at different scales. Large scale effects are assumed to play an important role on students with higher others-oriented perfectionism and adaptive perfectionism. Continuous wavelet 1D (Mexh analyses show the similar results and, large scale effects play an important role on students' behavior. In contrast, lower scale effects are assumed to play an important role on students with adaptive perfectionism and self-directed perfectionism
Localisation of directional scale-discretised wavelets on the sphere
McEwen, Jason D; Wiaux, Yves
2015-01-01
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients exactly, in theory and practice (to machine precision). Scale-discretised wavelets are closely related to spherical needlets (both were developed independently at about the same time) but relax the axisymmetric property of needlets so that directional signal content can be probed. Needlets have been shown to satisfy important quasi-exponential localisation and asymptotic uncorrelation properties. We show that these properties also hold for directional scale-discretised wavelets on the sphere and derive similar localisation and uncorrelation bounds in both the scalar and spin settings. Scale-discretised wavelets can thus be considered as directional needlets.
Implementation of Time-Scale Transformation Based on Continuous Wavelet Theory
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties.This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform.For an arbitrary given square-integrable function f(t),g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform.The result shows that time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.
Wavelet-based LASSO in functional linear regression.
Zhao, Yihong; Ogden, R Todd; Reiss, Philip T
2012-07-01
In linear regression with functional predictors and scalar responses, it may be advantageous, particularly if the function is thought to contain features at many scales, to restrict the coefficient function to the span of a wavelet basis, thereby converting the problem into one of variable selection. If the coefficient function is sparsely represented in the wavelet domain, we may employ the well-known LASSO to select a relatively small number of nonzero wavelet coefficients. This is a natural approach to take but to date, the properties of such an estimator have not been studied. In this paper we describe the wavelet-based LASSO approach to regressing scalars on functions and investigate both its asymptotic convergence and its finite-sample performance through both simulation and real-data application. We compare the performance of this approach with existing methods and find that the wavelet-based LASSO performs relatively well, particularly when the true coefficient function is spiky. Source code to implement the method and data sets used in the study are provided as supplemental materials available online.
Energy Technology Data Exchange (ETDEWEB)
Garcia R, A. [ININ, Carretera Mexico-Toluca S/N, 52750 La Marquesa, Ocoyoacac, Estado de Mexico (Mexico)]. e-mail: ramador@nuclear.inin.mx
2007-07-01
At the moment the signals are used to diagnose the state of the systems, by means of the extraction of their more important characteristics such as the frequencies, tendencies, changes and temporary evolutions. This characteristics are detected by means of diverse analysis techniques, as Autoregressive methods, Fourier Transformation, Fourier transformation in short time, Wavelet transformation, among others. The present work uses the one Wavelet transformation because it allows to analyze stationary, quasi-stationary and transitory signals in the time-frequency plane. It also describes a methodology to select the scales and the Wavelet function to be applied the one Wavelet transformation with the objective of detecting to the dominant system frequencies. (Author)
Wavelet Variance Analysis of EEG Based on Window Function
Institute of Scientific and Technical Information of China (English)
ZHENG Yuan-zhuang; YOU Rong-yi
2014-01-01
A new wavelet variance analysis method based on window function is proposed to investigate the dynamical features of electroencephalogram (EEG).The ex-prienmental results show that the wavelet energy of epileptic EEGs are more discrete than normal EEGs, and the variation of wavelet variance is different between epileptic and normal EEGs with the increase of time-window width. Furthermore, it is found that the wavelet subband entropy (WSE) of the epileptic EEGs are lower than the normal EEGs.
Image denoising exploiting inter- and intra-scale dependency in complex wavelet domain
Institute of Scientific and Technical Information of China (English)
Fengxia Yan; Lizhi Cheng
2007-01-01
A new locally adaptive image denoising method, which exploits the intra-scale and inter-scale dependency in the dual-tree complex wavelet domain, is presented. Firstly, a recently emerged bivariate shrinkage rule is extended to a complex coefficient and its neighborhood, the corresponding nonlinear threshold functions are derived from the models using Bayesian estimation theory. Secondly, an adaptive weight, which is able to capture the inter-scale dependency of the complex wavelet coefficients, is combined to the obtained bishrink threshold. The experimental results demonstrate an improved denoising performance over related earlier techniques both in peak signal-to-noise ratio (PSNR) and visual effect.
Nonlinear wavelet estimation of regression function with random desigm
Institute of Scientific and Technical Information of China (English)
张双林; 郑忠国
1999-01-01
The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov space Bp,q? is proved under quite genera] assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.
Based on the Wavelet Function of Power Network Fault Location
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Fan YU
2013-04-01
Full Text Available In order to improve the measurement accuracy, in the traditional measuring method based on, by avoiding wave speed influence on fault location of transmission line method, and compares it with the combination of wavelet transform. This article selects dBN wavelet and three B spline wavelet contrast, compared them with new methods, through the Xi'an City Power Supply Bureau of the actual fault data validation. The results show that, with3 B spline wavelet and the new method combined with the location results are closer to the actual distance, its accuracy is higher than that of db3wavelet transform and a new method derived from the results, the error is far less than the db3 wavelet function, location is satisfactory.
A time-scale analysis of systematic risk: wavelet-based approach
Khalfaoui Rabeh, K; Boutahar Mohamed, B
2011-01-01
The paper studies the impact of different time-scales on the market risk of individual stock market returns and of a given portfolio in Paris Stock Market by applying the wavelet analysis. To investigate the scaling properties of stock market returns and the lead/lag relationship between them at different scales, wavelet variance and crosscorrelations analyses are used. According to wavelet variance, stock returns exhibit long memory dynamics. The wavelet cross-correlation analysis shows that...
Study of Denoising in TEOAE Signals Using an Appropriate Mother Wavelet Function
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Habib Alizadeh Dizaji
2007-06-01
Full Text Available Background and Aim: Matching a mother wavelet to class of signals can be of interest in signal analysis and denoising based on wavelet multiresolution analysis and decomposition. As transient evoked otoacoustic emissions (TEOAES are contaminated with noise, the aim of this work was to provide a quantitative approach to the problem of matching a mother wavelet to TEOAE signals by using tuning curves and to use it for analysis and denoising TEOAE signals. Approximated mother wavelet for TEOAE signals was calculated using an algorithm for designing wavelet to match a specified signal.Materials and Methods: In this paper a tuning curve has used as a template for designing a mother wavelet that has maximum matching to the tuning curve. The mother wavelet matching was performed on tuning curves spectrum magnitude and phase independent of one another. The scaling function was calculated from the matched mother wavelet and by using these functions, lowpass and highpass filters were designed for a filter bank and otoacoustic emissions signal analysis and synthesis. After signal analyzing, denoising was performed by time windowing the signal time-frequency component.Results: Aanalysis indicated more signal reconstruction improvement in comparison with coiflets mother wavelet and by using the purposed denoising algorithm it is possible to enhance signal to noise ratio up to dB.Conclusion: The wavelet generated from this algorithm was remarkably similar to the biorthogonal wavelets. Therefore, by matching a biorthogonal wavelet to the tuning curve and using wavelet packet analysis, a high resolution time-frequency analysis for the otoacoustic emission signals is possible.
Wavelet treatment of the intrachain correlation functions of homopolymers in dilute solutions
Fedorov, M. V.; Chuev, G. N.; Kuznetsov, Yu. A.; Timoshenko, E. G.
2004-11-01
Discrete wavelets are applied to the parametrization of the intrachain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulations. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. The quality of the approximation has been assessed by calculation of the scaling exponents obtained from the des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in better agreement with those from recent renormalization group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.
Scale-Dependent Representations of Relief Based on Wavelet Analysis
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Automatic generalization of geographic information is the core of multi-scale representation of spatial data,but the scale-dependent generalization methods are far from abundant because of its extreme complicacy.This paper puts forward a new consistency model about scale-dependent representations of relief based on wavelet analysis,and discusses the thresholds in the model so as to acquire the continual representations of relief with different details between scales.The model not only meets the need of automatic generalization but also is scale-dependent completely.Some practical examples are given.
Multi-Scale SSA or Data-Adaptive Wavelets
Yiou, P.; Sornette, D.; Sornette, D.; Sornette, D.; Ghil, M.; Ghil, M.
2001-05-01
Using multi-scale ideas from wavelet analysis, the singular-spectrum analysis (SSA) is extended to the study of nonstationary time series, including the case where their variance diverges. The wavelet transform is similar to a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W proportional to M to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components. The proposed multi-scale SSA is a local SSA analysis within a moving window of width Mwavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signal's correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied to the monthly values of the Southern Oscillation index (SOI) which captures major features of the El Niño/Southern Oscillation in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil's staircase scenario for the El Niño/Southern Oscillation phenomenon.
2-D NONSEPARABLE SCALING FUNCTION INTERPOLATION AND APPROXIMATION
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system.Several equivalent statements of accuracy of nonseparable scaling function are also given.In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.
The transverse Talbot effect: Scaling analyses based on wavelet transforms
Rosu, H C; Ludu, A
2013-01-01
Berry and Klein [J. Mod. Opt. 43, 2139 (1996)] studied the fractal properties of the paraxial diffracted field behind a Ronchi grating. In particular, they studied the transverse Talbot images formed at fractional distances in units of the Talbot distance chosen from the Fibonacci convergents to the complement of the inverse golden mean zeta_G=(3-square root of 5)/2. Here, we analyze these Talbot images with two well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We use the widths of the singularity spectra, Delta(alpha)=alpha_H-alpha_min, as a characteristic feature of the Talbot images. The tau scaling exponents of the q moments are linear in q within the two methods, which is a strong argument in favor of the monofractality of the transverse diffractive paraxial field
Wavelets and Geometric Structure for Function Spaces
Institute of Scientific and Technical Information of China (English)
Qi Xiang YANG
2004-01-01
With Littlewood-Paley analysis, Peetre and Triebel classified, systematically, almost all the usual function spaces into two classes of spaces: Besov spaces (B)s,q p(s ∈ R,0 ＜ p,q ≤∞) and Triebel-Lizorkin spaces (F)s,q p(s∈R,0＜p＜∞,0＜q≤∞); but the structure of dual spaces (D)s,q p of (F)s,q p(s∈R, 0＜p≤1≤q≤∞) is very different from that of Besov spaces or that of Triebel-Lizorkin spaces, and their structure cannot be analysed easily in the Littlewood-Paley analysis. Our main goal is to characterize (D)s,q p (s ∈ R, 0＜p= 1≤q≤∞) in tent spaces with wavelets. By the way, some applications are given: (i) Triebel-Lizorkin spaces for p = ∞ defined by Littlewood-Paley analysis cannot serve as the dual spaces of Triebel-Lizorkin spaces for p = 1; (ii) Some inclusion relations among these above spaces and some relations among(B)o,q1,(F)o,q1 and L1 are studied.
On the optimal choice of wavelet function for multiscale honed surface characterization
Energy Technology Data Exchange (ETDEWEB)
Mezghani, S; Mansori, M El [Arts and Metiers ParisTech, LMPF, rue St Dominique - BP 508, 51006 Chalons-en-Champagne (France); Sabri, L [RENAULT S.A.S., Direction de la Mecanique/Direction de l' Ingenierie Process, Rueil Malmaison, Paris (France); Zahouani, H, E-mail: sabeur.mezghani@ensam.eu [Ecole Centrale de Lyon, LTDS UMR CNRS 5513, 36 avenue Guy de Collongue, 69131 Ecully Cedex (France)
2011-08-19
Multiscale surface topography characterization is mostly suited than standard approaches because it is more adapted to the multi-stage process generation. Wavelet transform represents a power tool to perform the multiscale decomposition of the surface topography in a wide range of wavelength. However, characterization results depend closely on the topography data acquisition instrument (resolution, height accuracy, sensitivity...) and also on the wavelet analysis method (discrete or continuous transform). In particular, the choice of wavelet function can have significant effect on the analysis results. In this paper, we present experimental work on a number of popular wavelets functions with the aim of finding wavelets that exhibit optimal description of honed surface features when continuous wavelet transform is used. We demonstrate that the regularity property of wavelet function has a significant influence on the characterization performances. This comparative study shows also that the Morlet wavelet is the more adapted wavelet basis function for multiscale characterization of honed surfaces using continuous wavelet transform.
Wu, Jiao; Liu, Fang; Jiao, L C; Wang, Xiaodong; Hou, Biao
2011-12-01
Most wavelet-based reconstruction methods of compressive sensing (CS) are developed under the independence assumption of the wavelet coefficients. However, the wavelet coefficients of images have significant statistical dependencies. Lots of multivariate prior models for the wavelet coefficients of images have been proposed and successfully applied to the image estimation problems. In this paper, the statistical structures of the wavelet coefficients are considered for CS reconstruction of images that are sparse or compressive in wavelet domain. A multivariate pursuit algorithm (MPA) based on the multivariate models is developed. Several multivariate scale mixture models are used as the prior distributions of MPA. Our method reconstructs the images by means of modeling the statistical dependencies of the wavelet coefficients in a neighborhood. The proposed algorithm based on these scale mixture models provides superior performance compared with many state-of-the-art compressive sensing reconstruction algorithms.
Distinguishing Stationary/Nonstationary Scaling Processes Using Wavelet Tsallis q-Entropies
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Julio Ramirez Pacheco
2012-01-01
Full Text Available Classification of processes as stationary or nonstationary has been recognized as an important and unresolved problem in the analysis of scaling signals. Stationarity or nonstationarity determines not only the form of autocorrelations and moments but also the selection of estimators. In this paper, a methodology for classifying scaling processes as stationary or nonstationary is proposed. The method is based on wavelet Tsallis q-entropies and particularly on the behaviour of these entropies for scaling signals. It is demonstrated that the observed wavelet Tsallis q-entropies of 1/f signals can be modeled by sum-cosh apodizing functions which allocates constant entropies to a set of scaling signals and varying entropies to the rest and that this allocation is controlled by q. The proposed methodology, therefore, differentiates stationary signals from non-stationary ones based on the observed wavelet Tsallis entropies for 1/f signals. Experimental studies using synthesized signals confirm that the proposed method not only achieves satisfactorily classifications but also outperforms current methods proposed in the literature.
Steganography based on wavelet transform and modulus function
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image,in accordance with the visual property that human eyes are less sensitive to strong texture,a novel steganographic method based on wavelet and modulus function is presented.First,an image is divided into blocks of prescribed size,and every block is decomposed into one-level wavelet.Then,the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude.Finall,secret information is embedded by steganography based on modulus function. From the experimental results,the proposed method hides much more information and maintains a good visual quality of stego-image.Besides,the embedded data can be extracted from the stego-image without referencing the original image.
A simple structure wavelet transform circuit employing function link neural networks and SI filters
Mu, Li; Yigang, He
2016-12-01
Signal processing by means of analog circuits offers advantages from a power consumption viewpoint. Implementing wavelet transform (WT) using analog circuits is of great interest when low-power consumption becomes an important issue. In this article, a novel simple structure WT circuit in analog domain is presented by employing functional link neural network (FLNN) and switched-current (SI) filters. First, the wavelet base is approximated using FLNN algorithms for giving a filter transfer function that is suitable for simple structure WT circuit implementation. Next, the WT circuit is constructed with the wavelet filter bank, whose impulse response is the approximated wavelet and its dilations. The filter design that follows is based on a follow-the-leader feedback (FLF) structure with multiple output bilinear SI integrators and current mirrors as the main building blocks. SI filter is well suited for this application since the dilation constant across different scales of the transform can be precisely implemented and controlled by the clock frequency of the circuit with the same system architecture. Finally, to illustrate the design procedure, a seventh-order FLNN-approximated Gaussian wavelet is implemented as an example. Simulations have successfully verified that the designed simple structure WT circuit has low sensitivity, low-power consumption and litter effect to the imperfections.
Wang, Zhengzi; Ren, Zhong; Liu, Guodong
2016-10-01
In this paper, the wavelet threshold denoising method was used into the filtered back-projection algorithm of imaging reconstruction. To overcome the drawbacks of the traditional soft- and hard-threshold functions, a modified wavelet threshold function was proposed. The modified wavelet threshold function has two threshold values and two variants. To verify the feasibility of the modified wavelet threshold function, the standard test experiments were performed by using the software platform of MATLAB. Experimental results show that the filtered back-projection reconstruction algorithm based on the modified wavelet threshold function has better reconstruction effect because of more flexible advantage.
QUASI-INTERPOLATION AND APPROXIMATION VIA NONSEPARABLE SCALING FUNCTION
Institute of Scientific and Technical Information of China (English)
Enbing Lin; Ling Yi
2002-01-01
Quasi-interpolation has been audied in many papers, e.g. , [5]. Here we introduce nonseparable scal-ing function quasi-interpolation and show that its approximation can provide similar convergence propertiesas scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are alsogien. In the numerical experiments, it appears that nonseparable scaling function interpolation has betterconvergonce results than scalar wavelet systems in some cases.
Four-Point Wavelets and Their Applications
Institute of Scientific and Technical Information of China (English)
魏国富; 陈发来
2002-01-01
Multiresolution analysis (MRA) and wavelets provide useful and efficient tools for representing functions at multiple levels of details. Wavelet representations have been used in a broad range of applications, including image compression, physical simulation and numerical analysis. In this paper, the authors construct a new class of wavelets, called four-point wavelets,based on an interpolatory four-point subdivision scheme. They are of local support, symmetric and stable. The analysis and synthesis algorithms have linear time complexity. Depending on different weight parameters w, the scaling functions and wavelets generated by the four-point subdivision scheme are of different degrees of smoothness. Therefore the user can select better wavelets relevant to the practice among the classes of wavelets. The authors apply the fourpoint wavelets in signal compression. The results show that the four-point wavelets behave much better than B-spline wavelets in many situations.
Tzanis, A.
2012-04-01
GPR is an invaluable tool for civil and geotechnical engineering applications. One of the most significant objectives of such applications is the detection of fractures, inclined interfaces, empty or filled cavities frequently associated with jointing/faulting and a host of other oriented features. These types of target, especially fractures, are usually not good reflectors and are spatially localized. Their scale is therefore a factor significantly affecting their detectability. Quite frequently, systemic or extraneous noise, or other significant structural characteristics swamp the data with information which blurs, or even masks reflections from such targets, rendering their recognition difficult. This paper reports a method of extracting information (isolating) oriented and scale-dependent structural characteristics, based on oriented two-dimensional B-spline wavelet filters and Gabor wavelet filters. In addition to their advantageous properties (e.g. compact support, orthogonality etc), B-spline wavelets comprise a family with a broad spectrum of frequency localization properties and frequency responses that mimic, more or less, the shape of the radar source wavelet. For instance, the Ricker wavelet is also approximated by derivatives of Cardinal B-splines. An oriented two-dimensional B-spline filter is built by sidewise arranging a number of identical one-dimensional wavelets to create a matrix, tapering the edge-parallel direction with an orthogonal window function and rotating the resulting matrix to the desired orientation. The length of the one-dimensional wavelet (edge-normal direction) determines the width of the topographic features to be isolated. The number of parallel wavelets (edge-parallel direction) determines the feature length over which to smooth. The Gabor wavelets were produced by a Gabor kernel that is a product of an elliptical Gaussian and a complex plane wave: it is two-dimensional by definition. Their applications have hitherto focused
Ali, Abebe Mohammed; Skidmore, Andrew K.; Darvishzadeh, Roshanak; van Duren, Iris; Holzwarth, Stefanie; Mueller, Joerg
2016-12-01
Quantification of vegetation properties plays an important role in the assessment of ecosystem functions with leaf dry mater content (LDMC) and specific leaf area (SLA) being two key functional traits. For the first time, these two leaf traits have been estimated from the airborne images (HySpex) using the INFORM radiative transfer model and Continuous Wavelet Analysis (CWA). Ground truth data, were collected for 33 sample plots during a field campaign in July 2013 in the Bavarian Forest National Park, Germany, concurrent with the hyperspectral overflight. The INFORM model was used to simulate the canopy reflectance of the test site and the simulated spectra were transformed to wavelet features by applying CWA. Next, the top 1% strongly correlated wavelet features with the LDMC and SLA were used to develop predictive (regression) models. The two leaf traits were then retrieved using the CWA transformed HySpex imagery and the predictive models. The results were validated using R2 and the RMSE of the estimated and measured variables. Our results revealed strong correlations between six wavelet features and LDMC, as well as between four wavelet features and SLA. The wavelet features at 1741 nm (scale 5) and 2281 nm (scale 4) were the two most strongly correlated with LDMC and SLA respectively. The combination of all the identified wavelet features for LDMC yielded the most accurate prediction (R2 = 0.59 and RMSE = 4.39%). However, for SLA the most accurate prediction was obtained from the single most correlated feature: 2281 nm, scale 4 (R2 = 0.85 and RMSE = 4.90). Our results demonstrate the applicability of Continuous Wavelet Analysis (CWA) when inverting radiative transfer models, for accurate mapping of forest leaf functional traits.
Wavelet multiscale analysis for Hedge Funds: Scaling and strategies
Conlon, T.; Crane, M.; Ruskin, H. J.
2008-09-01
The wide acceptance of Hedge Funds by Institutional Investors and Pension Funds has led to an explosive growth in assets under management. These investors are drawn to Hedge Funds due to the seemingly low correlation with traditional investments and the attractive returns. The correlations and market risk (the Beta in the Capital Asset Pricing Model) of Hedge Funds are generally calculated using monthly returns data, which may produce misleading results as Hedge Funds often hold illiquid exchange-traded securities or difficult to price over-the-counter securities. In this paper, the Maximum Overlap Discrete Wavelet Transform (MODWT) is applied to measure the scaling properties of Hedge Fund correlation and market risk with respect to the S&P 500. It is found that the level of correlation and market risk varies greatly according to the strategy studied and the time scale examined. Finally, the effects of scaling properties on the risk profile of a portfolio made up of Hedge Funds is studied using correlation matrices calculated over different time horizons.
Institute of Scientific and Technical Information of China (English)
李建平; 唐远炎; 严中洪; 张万萍
2001-01-01
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When/N = 2k- 1 and N = 2k , the unified analytic constructions of orthogonal wavelet filters are put forward,respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
Hu, Wei; Si, Bing Cheng
2016-08-01
The scale-specific and localized bivariate relationships in geosciences can be revealed using bivariate wavelet coherence. The objective of this study was to develop a multiple wavelet coherence method for examining scale-specific and localized multivariate relationships. Stationary and non-stationary artificial data sets, generated with the response variable as the summation of five predictor variables (cosine waves) with different scales, were used to test the new method. Comparisons were also conducted using existing multivariate methods, including multiple spectral coherence and multivariate empirical mode decomposition (MEMD). Results show that multiple spectral coherence is unable to identify localized multivariate relationships, and underestimates the scale-specific multivariate relationships for non-stationary processes. The MEMD method was able to separate all variables into components at the same set of scales, revealing scale-specific relationships when combined with multiple correlation coefficients, but has the same weakness as multiple spectral coherence. However, multiple wavelet coherences are able to identify scale-specific and localized multivariate relationships, as they are close to 1 at multiple scales and locations corresponding to those of predictor variables. Therefore, multiple wavelet coherence outperforms other common multivariate methods. Multiple wavelet coherence was applied to a real data set and revealed the optimal combination of factors for explaining temporal variation of free water evaporation at the Changwu site in China at multiple scale-location domains. Matlab codes for multiple wavelet coherence were developed and are provided in the Supplement.
Institute of Scientific and Technical Information of China (English)
MAO Yibo
2003-01-01
The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-0rder and 2-0rder balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesn't increase the length of filters, which suggests that a relatively short balanced multiwavelet can be constructed from an existing unbalanced multi-wavelet as short as possible.
Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence
Institute of Scientific and Technical Information of China (English)
Zhen-yan XIA; Yan TIAN; Nan JIANG
2009-01-01
The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. Wavelet transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation or breakup of eddies are related to the vertical position in the boundary layer, and the energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.
Control of Weierstrass-Mandelbrot Function Model with Morlet Wavelets
Zhang, Li; Liu, Shutang; Yu, Chenglong
A Weierstrass-Mandelbrot function (WMF) model with Morlet wavelets is investigated. Its control relationships are derived quantitatively after proving the convergence of the controlled WMF model. Based on these relationships, it is shown that the scope of the WMF series increases with three parameters of the Morlet wavelets. But other parameters have opposite effect on the scope of the series. The results of simulated examples demonstrate the effectiveness of the control method. Moreover, two statistical characteristics of the series are obtained as the parameters change: One is multifractality of the series of the controlled WMF model, and the other is the Hurst exponent whose value stands for the long-time memory effect on the series.
The Brera Multi-scale Wavelet (BMW) ROSAT HRI source catalog; 1, the algorithm
Lazzati, D; Rosati, P; Panzera, M R; Tagliaferri, G; Lazzati, Davide; Campana, Sergio; Rosati, Piero; Panzera, Maria Rosa; Tagliaferri, Gianpiero
1999-01-01
We present a new detection algorithm based on the wavelet transform for the analysis of high energy astronomical images. The wavelet transform, due to its multi-scale structure, is suited for the optimal detection of point-like as well as extended sources, regardless of any loss of resolution with the off-axis angle. Sources are detected as significant enhancements in the wavelet space, after the subtraction of the non-flat components of the background. Detection thresholds are computed through Monte Carlo simulations in order to establish the expected number of spurious sources per field. The source characterization is performed through a multi-source fitting in the wavelet space. The procedure is designed to correctly deal with very crowded fields, allowing for the simultaneous characterization of nearby sources. To obtain a fast and reliable estimate of the source parameters and related errors, we apply a novel decimation technique which, taking into account the correlation properties of the wavelet transf...
Wavelets, Fractals, and Radial Basis Functions
2007-11-02
the constant as a linear combination of , irrespective of the scale . This nonunique way of writing the constant implies that itself cannot generate a...France, in 1986 and from Télécom Paris (ENST) in 1988. He received the Ph.D degree in electrical engineering in 1996 from ENST for a study on iterated...born in Zug, Switzerland, on April 9, 1958. He received the M.S. (summa cum laude) and Ph.D. degrees in electrical engineering in 1981 and 1984
Control effects of Morlet wavelet term on Weierstrass-Mandelbrot function model
Zhang, L.; Liu, S. T.; Yu, C.
2014-08-01
In this paper, we have investigated the control problem of the Weierstrass-Mandelbrot function model with Morlet wavelet term. Based on the corollary for its convergence, we have formulated several theorems about the monotonous effects of Morlet wavelet term on scope of the series. In addition, effects of Morlet wavelet term on two important statistical characteristics: multifractality and Hurst exponent have been calculated. We have used simulation examples to illustrate the control effects.
Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis
Yiou, P; Ghil, M
1998-01-01
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length $N$ whose intermittency can give rise to the divergence of their variance. SSA relies on the construction of the lag-covariance matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M 3/4 W 3/4 N. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive wavelets; successive eigenvectors of C_M correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency do...
Fragment approach to constrained density functional theory calculations using Daubechies wavelets
Energy Technology Data Exchange (ETDEWEB)
Ratcliff, Laura E., E-mail: lratcliff@anl.gov [Argonne Leadership Computing Facility, Argonne National Laboratory, Lemont, Illinois 60439 (United States); Université de Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France); Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry [Université de Grenoble Alpes, CEA, INAC-SP2M, L-Sim, F-38000 Grenoble (France)
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
Wavelet transform of generalized functions in $K^{\\prime}\\{ M_p\\}$ spaces
Indian Academy of Sciences (India)
R S Pathak; Abhishek Singh
2016-05-01
Using convolution theory in $K\\{ M_p\\}$ space we obtain bounded results for the wavelet transform. Calderón-type reproducing formula is derived in distribution sense as an application of the same. An inversion formula for the wavelet transform of generalized functions is established.
Wavelet Domain Image Reconstruction by Compactly-Supported Radial Basis Functions
Diago, Luis A.; Kitago, Masaki; Hagiwara, Ichiro
In this paper we propose the use of wavelets to accelerate the solution of the System of Linear Algebraic Equations that arise from the formulation of the problem of image interpolation from scattered data by means of Compactly-Supported Radial Basis Functions. Examples demonstrate the superiority of the solution in the wavelet domain using preconditioned iterative Krylov methods.
An Investigation of Wavelet Bases for Grid-Based Multi-Scale Simulations Final Report
Energy Technology Data Exchange (ETDEWEB)
Baty, R.S.; Burns, S.P.; Christon, M.A.; Roach, D.W.; Trucano, T.G.; Voth, T.E.; Weatherby, J.R.; Womble, D.E.
1998-11-01
The research summarized in this report is the result of a two-year effort that has focused on evaluating the viability of wavelet bases for the solution of partial differential equations. The primary objective for this work has been to establish a foundation for hierarchical/wavelet simulation methods based upon numerical performance, computational efficiency, and the ability to exploit the hierarchical adaptive nature of wavelets. This work has demonstrated that hierarchical bases can be effective for problems with a dominant elliptic character. However, the strict enforcement of orthogonality was found to be less desirable than weaker semi-orthogonality or bi-orthogonality for solving partial differential equations. This conclusion has led to the development of a multi-scale linear finite element based on a hierarchical change of basis. The reproducing kernel particle method has been found to yield extremely accurate phase characteristics for hyperbolic problems while providing a convenient framework for multi-scale analyses.
A new wavelet-based thin plate element using B-spline wavelet on the interval
Jiawei, Xiang; Xuefeng, Chen; Zhengjia, He; Yinghong, Zhang
2008-01-01
By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class of wavelet-based plate element is constructed. In the construction of wavelet-based plate element, the element displacement field represented by the coefficients of wavelet expansions in wavelet space is transformed into the physical degree of freedoms in finite element space via the corresponding two-dimensional C1 type transformation matrix. Then, based on the associated generalized function of potential energy of thin plate bending and vibration problems, the scaling functions of B-spline wavelet on the interval (BSWI) at different scale are employed directly to form the multi-scale finite element approximation basis so as to construct BSWI plate element via variational principle. BSWI plate element combines the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples are studied to demonstrate the performances of the present element.
Cheng, Lizhi; Luo, Yong; Chen, Bo
2014-01-01
This book could be divided into two parts i.e. fundamental wavelet transform theory and method and some important applications of wavelet transform. In the first part, as preliminary knowledge, the Fourier analysis, inner product space, the characteristics of Haar functions, and concepts of multi-resolution analysis, are introduced followed by a description on how to construct wavelet functions both multi-band and multi wavelets, and finally introduces the design of integer wavelets via lifting schemes and its application to integer transform algorithm. In the second part, many applications are discussed in the field of image and signal processing by introducing other wavelet variants such as complex wavelets, ridgelets, and curvelets. Important application examples include image compression, image denoising/restoration, image enhancement, digital watermarking, numerical solution of partial differential equations, and solving ill-conditioned Toeplitz system. The book is intended for senior undergraduate stude...
Choosing Wavelet Methods, Filters, and Lengths for Functional Brain Network Construction.
Directory of Open Access Journals (Sweden)
Zitong Zhang
Full Text Available Wavelet methods are widely used to decompose fMRI, EEG, or MEG signals into time series representing neurophysiological activity in fixed frequency bands. Using these time series, one can estimate frequency-band specific functional connectivity between sensors or regions of interest, and thereby construct functional brain networks that can be examined from a graph theoretic perspective. Despite their common use, however, practical guidelines for the choice of wavelet method, filter, and length have remained largely undelineated. Here, we explicitly explore the effects of wavelet method (MODWT vs. DWT, wavelet filter (Daubechies Extremal Phase, Daubechies Least Asymmetric, and Coiflet families, and wavelet length (2 to 24-each essential parameters in wavelet-based methods-on the estimated values of graph metrics and in their sensitivity to alterations in psychiatric disease. We observe that the MODWT method produces less variable estimates than the DWT method. We also observe that the length of the wavelet filter chosen has a greater impact on the estimated values of graph metrics than the type of wavelet chosen. Furthermore, wavelet length impacts the sensitivity of the method to detect differences between health and disease and tunes classification accuracy. Collectively, our results suggest that the choice of wavelet method and length significantly alters the reliability and sensitivity of these methods in estimating values of metrics drawn from graph theory. They furthermore demonstrate the importance of reporting the choices utilized in neuroimaging studies and support the utility of exploring wavelet parameters to maximize classification accuracy in the development of biomarkers of psychiatric disease and neurological disorders.
A Mellin transform approach to wavelet analysis
Alotta, Gioacchino; Di Paola, Mario; Failla, Giuseppe
2015-11-01
The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin transform expression, with fractional moments obtained from a set of algebraic equations whose coefficient matrix applies for any scale a of the wavelet transform. Robustness and computationally efficiency of the proposed approach are shown in the paper.
On asymptotically optimal wavelet estimation of trend functions under long-range dependence
Beran, Jan; 10.3150/10-BEJ332
2012-01-01
We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and resolution parameters are derived. Due to adaptation to the properties of the underlying trend function, the approach shows very good performance for smooth trend functions while remaining competitive with minimax wavelet estimation for functions with discontinuities. Simulations illustrate the asymptotic results and finite-sample behavior.
A new method of choosing scales in wavelet transform for damping identification
Institute of Scientific and Technical Information of China (English)
HE Rui; LUO Wen-bo; WANG Ben-li
2008-01-01
A systematic study of the method of selecting scales in wavelet transform for damping identification in frequency domain was carried out. A method to select the scale with the modulus at the maximum was developed by extending the range of scales, it is proved that using this method in small damping ratio and linear system,we can achieve better results in identification of the closely-spaced model.
Dai, Xiaoyan; Guo, Zhongyang; Zhang, Liquan; Xu, Wencheng
2009-12-01
Soft classification methods can be used for mixed-pixel classification on remote sensing imagery by estimating different land cover class fractions of every pixel. However, the spatial distribution and location of these class components within the pixel remain unknown. To map land cover at subpixel scale and increase the spatial resolution of land cover classification maps, in this paper, a prediction model combining wavelet transform and Radial Basis Functions (RBF) neural network, abbreviated as Wavelet-RBFNN, is constructed by predicting high-frequency wavelet coefficients from low-frequency coefficients at the same resolution with RBF network and taking wavelet coefficients at coarser resolution as training samples. According to different land cover class fraction images obtained from mixed-pixel classification, based on the assumption of neighborhood dependence of wavelet coefficients, subpixel mapping on remote sensing imagery can be accomplished through two steps, i.e., prediction of land cover class compositions within subpixels and hard classification. The experimental results obtained with artificial images, QuickBird image and Landsat 7 ETM+ image indicate that the subpixel mapping method proposed in this paper can successfully produce super-resolution land cover classification maps from remote sensing imagery, outperforming cubic B-spline and Kriging interpolation method in visual effect and prediction accuracy. The Wavelet-RBFNN model can also be applied to simulate higher spatial resolution image, and automatically identify and locate land cover targets at the subpixel scales, when the cost and availability of high resolution imagery prohibit its use in many areas of work.
Large Scale Isosurface Bicubic Subdivision-Surface Wavelets for Representation and Visualization
Energy Technology Data Exchange (ETDEWEB)
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-01-05
We introduce a new subdivision-surface wavelet transform for arbitrary two-manifolds with boundary that is the first to use simple lifting-style filtering operations with bicubic precision. We also describe a conversion process for re-mapping large-scale isosurfaces to have subdivision connectivity and fair parameterizations so that the new wavelet transform can be used for compression and visualization. The main idea enabling our wavelet transform is the circular symmetrization of the filters in irregular neighborhoods, which replaces the traditional separation of filters into two 1-D passes. Our wavelet transform uses polygonal base meshes to represent surface topology, from which a Catmull-Clark-style subdivision hierarchy is generated. The details between these levels of resolution are quickly computed and compactly stored as wavelet coefficients. The isosurface conversion process begins with a contour triangulation computed using conventional techniques, which we subsequently simplify with a variant edge-collapse procedure, followed by an edge-removal process. This provides a coarse initial base mesh, which is subsequently refined, relaxed and attracted in phases to converge to the contour. The conversion is designed to produce smooth, untangled and minimally-skewed parameterizations, which improves the subsequent compression after applying the transform. We have demonstrated our conversion and transform for an isosurface obtained from a high-resolution turbulent-mixing hydrodynamics simulation, showing the potential for compression and level-of-detail visualization.
Institute of Scientific and Technical Information of China (English)
JIANG Nan; ZHANG Jin
2005-01-01
@@ Multi-scale decomposition by wavelet transform has been performed to velocity time sequences obtained by fine measurements of turbulent boundary layer flow. A conditional sampling technique for detecting multi-scale coherent eddy structures in turbulent field is proposed by using multi-scale instantaneous intensity factor and flatness factor of wavelet coefficients. Although the number of coherent eddy structures in the turbulent boundary layer is very small, their energy percentage with respect to the turbulence kinetic energy is high. Especially in buffer layer, the energy percentages of coherent structures are significantly higher than those in the logarithmic layer, indicating that the buffer layer is the most active region in the turbulent boundary layer. These multi-scale coherent eddy structures share some common dynamical characteristics and are responsible for the anomalous scaling law in the turbulent boundary layer.
Discovering the Merit of the Wavelet Transform for Object Classification
2004-03-01
key steps in object recognition. Typically, geometric primitives are extracted from an image using local analysis. However, the wavelet transform provides...network. This thesis examines the benefits of the wavelet transform as a preprocessor to a neural network for object recognition. Scaling of the...benefits of the wavelet transform , the effects of the various post-wavelet scaling functions, and the best neural network topology for this research. This is done by analyzing the system s performance on CAD models.
Bitenc, M.; Kieffer, D. S.; Khoshelham, K.
2015-08-01
The precision of Terrestrial Laser Scanning (TLS) data depends mainly on the inherent random range error, which hinders extraction of small details from TLS measurements. New post processing algorithms have been developed that reduce or eliminate the noise and therefore enable modelling details at a smaller scale than one would traditionally expect. The aim of this research is to find the optimum denoising method such that the corrected TLS data provides a reliable estimation of small-scale rock joint roughness. Two wavelet-based denoising methods are considered, namely Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT), in combination with different thresholding procedures. The question is, which technique provides a more accurate roughness estimates considering (i) wavelet transform (SWT or DWT), (ii) thresholding method (fixed-form or penalised low) and (iii) thresholding mode (soft or hard). The performance of denoising methods is tested by two analyses, namely method noise and method sensitivity to noise. The reference data are precise Advanced TOpometric Sensor (ATOS) measurements obtained on 20 × 30 cm rock joint sample, which are for the second analysis corrupted by different levels of noise. With such a controlled noise level experiments it is possible to evaluate the methods' performance for different amounts of noise, which might be present in TLS data. Qualitative visual checks of denoised surfaces and quantitative parameters such as grid height and roughness are considered in a comparative analysis of denoising methods. Results indicate that the preferred method for realistic roughness estimation is DWT with penalised low hard thresholding.
APPLICATION OF WAVELET THEORY IN RESEARCH ON WEIGHT FUNCTION OF MESHLESS METHOD
Institute of Scientific and Technical Information of China (English)
ZHANG Hong; ZHANG Xuan-bing; GE Xiu-run
2005-01-01
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis, so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions.Now, the useful new way to research weight function is found, and the numerical result is given.
Visualization of a Turbulent Jet Using Wavelets
Institute of Scientific and Technical Information of China (English)
Hui LI
2001-01-01
An application of multiresolution image analysis to turbulence was investigated in this paper, in order to visualize the coherent structure and the most essential scales governing turbulence. The digital imaging photograph of jet slice was decomposed by two-dimensional discrete wavelet transform based on Daubechies, Coifman and Baylkin bases. The best choice of orthogonal wavelet basis for analyzing the image of the turbulent structures was first discussed. It is found that these orthonormal wavelet families with index N＜10 were inappropriate for multiresolution image analysis of turbulent flow. The multiresolution images of turbulent structures were very similar when using the wavelet basis with the higher index number, even though wavelet bases are different functions. From the image components in orthogonal wavelet spaces with different scales, the further evident of the multi-scale structures in jet can be observed, and the edges of the vortices at different resolutions or scales and the coherent structure can be easily extracted.
Energy Technology Data Exchange (ETDEWEB)
Pereira, E. [Departamento Fisica-ICEx, UFMG, CP 702, Belo Horizonte MG 30.161-970 (Brazil); Procacci, A. [Departamento Matematica-ICEx, UFMG, CP 702, Belo Horizonte MG 30.161-970 (Brazil)
1997-03-01
Searching for a general and technically simple multiscale formalism to treat interacting fermions, we develop a (Wilson{endash}Kadanoff) block renormalization group mechanism, which, due to the property of {open_quotes}orthogonality between scales,{close_quotes} establishes a trivial link between the correlation functions and the effective potential flow, leading to simple expressions for the generating and correlation functions. Everything is based on the existence of {open_quotes}special configurations{close_quotes} (lattice wavelets) for multiscale problems: using a simple linear change of variables relating the initial fields to these configurations, we establish the formalism. The algebraic formulas show a perfect parallel with those obtained for bosonic problems, considered in previous works. {copyright} 1997 Academic Press, Inc.
Rotation invariant texture retrieval considering the scale dependence of Gabor wavelet.
Chaorong Li; Guiduo Duan; Fujin Zhong
2015-08-01
Obtaining robust and efficient rotation-invariant texture features in content-based image retrieval field is a challenging work. We propose three efficient rotation-invariant methods for texture image retrieval using copula model based in the domains of Gabor wavelet (GW) and circularly symmetric GW (CSGW). The proposed copula models use copula function to capture the scale dependence of GW/CSGW for improving the retrieval performance. It is well known that the Kullback-Leibler distance (KLD) is the commonly used similarity measurement between probability models. However, it is difficult to deduce the closed-form of KLD between two copula models due to the complexity of the copula model. We also put forward a kind of retrieval scheme using the KLDs of marginal distributions and the KLD of copula function to calculate the KLD of copula model. The proposed texture retrieval method has low computational complexity and high retrieval precision. The experimental results on VisTex and Brodatz data sets show that the proposed retrieval method is more effective compared with the state-of-the-art methods.
Wavelet analysis of MR functional data from the cerebellum
Energy Technology Data Exchange (ETDEWEB)
Karen, Romero Sánchez, E-mail: alphacentauri-hp@hotmail.com, E-mail: marcos-vaquezr@hotmail.com, E-mail: isabeldgg@hotmail.com; Vásquez Reyes Marcos, A., E-mail: alphacentauri-hp@hotmail.com, E-mail: marcos-vaquezr@hotmail.com, E-mail: isabeldgg@hotmail.com; González Gómez Dulce, I., E-mail: alphacentauri-hp@hotmail.com, E-mail: marcos-vaquezr@hotmail.com, E-mail: isabeldgg@hotmail.com; Hernández López, Javier M., E-mail: javierh@fcfm.buap.mx [Faculty of Physics and Mathematics, BUAP, Puebla, Pue (Mexico); Silvia, Hidalgo Tobón, E-mail: shidbon@gmail.com [Infant Hospital of Mexico, Federico Gómez, Mexico DF. Mexico and Physics Department, Universidad Autónoma Metropolitana. Iztapalapa, Mexico DF. (Mexico); Pilar, Dies Suarez, E-mail: pilydies@yahoo.com, E-mail: neurodoc@prodigy.net.mx; Eduardo, Barragán Pérez, E-mail: pilydies@yahoo.com, E-mail: neurodoc@prodigy.net.mx [Infant Hospital of Mexico, Federico Gómez, Mexico DF. (Mexico); Benito, De Celis Alonso, E-mail: benileon@yahoo.com [Faculty of Physics and Mathematics, BUAP, Puebla, Pue. Mexico and Foundation for Development Carlos Sigüenza. Puebla, Pue. (Mexico)
2014-11-07
The main goal of this project was to create a computer algorithm based on wavelet analysis of BOLD signals, which automatically diagnosed ADHD using information from resting state MR experiments. Male right handed volunteers (infants with ages between 7 and 11 years old) were studied and compared with age matched controls. Wavelet analysis, which is a mathematical tool used to decompose time series into elementary constituents and detect hidden information, was applied here to the BOLD signal obtained from the cerebellum 8 region of all our volunteers. Statistical differences between the values of the a parameters of wavelet analysis was found and showed significant differences (p<0.02) between groups. This difference might help in the future to distinguish healthy from ADHD patients and therefore diagnose ADHD.
Data-adaptive wavelets and multi-scale singular-spectrum analysis
Yiou, Pascal; Sornette, Didier; Ghil, Michael
2000-08-01
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series, including the case where intermittency gives rise to the divergence of their variance. The wavelet transform resembles a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W= MΔ t with Δ t as the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M≤ W≤ N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/ M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C(M) as data-adaptive wavelets; successive eigenvectors of C(M) correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain by a suitable localization of the signal’s correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied next to the monthly values of the Southern Oscillation Index (SOI) for 1933-1996; the SOI time series is widely believed to capture major features of the El Niño/Southern Oscillation (ENSO) in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil’s staircase scenario for the ENSO phenomenon (preliminary results of this study
Huang, S. Q.; Wang, Z. L.; Xie, T. G.; Li, Z. C.
2017-09-01
Speckle noise in synthetic aperture radar (SAR) image is produced by the coherent imaging mechanism, which brings a great impact on the change information acquisition of multi-temporal SAR images. Two-dimensional stationary wavelet transform (SWT) and bi-dimensional empirical mode decomposition (BEMD) are the non-stationary signal processing theory of multi-scale transform. According to their implementation process and SAR image characteristic, this paper proposed a new multi-temporal SAR image change detection method based on the combination of the stationary wavelet transform and the bi-dimensional intrinsic mode function (BIMF) features, called SWT-BIMF algorithm. The contribution of the new algorithm includes two aspects. One is the design of the two selections of decomposition features, that is, the speckle noise filtering; another is the selected features to perform the enhance processing, so more effective change information will obtain. The feasibility of the SWT-BIMF algorithm is verified by the measured SAR image data, and good experimental results are obtained.
Simons, Frederik J; Nolet, Guust; Daubechies, Ingrid C; Voronin, S; Judd, J S; Vetter, P A; Charlety, J; Vonesch, C
2011-01-01
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel computing. We discuss two possible types of discrete wavelet transforms in the angular dimension of the cubed sphere. We discuss benefits and drawbacks of these constructions and apply them to analyze the information present in two published seismic wavespeed models of the mantle, for the statistics and power of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the $\\ell_2$ norm of data fit and the $\\ell_1$ norm on the wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains of our...
On the wavelet optimized finite difference method
Jameson, Leland
1994-01-01
When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.
Parameterization and algebraic structure of 3-band orthogonal wavelet systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, a complete parameterization for the 3-band compact wavelet systems is presented. Using the parametric result, a program of the filterbank design is completed, which can give not only the filterbanks but also the graphs of all possible scaling functions and their corresponding wavelets. Especially some symmetric wavelets with small supports are given. Finally an algebraic structure for this kind of wavelet systems is characterized.
Wavelet Optimal Estimations for Density Functions under Severely Ill-Posed Noises
Directory of Open Access Journals (Sweden)
Rui Li
2013-01-01
Full Text Available Motivated by Lounici and Nickl's work (2011, this paper considers the problem of estimation of a density f based on an independent and identically distributed sample Y1,…,Yn from g=f*φ. We show a wavelet optimal estimation for a density (function over Besov ball Br,qs(L and Lp risk (1≤p<∞ in the presence of severely ill-posed noises. A wavelet linear estimation is firstly presented. Then, we prove a lower bound, which shows our wavelet estimator optimal. In other words, nonlinear wavelet estimations are not needed in that case. It turns out that our results extend some theorems of Pensky and Vidakovic (1999, as well as Fan and Koo (2002.
Tan, Liying; Ma, Jing; Wang, Guangming
2005-12-01
The image formation and the point-spread function of an optical system are analyzed by use of the wavelet basis function. The image described by a wavelet is no longer an indivisible whole image. It is, rather, a complex image consisting of many wavelet subimages, which come from the changes of different parameters (scale) a and c, and parameters b and d show the positions of wavelet subimages under different scales. A Gaussian frequency-modulated complex-valued wavelet function is introduced to express the point-spread function of an optical system and used to describe the image formation. The analysis, in allusion to the situation of illumination with a monochromatic plain light wave, shows that using the theory of wavelet optics to describe the image formation of an optical system is feasible.
Institute of Scientific and Technical Information of China (English)
CHENG Hao; YAN Hao; BAI Li-jun; WANG Bao-guo
2013-01-01
Background Previous studies have demonstrated that acupuncture could modulate various brain systems in the resting brain networks.Graph theoretical analysis offers a novel way to investigate the functional organization of the large-scale cortical networks modulated by acupuncture at whole brain level.In this study,we used wavelets correlation analysis to estimate the pairwise correlations between 90 cortical and subcortical human brain regions in normal human volunteers scanned during the post-stimulus resting state.Methods Thirty-two college students,all right-handed and acupuncture na(i)ve,participated in this study.Every participant received only one acupoint stimulation,resulting in 16 subjects in one group.Both structural functional magnetic resonance imaging (fMRI) data (3D sequence with a voxel size of 1 mm3 for anatomical localization) and functional fMRI data (TR=1500 ms,TE=30 ms,flip angle=90°) were collected for each subject.After thresholding the resulting scale-specific wavelet correlation matrices to generate undirected binary graphs,we compared graph metrics of brain organization following verum manual acupuncture (ACU) and sham acupuncture (SHAM) groups.Results The topological parameters of the large-scale brain networks in ACU group were different from those of the SHAM group at multiple scales.There existed distinct modularity functional brain networks during the post-stimulus resting state following ACU and SHAM at multiple scales.Conclusions The distinct modulation patterns of the resting brain attributed to the specific effects evoked by acupuncture.In addition,we also identified that there existed frequency-specific modulation in the post-stimulus resting brain following ACU and SHAM.The modulation may be related to the effects of verum acupuncture on modulating special disorder treatment.This preliminary finding may provide a new clue to understand the relatively functionoriented specificity of acupuncture effects.
Design Methodology of a New Wavelet Basis Function for Fetal Phonocardiographic Signals
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Vijay S. Chourasia
2013-01-01
Full Text Available Fetal phonocardiography (fPCG based antenatal care system is economical and has a potential to use for long-term monitoring due to noninvasive nature of the system. The main limitation of this technique is that noise gets superimposed on the useful signal during its acquisition and transmission. Conventional filtering may result into loss of valuable diagnostic information from these signals. This calls for a robust, versatile, and adaptable denoising method applicable in different operative circumstances. In this work, a novel algorithm based on wavelet transform has been developed for denoising of fPCG signals. Successful implementation of wavelet theory in denoising is heavily dependent on selection of suitable wavelet basis function. This work introduces a new mother wavelet basis function for denoising of fPCG signals. The performance of newly developed wavelet is found to be better when compared with the existing wavelets. For this purpose, a two-channel filter bank, based on characteristics of fPCG signal, is designed. The resultant denoised fPCG signals retain the important diagnostic information contained in the original fPCG signal.
Wavelet transform analysis of the small-scale X-ray structure of the cluster Abell 1367
Grebeney, S. A.; Forman, W.; Jones, C.; Murray, S.
1995-01-01
We have developed a new technique based on a wavelet transform analysis to quantify the small-scale (less than a few arcminutes) X-ray structure of clusters of galaxies. We apply this technique to the ROSAT position sensitive proportional counter (PSPC) and Einstein high-resolution imager (HRI) images of the central region of the cluster Abell 1367 to detect sources embedded within the diffuse intracluster medium. In addition to detecting sources and determining their fluxes and positions, we show that the wavelet analysis allows a characterization of the sources extents. In particular, the wavelet scale at which a given source achieves a maximum signal-to-noise ratio in the wavelet images provides an estimate of the angular extent of the source. To account for the widely varying point response of the ROSAT PSPC as a function of off-axis angle requires a quantitative measurement of the source size and a comparison to a calibration derived from the analysis of a Deep Survey image. Therefore, we assume that each source could be described as an isotropic two-dimensional Gaussian and used the wavelet amplitudes, at different scales, to determine the equivalent Gaussian Full Width Half-Maximum (FWHM) (and its uncertainty) appropriate for each source. In our analysis of the ROSAT PSPC image, we detect 31 X-ray sources above the diffuse cluster emission (within a radius of 24 min), 16 of which are apparently associated with cluster galaxies and two with serendipitous, background quasars. We find that the angular extents of 11 sources exceed the nominal width of the PSPC point-spread function. Four of these extended sources were previously detected by Bechtold et al. (1983) as 1 sec scale features using the Einstein HRI. The same wavelet analysis technique was applied to the Einstein HRI image. We detect 28 sources in the HRI image, of which nine are extended. Eight of the extended sources correspond to sources previously detected by Bechtold et al. Overall, using both the
Wavelet-based method for image filtering using scale-space continuity
Jung, Claudio R.; Scharcanski, Jacob
2001-04-01
This paper proposes a novel technique to reduce noise while preserving edge sharpness during image filtering. This method is based on the image multiresolution decomposition by a discrete wavelet transform, given a proper wavelet basis. In the transform spaces, edges are implicitly located and preserved, at the same time that image noise is filtered out. At each resolution level, geometric continuity is used to preserve edges that are not isolated. Finally, we compare consecutive levels to preserve edges having continuity along scales. As a result, the proposed technique produces a filtered version of the original image, where homogeneous regions appear segmented by well-defined edges. Possible applications include image presegmentation and image denoising.
The Brera Multi-scale Wavelet Chandra Survey. The serendipitous source catalogue
Romano, P; Mignani, R P; Moretti, A; Panzera, M R; Tagliaferri, G; Mottini, M
2009-01-01
We present the Brera Multi-scale Wavelet Chandra (BMW-Chandra) source catalogue drawn from essentially all Chandra ACIS-I pointed observations with an exposure time in excess of 10ks public as of March 2003 (136 observations). Using the wavelet detection algorithm developed by Lazzati et al. (1999) and Campana et al. (1999), which can characterise both point-like and extended sources, we identified 21325 sources. Among them, 16758 are serendipitous, i.e. not associated with the targets of the pointings. This makes our catalogue the largest compilation of Chandra sources to date. The 0.5-10keV absorption corrected fluxes of these sources range from 3E-16 to 9E-12 erg/cm2/s with a median of 7E-15 erg/cm2/s. The catalogue consists of count rates and relative errors in three energy bands (total, 0.5-7keV; soft, 0.5-2keV; and hard, 2-7keV), where the detection was performed, and source positions relative to the highest signal-to-noise detection among the three bands. The wavelet algorithm also provides an estimate...
The fast wavelet X-ray transform
R.A. Zuidwijk; P.M. de Zeeuw (Paul)
1999-01-01
textabstractThe wavelet X-ray transform computes one-dimensional wavelet transforms along lines in Euclidian space in order to perform a directional time-scale analysis of functions in several variables. A fast algorithm is proposed which executes this transformation starting with values given on a
Determination of jumps for functions based on Malvar-Coifman-Meyer conjugate wavelets
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we discuss determination of jumps for non-periodic function based on Malvar-Cofiman-Meyer (MCM) conjugate wavelets. We prove the equality of Lukacs type. Furthermore we establish several criteria on concentration factors for functions that satisfy weak-smoothness condition of Dini type.
Heart Disease Detection Using Wavelets
González S., A.; Acosta P., J. L.; Sandoval M., M.
2004-09-01
We develop a wavelet based method to obtain standardized gray-scale chart of both healthy hearts and of hearts suffering left ventricular hypertrophy. The hypothesis that early bad functioning of heart can be detected must be tested by comparing the wavelet analysis of the corresponding ECD with the limit cases. Several important parameters shall be taken into account such as age, sex and electrolytic changes.
The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression
Energy Technology Data Exchange (ETDEWEB)
Bradley, J.N.; Brislawn, C.M. [Los Alamos National Lab., NM (United States); Hopper, T. [Federal Bureau of Investigation, Washington, DC (United States)
1993-05-01
The FBI has recently adopted a standard for the compression of digitized 8-bit gray-scale fingerprint images. The standard is based on scalar quantization of a 64-subband discrete wavelet transform decomposition of the images, followed by Huffman coding. Novel features of the algorithm include the use of symmetric boundary conditions for transforming finite-length signals and a subband decomposition tailored for fingerprint images scanned at 500 dpi. The standard is intended for use in conjunction with ANSI/NBS-CLS 1-1993, American National Standard Data Format for the Interchange of Fingerprint Information, and the FBI`s Integrated Automated Fingerprint Identification System.
The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression
Energy Technology Data Exchange (ETDEWEB)
Bradley, J.N.; Brislawn, C.M. (Los Alamos National Lab., NM (United States)); Hopper, T. (Federal Bureau of Investigation, Washington, DC (United States))
1993-01-01
The FBI has recently adopted a standard for the compression of digitized 8-bit gray-scale fingerprint images. The standard is based on scalar quantization of a 64-subband discrete wavelet transform decomposition of the images, followed by Huffman coding. Novel features of the algorithm include the use of symmetric boundary conditions for transforming finite-length signals and a subband decomposition tailored for fingerprint images scanned at 500 dpi. The standard is intended for use in conjunction with ANSI/NBS-CLS 1-1993, American National Standard Data Format for the Interchange of Fingerprint Information, and the FBI's Integrated Automated Fingerprint Identification System.
The Brera Multi-scale Wavelet HRI Cluster Survey: I Selection of the Sample and Number Counts
Moretti, A; Campana, S; Lazzati, D; Panzera, M R; Tagliaferri, G; Arena, S; Braglia, F; Dell'Antonio, I; Longhetti, M
2004-01-01
We describe the construction of the Brera Multi-scale Wavelet (BMW) HRI Cluster Survey, a deep sample of serendipitous X-ray selected clusters of galaxies based on the ROSAT HRI archive. This is the first cluster catalog exploiting the high angular resolution of this instrument. Cluster candidates are selected on the basis of their X-ray extension only, a parameter which is well measured by the BMW wavelet detection algorithm. The survey includes 154 candidates over a total solid angle of ~160 deg2 at 10^{-12}erg s^{-1} cm^{-2} and ~80 deg^2 at 1.8*10^{-13} erg s^{-1}$ cm^{-2}. At the same time, a fairly good sky coverage in the faintest flux bins (3-5*10^{-14}erg s^{-1} cm^{-2}) gives this survey the capability to detect a few clusters with z\\sim 1-1.2, depending on evolution. We present the results of extensive Monte Carlo simulations, providing a complete statistical characterization of the survey selection function and contamination level. We also present a new estimate of the surface density of clusters ...
Energy Technology Data Exchange (ETDEWEB)
Maiolo, M., E-mail: massimo.maiolo@zhaw.ch [SUPSI, Department of Innovative Technology, Galleria 2, 6928 Manno (Switzerland); ZHAW, Institut für Angewandte Simulation, Grüental, CH-8820 Wädenswil (Switzerland); Vancheri, A., E-mail: alberto.vancheri@supsi.ch [SUPSI, Department of Innovative Technology, Galleria 2, 6928 Manno (Switzerland); Krause, R., E-mail: rolf.krause@usi.ch [USI, Institute of Computational Science, Via Buffi 13, 6906 Lugano (Switzerland); Danani, A., E-mail: andrea.danani@supsi.ch [SUPSI, Department of Innovative Technology, Galleria 2, 6928 Manno (Switzerland)
2015-11-01
In this paper, we apply Multiresolution Analysis (MRA) to develop sparse but accurate representations for the Multiscale Coarse-Graining (MSCG) approximation to the many-body potential of mean force. We rigorously framed the MSCG method into MRA so that all the instruments of this theory become available together with a multitude of new basis functions, namely the wavelets. The coarse-grained (CG) force field is hierarchically decomposed at different resolution levels enabling to choose the most appropriate wavelet family for each physical interaction without requiring an a priori knowledge of the details localization. The representation of the CG potential in this new efficient orthonormal basis leads to a compression of the signal information in few large expansion coefficients. The multiresolution property of the wavelet transform allows to isolate and remove the noise from the CG force-field reconstruction by thresholding the basis function coefficients from each frequency band independently. We discuss the implementation of our wavelet-based MSCG approach and demonstrate its accuracy using two different condensed-phase systems, i.e. liquid water and methanol. Simulations of liquid argon have also been performed using a one-to-one mapping between atomistic and CG sites. The latter model allows to verify the accuracy of the method and to test different choices of wavelet families. Furthermore, the results of the computer simulations show that the efficiency and sparsity of the representation of the CG force field can be traced back to the mathematical properties of the chosen family of wavelets. This result is in agreement with what is known from the theory of multiresolution analysis of signals.
Denoising functional MR images : A comparison of wavelet denoising and Gaussian smoothing
Wink, Alle Meije; Roerdink, Jos B.T.M.
2004-01-01
We present a general wavelet-based denoising scheme for functional magnetic resonance imaging (fMRI) data and compare it to Gaussian smoothing, the traditional denoising method used in fMRI analysis. One-dimensional WaveLab thresholding routines were adapted to two-dimensional images, and applied to
ON BANDLIMITED SCALING FUNCTION
Institute of Scientific and Technical Information of China (English)
Wei Chen; Qiao Yang; Wei-jun Jiang; Si-long Peng
2002-01-01
This paper discuss band-limited scaling function, especially on the interval band case and three interval bands case, its relationship to oversampling property and weakly translation invariance are also studied. At the end, we propose an open problem.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper puts forward wavelet transform method to identify P and S phases in three component seismograms using polarization information contained in the wavelet transform coefficients of signal. The P and S wave locator functions are constructed by using eigenvalue analysis method to wavelet transform coefficient across several scales. Locator functions formed by wavelet transform have stated noise resistance capability, and is proved to be very effective in identifying the P and S arrivals of the test data and actual earthquake data.
Directory of Open Access Journals (Sweden)
D.R. Hughes
2004-01-01
Full Text Available A relatively overlooked factor in both global and local methods of health monitoring is the nonlinear stiffness of structures caused by the cycling of cracks and delaminations. Global methods of health monitoring use modal parameters or frequency response functions in an inverse procedure to quantify damage in structures with thick sections. Global approaches use fewer sensors that detect only significantly large damage in structures due to damage caused by transient vibration. However, local methods use Lamb wave propagation to detect small damage within a structure by an array of closely spaced sensors and actuators. Local methods also become more difficult to use on thick or non-homogeneous materials because wave propagation becomes complex. This paper develops a combined time series and wavelet analysis technique to improve damage detection in either thick, complex geometry, or non-homogeneous materials. A wavelet transmittance function (WTF is defined as the ratio of continuous wavelet transforms from the time responses at different locations on a structure. A new damage indicator was developed based upon wavelet transmittance function. The novelty of the method lies in the fact that a near real time inference about the damage and the approximate extent of damage can be drawn without historical data. A simulated model is illustrated to highlight the potential of the new damage indicator on a thick aluminum specimen. Then, experimental signal data from two sets of different experiments conducted on thick structures with a crack and a delamination were analyzed using the wavelet transmittance function to detect the presence and extent of the damages as reflected on the WTF maps. This paper mainly deals with the development of WTF and the associated damage indicator by analyzing the simulated and experimental sets of data.
The Brera Multi-scale Wavelet ROSAT HRI source catalogue (BMW-HRI)
Panzera, M R; Covino, S; Lazzati, D; Mignani, R P; Moretti, A; Tagliaferri, G
2003-01-01
We present the Brera Multi-scale Wavelet ROSAT HRI source catalogue (BMW-HRI) derived from all ROSAT HRI pointed observations with exposure time longer than 100 s available in the ROSAT public archives. The data were analyzed automatically using a wavelet detection algorithm suited to the detection and characterization of both point-like and extended sources. This algorithm is able to detect and disentangle sources in very crowded fields and/or in presence of extended or bright sources. Images have been also visually inspected after the analysis to ensure verification. The final catalogue, derived from 4,303 observations, consists of 29,089 sources detected with a detection probability of greater or equal 4.2 sigma. For each source, the primary catalogue entries provide name, position, count rate, flux and extension along with the relative errors. In addition, results of cross-correlations with existing catalogues at different wavelengths (FIRST, IRAS, 2MASS and GSC2) are also reported. All these information ...
WAVELET-BASED ESTIMATORS OF MEAN REGRESSION FUNCTION WITH LONG MEMORY DATA
Institute of Scientific and Technical Information of China (English)
LI Lin-yuan; XIAO Yi-min
2006-01-01
This paper provides an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.
Piersanti, Mirko; Materassi, Massimo; Spogli, Luca; Cicone, Antonio; Alberti, Tommaso
2016-04-01
Highly irregular fluctuations of the power of trans-ionospheric GNSS signals, namely radio power scintillation, are, at least to a large extent, the effect of ionospheric plasma turbulence, a by-product of the non-linear and non-stationary evolution of the plasma fields defining the Earth's upper atmosphere. One could expect the ionospheric turbulence characteristics of inter-scale coupling, local randomness and high time variability to be inherited by the scintillation on radio signals crossing the medium. On this basis, the remote sensing of local features of the turbulent plasma could be expected as feasible by studying radio scintillation. The dependence of the statistical properties of the medium fluctuations on the space- and time-scale is the distinctive character of intermittent turbulent media. In this paper, a multi-scale statistical analysis of some samples of GPS radio scintillation is presented: the idea is that assessing how the statistics of signal fluctuations vary with time scale under different Helio-Geophysical conditions will be of help in understanding the corresponding multi-scale statistics of the turbulent medium causing that scintillation. In particular, two techniques are tested as multi-scale decomposition schemes of the signals: the discrete wavelet analysis and the Empirical Mode Decomposition. The discussion of the results of the one analysis versus the other will be presented, trying to highlight benefits and limits of each scheme, also under suitably different helio-geophysical conditions.
Time Scale Analysis of Interest Rate Spreads and Output Using Wavelets
Directory of Open Access Journals (Sweden)
Marco Gallegati
2013-04-01
Full Text Available This paper adds to the literature on the information content of different spreads for real activity by explicitly taking into account the time scale relationship between a variety of monetary and financial indicators (real interest rate, term and credit spreads and output growth. By means of wavelet-based exploratory data analysis we obtain richer results relative to the aggregate analysis by identifying the dominant scales of variation in the data and the scales and location at which structural breaks have occurred. Moreover, using the “double residuals” regression analysis on a scale-by-scale basis, we find that changes in the spread in several markets have different information content for output at different time frames. This is consistent with the idea that allowing for different time scales of variation in the data can provide a fruitful understanding of the complex dynamics of economic relationships between variables with non-stationary or transient components, certainly richer than those obtained using standard time domain methods.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.
Directory of Open Access Journals (Sweden)
Elaheh Saeedi
2014-07-01
Full Text Available In this paper, a decentralized adaptive controller with using wavelet neural network is used for a class of large-scale nonlinear systems with time- delay unknown nonlinear non- affine subsystems. The entered interruptions in subsystems are considered nonlinear with time delay, this is closer the reality, compared with the case in which the delay is not considered for interruptions. In this paper, the output weights of wavelet neural network and the other parameters of wavelet are adjusted online. The stability of close loop system is guaranteed with using the Lyapanov- Krasovskii method. Moreover the stability of close loop systems, guaranteed tracking error is converging to neighborhood zero and also all of the signals in the close loop system are bounded. Finally, the proposed method, simulated and applied for the control of two inverted pendulums that connected by a spring and the computer results, show that the efficiency of suggested method in this paper.
[A new wavelet image de-noising method based on new threshold function].
Xing, Guoquan; Ye, Huashan; Zhang, Yuxia; Yan, Yu
2013-08-01
In order to improve image de-noising effect,a new threshold function de-noising method based on wavelet analysis was proposed, which can overcome the continuity problem of the hard-threshold function, and eliminate the constant deviation of the soft one by constructing a new threshold function. Experimental results showed that the new threshold function could obtain higher peak signal to noise ratio (PSNR) in image de-nosing. A better denoising effect could be obtained compared with the hard-threshold function, the soft one, the semi-soft one, the cubic polynomial interpolation semi-soft one, and the asymptotic semi-soft one.
Navigation of autonomous mobile robot using different activation functions of wavelet neural network
Directory of Open Access Journals (Sweden)
Panigrahi Pratap Kumar
2015-03-01
Full Text Available An autonomous mobile robot is a robot which can move and act autonomously without the help of human assistance. Navigation problem of mobile robot in unknown environment is an interesting research area. This is a problem of deducing a path for the robot from its initial position to a given goal position without collision with the obstacles. Different methods such as fuzzy logic, neural networks etc. are used to find collision free path for mobile robot. This paper examines behavior of path planning of mobile robot using three activation functions of wavelet neural network i.e. Mexican Hat, Gaussian and Morlet wavelet functions by MATLAB. The simulation result shows that WNN has faster learning speed with respect to traditional artificial neural network.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A new method of resolving overlapped peak, Fourier self-deconvolution (FSD) using approximation CN obtained from frequency domain wavelet transform of F(ω) yielded by Fourier transform of overlapped peak signals f(t) as the linear function, was presented in this paper.Compared with classical FSD, the new method exhibits excellent resolution for different overlapped peak signals such as HPLC signals, and have some characteristics such as an extensive applicability for any overlapped peak shape signals and a simple operation because of no selection procedure of the linear function. Its excellent resolution for those different overlapped peak signals is mainly because F(ω) obtained from Fourier transform of f(t) and CN obtained from wavelet transform of F(ω) have the similar linearity and peak width. The effect of those fake peaks can be eliminated by the algorithm proposed by authors. This method has good potential in the process of different overlapped peak signals.
Construction of compactly supported orthonormal wavelets with beautiful structure
Institute of Scientific and Technical Information of China (English)
PENG Lizhong; WANG Yongge
2004-01-01
In this paper, a new method of constructing symmetric (antisymmetric) scaling and wavelet filters is introduced, and we get a new type of wavelet system that has very beautiful structure. Using this kind of wavelet system, we can achieve filters with the properties: rational, symmetric or antisymmetric, the lengths of the filters are shorter and the corresponding functions have higher smoothness, so they have good prospect in applications.
Rotation Invariant Face Detection Using Wavelet, PCA and Radial Basis Function Networks
Kamruzzaman, S M; Islam, Md Saiful; Haque, Md Emdadul; Alam, Mohammad Shamsul
2010-01-01
This paper introduces a novel method for human face detection with its orientation by using wavelet, principle component analysis (PCA) and redial basis networks. The input image is analyzed by two-dimensional wavelet and a two-dimensional stationary wavelet. The common goals concern are the image clearance and simplification, which are parts of de-noising or compression. We applied an effective procedure to reduce the dimension of the input vectors using PCA. Radial Basis Function (RBF) neural network is then used as a function approximation network to detect where either the input image is contained a face or not and if there is a face exists then tell about its orientation. We will show how RBF can perform well then back-propagation algorithm and give some solution for better regularization of the RBF (GRNN) network. Compared with traditional RBF networks, the proposed network demonstrates better capability of approximation to underlying functions, faster learning speed, better size of network, and high ro...
Institute of Scientific and Technical Information of China (English)
LIU Delin; LIU Xianzhao; LI Bicheng; ZHAO Shiwei; LI Xiguo
2009-01-01
Based on monOdy river runoff and meteorological data, a method of Morlet wavelet transform was used to analyze the multiple time scale characteristics of river runoffin the Dagnjia River Basin, Yantai City, Shandong Province. The results showed that the total annual river runoff in the Dagujia River Basin decreased significantly from 1966 to 2004, and the rate of decrease was 48×106m3/10yr, which was higher than the mean value of most rivers in China. Multiple time scale characteristics existed, which accounted for different aspects of the changes in annual river runoff, and the major periods of the runoff time series were identified as about 28 years, 14 years and 4 years with decreasing levels of fluctuation. The river runoff evolution process was controlled by changes in precipitation to a certain extent, but it was also greatly influenced by human activities. Also, for different time periods and scales, the impacts of climate changes and human activities on annual river runoff evolution occurred at the same time. Changes in the annual river runoffwere mainly associated with climate change before the 1980s and with human activities after 1981.
Lahmiri, Salim; Boukadoum, Mounir
2015-08-01
We present a new ensemble system for stock market returns prediction where continuous wavelet transform (CWT) is used to analyze return series and backpropagation neural networks (BPNNs) for processing CWT-based coefficients, determining the optimal ensemble weights, and providing final forecasts. Particle swarm optimization (PSO) is used for finding optimal weights and biases for each BPNN. To capture symmetry/asymmetry in the underlying data, three wavelet functions with different shapes are adopted. The proposed ensemble system was tested on three Asian stock markets: The Hang Seng, KOSPI, and Taiwan stock market data. Three statistical metrics were used to evaluate the forecasting accuracy; including, mean of absolute errors (MAE), root mean of squared errors (RMSE), and mean of absolute deviations (MADs). Experimental results showed that our proposed ensemble system outperformed the individual CWT-ANN models each with different wavelet function. In addition, the proposed ensemble system outperformed the conventional autoregressive moving average process. As a result, the proposed ensemble system is suitable to capture symmetry/asymmetry in financial data fluctuations for better prediction accuracy.
Use of wavelets to compare simulated yield patterns for precision agriculture at the field scale
Verhagen, A.; Stein, A.; Epinat, V.
2000-01-01
In this paper spatial patterns of simulated water limited potato production for a farm field in the Netherlands are analyzed using wavelets. The simulated yield patterns are decomposed using wavelets into crystals with a varying resolution. These crystals are used to relate the simulated spatial
Directory of Open Access Journals (Sweden)
Xinming Zhang
2009-01-01
Full Text Available A wavelet Galerkin finite-element method is proposed by combining the wavelet analysis with traditional finite-element method to analyze wave propagation phenomena in fluid-saturated porous medium. The scaling functions of Daubechies wavelets are considered as the interpolation basis functions to replace the polynomial functions, and then the wavelet element is constructed. In order to overcome the integral difficulty for lacking of the explicit expression for the Daubechies wavelets, a kind of characteristic function is introduced. The recursive expression of calculating the function values of Daubechies wavelets on the fraction nodes is deduced, and the rapid wavelet transform between the wavelet coefficient space and the wave field displacement space is constructed. The results of numerical simulation demonstrate that the method is effective.
Sparse tensor product wavelet approximation of singular functions
Dauge, M.; Stevenson, R.
2010-01-01
On product domains, sparse-grid approximation yields optimal, dimension-independent convergence rates when the function that is approximated has L-2-bounded mixed derivatives of a sufficiently high order. We show that the solution of Poisson's equation on the n-dimensional hypercube with Dirichlet
Orthogonal M-band compactly supported interpolating wavelet theory
Institute of Scientific and Technical Information of China (English)
张建康; 保铮
1999-01-01
Recently, 2-band interpolating wavelet transform has attracted much attention. It has the following several features: (ⅰ)The wavelet series transform coefficients of a signal in the multiresolution subspace are exactly consistent with its discrete wavelet transform coefficints; (ⅱ)good approximation performance; (ⅲ)efficiency in computation.However orthogonal 2-band compactly supported interpolating wavelet transform is only the first order. In order to overcome this shortcoming, the orthogonal M-band compactly supported interpolating wavelet basis is established. First, the unitary interpolating scaling filters of the length L=MK are characterized. Second, a scheme is given to design highorder unitary interpolating scaling filters. Third, a parameterization of the unitary interpolating scaling filters of the length L=4M is made. Fourth, the orthogonal 2-order and 3-order three-band compactly supported interpolating scaling functions are constructed. Finally, the properties of the orthogonal M-band c
The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method
Directory of Open Access Journals (Sweden)
Zhibo Yang
2014-01-01
Full Text Available A B-spline wavelet on interval (BSWI finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.
Reproducing wavelet kernel method in nonlinear system identification
Institute of Scientific and Technical Information of China (English)
WEN Xiang-jun; XU Xiao-ming; CAI Yun-ze
2008-01-01
By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identifica-tion scheme using wavelet support vector machines ( WSVM ) estimator is proposed for nonlinear dynamic sys-tems. The good approximating properties of wavelet kernel function enhance the generalization ability of the pro-posed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
Directory of Open Access Journals (Sweden)
Stefania Salvatore
2016-07-01
Full Text Available Abstract Background Wastewater-based epidemiology (WBE is a novel approach in drug use epidemiology which aims to monitor the extent of use of various drugs in a community. In this study, we investigate functional principal component analysis (FPCA as a tool for analysing WBE data and compare it to traditional principal component analysis (PCA and to wavelet principal component analysis (WPCA which is more flexible temporally. Methods We analysed temporal wastewater data from 42 European cities collected daily over one week in March 2013. The main temporal features of ecstasy (MDMA were extracted using FPCA using both Fourier and B-spline basis functions with three different smoothing parameters, along with PCA and WPCA with different mother wavelets and shrinkage rules. The stability of FPCA was explored through bootstrapping and analysis of sensitivity to missing data. Results The first three principal components (PCs, functional principal components (FPCs and wavelet principal components (WPCs explained 87.5-99.6 % of the temporal variation between cities, depending on the choice of basis and smoothing. The extracted temporal features from PCA, FPCA and WPCA were consistent. FPCA using Fourier basis and common-optimal smoothing was the most stable and least sensitive to missing data. Conclusion FPCA is a flexible and analytically tractable method for analysing temporal changes in wastewater data, and is robust to missing data. WPCA did not reveal any rapid temporal changes in the data not captured by FPCA. Overall the results suggest FPCA with Fourier basis functions and common-optimal smoothing parameter as the most accurate approach when analysing WBE data.
Tzanis, Andreas
2013-02-01
The Ground Probing Radar (GPR) is a valuable tool for near surface geological, geotechnical, engineering, environmental, archaeological and other work. GPR images of the subsurface frequently contain geometric information (constant or variable-dip reflections) from various structures such as bedding, cracks, fractures, etc. Such features are frequently the target of the survey; however, they are usually not good reflectors and they are highly localized in time and in space. Their scale is therefore a factor significantly affecting their detectability. At the same time, the GPR method is very sensitive to broadband noise from buried small objects, electromagnetic anthropogenic activity and systemic factors, which frequently blurs the reflections from such targets. This paper introduces a method to de-noise GPR data and extract geometric information from scale-and-dip dependent structural features, based on one-dimensional B-Spline Wavelets, two-dimensional directional B-Spline Wavelet (BSW) Filters and two-dimensional Gabor Filters. A directional BSW Filter is built by sidewise arranging s identical one-dimensional wavelets of length L, tapering the s-parallel direction (span) with a suitable window function and rotating the resulting matrix to the desired orientation. The length L of the wavelet defines the temporal and spatial scale to be isolated and the span determines the length over which to smooth (spatial resolution). The Gabor Filter is generated by multiplying an elliptical Gaussian by a complex plane wave; at any orientation the temporal or spatial scale(s) to be isolated are determined by the wavelength. λ of the plane wave and the spatial resolution by the spatial aspect ratio γ, which specifies the ellipticity of the support of the Gabor function. At any orientation, both types of filter may be tuned at any frequency or spatial wavenumber by varying the length or the wavelength respectively. The filters can be applied directly to two
Topology in galaxy distributions: method for a multi-scale analysis. A use of the wavelet transform.
Escalera, E.; MacGillivray, H. T.
1995-06-01
We report the 2D analysis of distributions of galaxies in a search for structures on all scales, from groups up to superclusters (including the identification of voids), based on the use of the wavelet transform. The wavelet method is an objective, multi-scale technique which gives the position, dimension and probability for each individual feature (both structures and voids) detected. We are currently performing the analysis on data from the COSMOS/UKST Southern Sky Galaxy Catalogue. The subsample used in our investigation contains some 2.5x10^6^ galaxies in an area of ~140x45 degrees around the South Galactic Pole. This is the first search for multi-scale objects on such an extended database, allowing us to cover many related topics in present-day Cosmology: realisation of superclusters as large-scale entities in their own right (as opposed to being considered merely as regions of enhanced cluster numbers); improvement in the definition of clusters of galaxies with a new approach to their general behaviour (distribution, typical sizes, state of evolution, etc.); and the objective characterisation of voids, which is exclusive to the wavelet method. In the present paper, we demonstrate the power of the technique by applying it to a selected field covering approximately 3000deg^2^ in the Grus-Sculptor region. In this area, we find 7 large scale structures (of more than 5 degrees in extent) and 26 structures of smaller scales (cluster-sized down to 1 degree, or group-sized down to 0.5 degrees). Sixteen of these small scale aggregates are connected with the large scale structures while ten appear isolated in the field. All these features are significant, having high confidence levels for detection. Voids are also detected in this area, likewise with high significance levels.
Directory of Open Access Journals (Sweden)
Roerdink Jos BTM
2008-04-01
Full Text Available Abstract Background We present a simple, data-driven method to extract haemodynamic response functions (HRF from functional magnetic resonance imaging (fMRI time series, based on the Fourier-wavelet regularised deconvolution (ForWaRD technique. HRF data are required for many fMRI applications, such as defining region-specific HRFs, effciently representing a general HRF, or comparing subject-specific HRFs. Results ForWaRD is applied to fMRI time signals, after removing low-frequency trends by a wavelet-based method, and the output of ForWaRD is a time series of volumes, containing the HRF in each voxel. Compared to more complex methods, this extraction algorithm requires few assumptions (separability of signal and noise in the frequency and wavelet domains and the general linear model and it is fast (HRF extraction from a single fMRI data set takes about the same time as spatial resampling. The extraction method is tested on simulated event-related activation signals, contaminated with noise from a time series of real MRI images. An application for HRF data is demonstrated in a simple event-related experiment: data are extracted from a region with significant effects of interest in a first time series. A continuous-time HRF is obtained by fitting a nonlinear function to the discrete HRF coeffcients, and is then used to analyse a later time series. Conclusion With the parameters used in this paper, the extraction method presented here is very robust to changes in signal properties. Comparison of analyses with fitted HRFs and with a canonical HRF shows that a subject-specific, regional HRF significantly improves detection power. Sensitivity and specificity increase not only in the region from which the HRFs are extracted, but also in other regions of interest.
FPGA Implementations of Bireciprocal Lattice Wave Discrete Wavelet Filter Banks
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Jassim M. Abdul-Jabbar
2012-06-01
Full Text Available In this paper, a special type of IIR filter banks; that is the bireciprocal lattice wave digital filter (BLWDF bank, is presented to simulate scaling and wavelet functions of six-level wavelet transform. 1st order all-pass sections are utilized for the realization of such filter banks in wave lattice structures. The resulting structures are a bireciprocal lattice wave discrete wavelet filter banks (BLW-DWFBs. Implementation of these BLW-DWFBs are accomplished on Spartan-3E FPGA kit. Implementation complexity and operating frequency characteristics of such discrete wavelet 5th order filter bank is proved to be comparable to the corresponding characteristics of the lifting scheme implementation of Bio. 5/3 wavelet filter bank. On the other hand, such IIR filter banks possess superior band discriminations and perfect roll-off frequency characteristics when compared to their Bio. 5/3 wavelet FIR counterparts.
WAVELET RATIONAL FILTERS AND REGULARITY ANALYSIS
Institute of Scientific and Technical Information of China (English)
Zheng Kuang; Ming-gen Cui
2000-01-01
In this paper, we choose the trigonometric rational functions as wavelet filters and use them to derive various wavelets. Especially for a certain family of wavelets generated by the rational filters, the better smoothness results than Daubechies' are obtained.
A new approach of watermarking technique by means multichannel wavelet functions
Agreste, Santa; Puccio, Luigia
2012-12-01
The digital piracy involving images, music, movies, books, and so on, is a legal problem that has not found a solution. Therefore it becomes crucial to create and to develop methods and numerical algorithms in order to solve the copyright problems. In this paper we focus the attention on a new approach of watermarking technique applied to digital color images. Our aim is to describe the realized watermarking algorithm based on multichannel wavelet functions with multiplicity r = 3, called MCWM 1.0. We report a large experimentation and some important numerical results in order to show the robustness of the proposed algorithm to geometrical attacks.
THREE-DIMENSIONAL ANALYSIS OF FUNCTIONALLY GRADED PLATE BASED ON THE HAAR WAVELET METHOD
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied.
Rahbar, Kambiz; Faez, Karim; Attaran-Kakhki, Ebrahim
2012-06-01
Reduction of image quality under the effects of wavefront aberration of the optical system has a direct impact on the vision system's performance. This paper tries to estimate the amount of aberration with the use of wavelet transform profilometry. The basic idea is based on the principle that under aberration effects, the position of the fringes' image on the image plane will change, and this change correlates with the amount of aberration. So the distribution of aberration function can directly be extracted through measuring the amount of changes in the fringes' image on the image plane. Experimental results and the empirical validity of this idea are evaluated.
Institute of Scientific and Technical Information of China (English)
刘希强; 周惠兰; 曹文海; 李红; 李永红; 季爱东
2002-01-01
Based on the characteristics of gradual change style seismic signal onset which has more high frequency signal components but less magnitude, this paper selects Gauss linear frequency modulation wavelet as base function to study the change characteristics of Gauss linear frequency modulation wavelet transform with difference wavelet and signal parameters, analyzes the error origin of seismic phases identification on the basis of Gauss linear frequency modulation wavelet transform, puts forward a kind of new method identifying gradual change style seismic phases with background noise which is called fixed scale wavelet transform ratio, and presents application examples about simulation digital signal and actual seismic phases recording onsets identification.
Applications of a fast, continuous wavelet transform
Energy Technology Data Exchange (ETDEWEB)
Dress, W.B.
1997-02-01
A fast, continuous, wavelet transform, based on Shannon`s sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon`s sampling theorem lets us view the Fourier transform of the data set as a continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time- domain sampling of the signal under analysis. Computational cost and nonorthogonality aside, the inherent flexibility and shift invariance of the frequency-space wavelets has advantages. The method has been applied to forensic audio reconstruction speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants` heart beats. Audio reconstruction is aided by selection of desired regions in the 2-D representation of the magnitude of the transformed signal. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass-spring system (e.g., a vehicle) by an occupants beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, features such as the glottal closing rate and word and phrase segmentation may be extracted from voice data.
Directory of Open Access Journals (Sweden)
Donald A. McLaren
2013-04-01
Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.
Activation detection in functional near-infrared spectroscopy by wavelet coherence
Zhang, Xin; Yu, Jian; Zhao, Ruirui; Xu, Wenting; Niu, Haijing; Zhang, Yujin; Zuo, Nianming; Jiang, Tianzi
2015-01-01
Functional near-infrared spectroscopy (fNIRS) detects hemodynamic responses in the cerebral cortex by transcranial spectroscopy. However, measurements recorded by fNIRS not only consist of the desired hemodynamic response but also consist of a number of physiological noises. Because of these noises, accurately detecting the regions that have an activated hemodynamic response while performing a task is a challenge when analyzing functional activity by fNIRS. In order to better detect the activation, we designed a multiscale analysis based on wavelet coherence. In this method, the experimental paradigm was expressed as a binary signal obtained while either performing or not performing a task. We convolved the signal with the canonical hemodynamic response function to predict a possible response. The wavelet coherence was used to investigate the relationship between the response and the data obtained by fNIRS at each channel. Subsequently, the coherence within a region of interest in the time-frequency domain was summed to evaluate the activation level at each channel. Experiments on both simulated and experimental data demonstrated that the method was effective for detecting activated channels hidden in fNIRS data.
Institute of Scientific and Technical Information of China (English)
ZHANG Xiaodong; BI Guangguo
2001-01-01
A wavelet packet function based multiple access (WPMA) system is developed in this paper to maximize capacity and improve receiver performance over frequency selective multipath fading channels. To design an efficient receiver that mitigates residual multiple access interference (MAI) and intersymbol interference, while improving received signal-to-interference and noise ratio (SINR) simultaneously on the uplink, a multichannel decision feedback equalizer (DFE) following a wavelet packet function based RAKE receiver is proposed. Simulation results show that, over GSM TU channels the developed receiver performs quite well if the power of each user is perfectly controlled or the space diversity combining (SDC) technique is applied.
Jensen's Functionals on Time Scales
Directory of Open Access Journals (Sweden)
Matloob Anwar
2012-01-01
Full Text Available We consider Jensen’s functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. By applying the properties of Jensen’s functionals on these means, we obtain several refinements and converses of Hölder’s inequality on time scales.
Sadabadi, Mahdiye Sadat; Shafiee, Masoud; Karrari, Mehdi
2008-07-01
In this paper, parameter identification of two-dimensional continuous-time systems via two-dimensional modulating functions is proposed. In the proposed method, trigonometric functions and sine-cosine wavelets are used as modulating functions. By this, a partial differential equation on the finite-time intervals is converted into an algebraic equation linear in parameters. The parameters of the system can then be estimated using the least square algorithms. The underlying computations utilize a two-dimensional fast Fourier transform algorithm, without the need for estimating the unknown initial or boundary conditions, at the beginning of each finite-time interval. Numerical simulations are presented to show the effectiveness of the proposed algorithm.
Affine density in wavelet analysis
Kutyniok, Gitta
2007-01-01
In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems. This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
Detecting the BAO using Discrete Wavelet Packets
Garcia, Noel Anthony; Wu, Yunyun; Kadowaki, Kevin; Pando, Jesus
2017-01-01
We use wavelet packets to investigate the clustering of matter on galactic scales in search of the Baryon Acoustic Oscillations. We do so in two ways. We develop a wavelet packet approach to measure the power spectrum and apply this method to the CMASS galaxy catalogue from the Sloan Digital Sky Survey (SDSS). We compare the resulting power spectrum to published BOSS results by measuring a parameter β that compares our wavelet detected oscillations to the results from the SDSS collaboration. We find that β=1 indicating that our wavelet packet methods are detecting the BAO at a similar level as traditional Fourier techniques. We then use wavelet packets to decompose, denoise, and then reconstruct the galaxy density field. Using this denoised field, we compute the standard two-point correlation function. We are able to successfully detect the BAO at r ≈ 105 h-1 Mpc in line with previous SDSS results. We conclude that wavelet packets do reproduce the results of the key clustering statistics computed by other means. The wavelet packets show distinct advantages in suppressing high frequency noise and in keeping information localized.
Institute of Scientific and Technical Information of China (English)
DENG Ke; ZHANG Lu; LUO Mao-Kang
2011-01-01
@@ Aiming at the shortage of conventional threshold function in wavelet noise reduction of chaotic signals, we propose a wavelet-packet noise reduction method of chaotic signals based on a new higher order threshold function.The method retains the useful high-frequency information, and the threshold function is continuous and derivable, therefore it is more consistent with the characteristics of the continuous signal.Contrast simulation experiment shows that the effect of noise reduction and the precision of noise reduction of chaotic signals both are improved.%Aiming at the shortage of conventional threshold function in wavelet noise reduction of chaotic signals, we propose a wavelet-packet noise reduction method of chaotic signals based on a new higher order threshold function. The method retains the useful high-frequency information, and the threshold function is continuous and derivable,therefore it is more consistent with the characteristics of the continuous signal. Contrast simulation experiment shows that the effect of noise reduction and the precision of noise reduction of chaotic signals both are improved.
Directory of Open Access Journals (Sweden)
Akimov Pavel Alekseevich
2012-10-01
Full Text Available Part 1 of this paper represents an introduction into the multi-resolution wavelet analysis. The wavelet-based analysis is an exciting new problem-solving tool used by mathematicians, scientists and engineers. In the paper, the authors try to present the fundamental elements of the multi-resolution wavelet analysis in a way that is accessible to an engineer, a scientist and an applied mathematician both as a theoretical approach and as a potential practical method of solving problems (particularly, boundary problems of structural mechanics and mathematical physics. The main goal of the contemporary wavelet research is to generate a set of basic functions (or general expansion functions and transformations that will provide an informative, efficient and useful description of a function or a signal. Another central idea is that of multi-resolution whereby decomposition of a signal represents the resolution of the detail. The multi-resolution decomposition seems to separate components of a signal in a way that is superior to most other methods of analysis, processing or compression. Due to the ability of the discrete wavelet transformation technique to decompose a signal at different independent scaling levels and to do it in a very flexible way, wavelets can be named "the microscopes of mathematics". Indeed, the use of the wavelet analysis and wavelet transformations requires a new point of view and a new method of interpreting representations.
Exact reconstruction with directional wavelets on the sphere
Wiaux, Y; Vandergheynst, P; Blanc, O
2007-01-01
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of intere...
Energy Technology Data Exchange (ETDEWEB)
Yang, J.J., E-mail: jjyang@scu.edu.cn; Miao, F.M.; Tang, J., E-mail: tangjun@scu.edu.cn; Yang, Y.Y.; Liao, J.L.; Liu, N.
2014-01-01
Kinetic surface roughening of TaN thin films deposited by reactive sputtering was investigated by using atomic force microscopy. Wavelet transform method incorporating power spectrum density analysis was applied to extract the global and local surface morphologies of the films. Then the dynamical exponents of global and local surface roughening were calculated in terms of dynamic scaling theory. The results show that the kinetic surface roughening of TaN thin films exhibits multi-scale characteristics, where a set of local dynamical exponents (α{sub l} = 0.95, β{sub l} = 0.24) and global dynamical exponents (α{sub g} = 1.56, β{sub g} = 0.71) was obtained. The local surface roughening is dominated by the competition between linear surface diffusion and deposition flux noise, while the global surface roughening displays anomalous rapid-roughening behavior due to the preferred grain growth. - Highlights: • Film surface multi-scale behaviors were characterized by wavelet transform. • Microscopic mechanisms of surface multi-scale behaviors were investigated.
Directory of Open Access Journals (Sweden)
Cheng-Wei Fei
2013-01-01
Full Text Available In order to correctly analyze aeroengine whole-body vibration signals, Wavelet Correlation Feature Scale Entropy (WCFSE and Fuzzy Support Vector Machine (FSVM (WCFSE-FSVM method was proposed by fusing the advantages of the WCFSE method and the FSVM method. The wavelet coefficients were known to be located in high Signal-to-Noise Ratio (S/N or SNR scales and were obtained by the Wavelet Transform Correlation Filter Method (WTCFM. This method was applied to address the whole-body vibration signals. The WCFSE method was derived from the integration of the information entropy theory and WTCFM, and was applied to extract the WCFSE values of the vibration signals. Among the WCFSE values, the WFSE1 and WCFSE2 values on the scale 1 and 2 from the high band of vibration signal were believed to acceptably reflect the vibration feature and were selected to construct the eigenvectors of vibration signals as fault samples to establish the WCFSE-FSVM model. This model was applied to aeroengine whole-body vibration fault diagnosis. Through the diagnoses of four vibration fault modes and the comparison of the analysis results by four methods (SVM, FSVM, WESE-SVM, WCFSE-FSVM, it is shown that the WCFSE-FSVM method is characterized by higher learning ability, higher generalization ability and higher anti-noise ability than other methods in aeroengine whole-vibration fault analysis. Meanwhile, this present study provides a useful insight for the vibration fault diagnosis of complex machinery besides an aeroengine.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The multi-scale characteristics of wave significant height (Hs) in eastern China seas were revealed by multi-scale wavelet analysis. In order to understand the relation between wave and wind, the TOPEX/Poseidon measurements of Hs and wind speed were analyzed. The result showed that Hs and wind speed change in multi-scale at one-, two-month, half-, one- and two-year cycles. But in a larger time scale, the variations in Hs and wind speed are different. Hs has a five-year cycle similar to the cycle of ENSO variation, while the wind speed has no such cycle. In the time domain, the correlation between Hs and ENSO is unclear.
Thurner, S; Lowen, S B; Teich, M C; Thurner, Stefan; Feurstein, Markus C.; Lowen, Steven B.; Teich, Malvin C.
1998-01-01
Receiver-operating-characteristic (ROC) analysis was used to assess the suitability of various heart rate variability (HRV) measures for correctly classifying electrocardiogram records of varying lengths as normal or revealing the presence of heart failure. Scale-dependent HRV measures were found to be substantially superior to scale-independent measures (scaling exponents) for discriminating the two classes of data over a broad range of record lengths. The wavelet-coefficient standard deviation at a scale near 32 heartbeat intervals, and its spectral counterpart near 1/32 cycles per interval, provide reliable results using record lengths just minutes long. A jittered integrate-and-fire model built around a fractal Gaussian-noise kernel provides a realistic, though not perfect, simulation of heartbeat sequences.
Institute of Scientific and Technical Information of China (English)
HE Xiao-bo; ZHOU Hui-lan
2005-01-01
The arrival times of first teleseismic phases are difficult to be measured precisely because of slowly and gradually changed onsets and weak amplitudes. The arrival times measured manually are usually behind the real ones. In this paper, using the ratio method of fixed scale wavelet transformations improved by us, the arrival times for the first arrival phases (such as P and PKIKP) at the teleseismic and far-teleseimic distances were measured. The results are reasonable and reliable based on the analysis and discussion of the reliabilifies and errors.
Aboufadel, Edward
1999-01-01
An accessible and practical introduction to wavelets. With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra. The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets
Institute of Scientific and Technical Information of China (English)
WANG Jian; GAO Jingxiang; XU Changhui
2006-01-01
Wavelet theory is efficient as an adequate tool for analyzing single epoch GPS deformation signal. Wavelet analysis technique on gross error detection and recovery is advanced. Criteria of wavelet function choosing and Mallat decomposition levels decision are discussed. An effective deformation signal extracting method is proposed, that is wavelet noise reduction technique considering gross error recovery, which combines wavelet multi-resolution gross error detection results. Time position recognizing of gross errors and their repairing performance are realized. In the experiment, compactly supported orthogonal wavelet with short support block is more efficient than the longer one when discerning gross errors, which can obtain more finely analyses. And the shape of discerned gross error of short support wavelet is simpler than that of the longer one. Meanwhile, the time scale is easier to identify.
Multi scale risk measurement in electricity market:a wavelet based value at risk approach
Institute of Scientific and Technical Information of China (English)
Guu; Sy-Ming; Lai; Kin; Keung
2008-01-01
Value at risk (VaR) is adopted to measure the risk level in the electricity market. To estimate VaR at higher accuracy and reliability, the wavelet variance decomposed approach for value at risk estimates (WVDVaR) is proposed. Empirical studies conduct in five Australian electricity markets, which evaluate the performances of both the proposed approach and the traditional ARMA-GARCH approach using the Kupiec backtesting procedure. Experimental results suggest that the proposed approach measures electricity ...
Applications of a fast continuous wavelet transform
Dress, William B.
1997-04-01
A fast, continuous, wavelet transform, justified by appealing to Shannon's sampling theorem in frequency space, has been developed for use with continuous mother wavelets and sampled data sets. The method differs from the usual discrete-wavelet approach and from the standard treatment of the continuous-wavelet transform in that, here, the wavelet is sampled in the frequency domain. Since Shannon's sampling theorem lets us view the Fourier transform of the data set as representing the continuous function in frequency space, the continuous nature of the functions is kept up to the point of sampling the scale-translation lattice, so the scale-translation grid used to represent the wavelet transform is independent of the time-domain sampling of the signal under analysis. Although more computationally costly and not represented by an orthogonal basis, the inherent flexibility and shift invariance of the frequency-space wavelets are advantageous for certain applications. The method has been applied to forensic audio reconstruction, speaker recognition/identification, and the detection of micromotions of heavy vehicles associated with ballistocardiac impulses originating from occupants' heart beats. Audio reconstruction is aided by selection of desired regions in the 2D representation of the magnitude of the transformed signals. The inverse transform is applied to ridges and selected regions to reconstruct areas of interest, unencumbered by noise interference lying outside these regions. To separate micromotions imparted to a mass- spring system by an occupant's beating heart from gross mechanical motions due to wind and traffic vibrations, a continuous frequency-space wavelet, modeled on the frequency content of a canonical ballistocardiogram, was used to analyze time series taken from geophone measurements of vehicle micromotions. By using a family of mother wavelets, such as a set of Gaussian derivatives of various orders, different features may be extracted from voice
Review Paper :Comparative Analysis Of Mother Wavelet Functions With The ECG Signals
Directory of Open Access Journals (Sweden)
Kapil Tajane
2014-01-01
Full Text Available Electrocardiographic ECG gives the information about electrical activity of the heart captured over time by attaching an external electrode to the skin. Now a days ECG signal is used as a baseline to determine the hearts condition. It is very much essential to detect and process ECG signal accurately. ECG consists of various types of noise such as muscle noise, baseline wander and power line interference etc. To remove such types of noise wavelet transform is used. Mother wavelet is an effective tool for denoising such signals. But selection of proper mother wavelet for the ECG signal is again a challenging task. This paper gives the survey about the wavelet transforms useful for ECG denoising. The different wavelet transform are compared and from that we can decide which one is more suitable.
Scaled density functional theory correlation functionals.
Ghouri, Mohammed M; Singh, Saurabh; Ramachandran, B
2007-10-18
We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.
Wavelet Scattering Regression of Quantum Chemical Energies
Hirn, Matthew; Poilvert, Nicolas
2016-01-01
We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is represented by an electronic density function. A multiscale invariant dictionary is calculated with wavelet scattering invariants. It cascades a first wavelet transform which separates scales, with a second wavelet transform which computes interactions across scales. Sparse scattering regressions give state of the art results over two databases of organic planar molecules. On these databases, the regression error is of the order of the error produced by DFT codes, but at a fraction of the computational cost.
Fang, Zhufeng; Bogena, Heye; Kollet, Stefan; Koch, Julian; Vereecken, Harry
2015-10-01
Soil moisture plays a key role in the water and energy balance in soil, vegetation and atmosphere systems. According to Wood et al. (2011) there is a grand need to increase global-scale hyper-resolution water-energy-biogeochemistry land surface modelling capabilities. These modelling capabilities should also recognize epistemic uncertainties, as well as the nonlinearity and hysteresis in its dynamics. Unfortunately, it is not clear how to parameterize hydrological processes as a function of scale, and how to test deterministic models with regard to epistemic uncertainties. In this study, high resolution long-term simulations were conducted in the highly instrumented TERENO hydrological observatory of the Wüstebach catchment. Soil hydraulic parameters were derived using inverse modelling with the Hydrus-1D model using the global optimization scheme SCE-UA and soil moisture data from a wireless soil moisture sensor network. The estimated parameters were then used for 3D simulations of water transport using the integrated parallel simulation platform ParFlow-CLM. The simulated soil moisture dynamics, as well as evapotranspiration (ET) and runoff, were compared with long-term field observations to illustrate how well the model was able to reproduce the water budget dynamics. We investigated different anisotropies of hydraulic conductivity to analyze how fast lateral flow processes above the underlying bedrock affect the simulation results. For a detail investigation of the model results we applied the empirical orthogonal function (EOF) and wavelet coherence methods. The EOF analysis of temporal-spatial patterns of simulated and observed soil moisture revealed that introduction of heterogeneity in the soil porosity effectively improves estimates of soil moisture patterns. Our wavelet coherence analysis indicates that wet and dry seasons have significant effect on temporal correlation between observed and simulated soil moisture and ET. Our study demonstrates the
Goossens, Bart; Aelterman, Jan; Luong, Hiep; Pizurica, Aleksandra; Philips, Wilfried
2013-02-01
In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU.
The application of modeling and prediction with MRA wavelet network
Institute of Scientific and Technical Information of China (English)
LU Shu-ping; YANG Xue-jing; ZHAO Xi-ren
2004-01-01
As there are lots of non-linear systems in the real engineering, it is very important to do more researches on the modeling and prediction of non-linear systems. Based on the multi-resolution analysis (MRA) of wavelet theory, this paper combined the wavelet theory with neural network and established a MRA wavelet network with the scaling function and wavelet function as its neurons. From the analysis in the frequency domain, the results indicated that MRA wavelet network was better than other wavelet networks in the ability of approaching to the signals. An essential research was carried out on modeling and prediction with MRA wavelet network in the non-linear system. Using the lengthwise sway data received from the experiment of ship model, a model of offline prediction was established and was applied to the short-time prediction of ship motion. The simulation results indicated that the forecasting model improved the prediction precision effectively, lengthened the forecasting time and had a better prediction results than that of AR linear model.The research indicates that it is feasible to use the MRA wavelet network in the short -time prediction of ship motion.
Optical encryption with cascaded fractional wavelet transforms
Institute of Scientific and Technical Information of China (English)
BAO Liang-hua; CHEN Lin-fei; ZHAO Dao-mu
2006-01-01
On the basis of fractional wavelet transform, we propose a new method called cascaded fractional wavelet transform to encrypt images. It has the virtues of fractional Fourier transform and wavelet transform. Fractional orders, standard focal lengths and scaling factors are its keys. Multistage fractional Fourier transforms can add the keys easily and strengthen information security. This method can also realize partial encryption just as wavelet transform and fractional wavelet transform. Optical realization of encryption and decryption is proposed. Computer simulations confirmed its possibility.
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
Zhao, Bin
2015-02-01
Temperature-pressure coupled field analysis of liquefied petroleum gas (LPG) tank under jet fire can offer theoretical guidance for preventing the fire accidents of LPG tank, the application of super wavelet finite element on it is studied in depth. First, review of related researches on heat transfer analysis of LPG tank under fire and super wavelet are carried out. Second, basic theory of super wavelet transform is studied. Third, the temperature-pressure coupled model of gas phase and liquid LPG under jet fire is established based on the equation of state, the VOF model and the RNG k-ɛ model. Then the super wavelet finite element formulation is constructed using the super wavelet scale function as interpolating function. Finally, the simulation is carried out, and results show that the super wavelet finite element method has higher computing precision than wavelet finite element method.
Diagnosis method based on wavelet coefficient scale relativity correlation dimension for fault
Institute of Scientific and Technical Information of China (English)
2008-01-01
Correlation dimension as a tool to describe machinery condition is introduced.Vibration signals of the fan under different working conditions are analyzed using a threshold filtering algorithm based on the region relativity of the wavelet coefficients for reducing noise.The result shows that the characteristics of the signal could be preserved completely.The correlation dimension is able to identify conditions of the fan with faults compared with the normal condition,thereby providing an effective technology for condition monitoring and fault diagnosis of mechanical equipment.
Controlling the Beam Halo-Chaos via Wavelet-Based Feedback Periodically
Institute of Scientific and Technical Information of China (English)
2001-01-01
In our recent work, worth mentioning in particular is the wavelet-based feedback controller, which works much better than the others for controlling the proton beam haio-chaos, where the master wavelet function isor, in a simplified form,and generalized form:(1)(2)(3)where a and b are scaling and translation constants, respectively. C is a selected constant. The
Usowicz, Jerzy, B.; Marczewski, Wojciech; Usowicz, Boguslaw; Lipiec, Jerzy; Lukowski, Mateusz I.
2010-05-01
This paper presents the results of the time series analysis of the soil moisture observed at two test sites Podlasie, Polesie, in the Cal/Val AO 3275 campaigns in Poland, during the interval 2006-2009. The test sites have been selected on a basis of their contrasted hydrological conditions. The region Podlasie (Trzebieszow) is essentially drier than the wetland region Polesie (Urszulin). It is worthwhile to note that the soil moisture variations can be represented as a non-stationary random process, and therefore appropriate analysis methods are required. The so-called Empirical Mode Decomposition (EMD) method has been chosen, since it is one of the best methods for the analysis of non-stationary and nonlinear time series. To confirm the results obtained by the EMD we have also used the wavelet methods. Firstly, we have used EMD (analyze step) to decompose the original time series into the so-called Intrinsic Mode Functions (IMFs) and then by grouping and addition similar IMFs (synthesize step) to obtain a few signal components with corresponding temporal scales. Such an adaptive procedure enables to decompose the original time series into diurnal, seasonal and trend components. Revealing of all temporal scales which operates in the original time series is our main objective and this approach may prove to be useful in other studies. Secondly, we have analyzed the soil moisture time series from both sites using the cross-wavelet and wavelet coherency. These methods allow us to study the degree of spatial coherence, which may vary in various intervals of time. We hope the obtained results provide some hints and guidelines for the validation of ESA SMOS data. References: B. Usowicz, J.B. Usowicz, Spatial and temporal variation of selected physical and chemical properties of soil, Institute of Agrophysics, Polish Academy of Sciences, Lublin 2004, ISBN 83-87385-96-4 Rao, A.R., Hsu, E.-C., Hilbert-Huang Transform Analysis of Hydrological and Environmental Time Series
Directory of Open Access Journals (Sweden)
Barbosa Daniel C
2012-01-01
Full Text Available Abstract Background Wireless capsule endoscopy has been introduced as an innovative, non-invasive diagnostic technique for evaluation of the gastrointestinal tract, reaching places where conventional endoscopy is unable to. However, the output of this technique is an 8 hours video, whose analysis by the expert physician is very time consuming. Thus, a computer assisted diagnosis tool to help the physicians to evaluate CE exams faster and more accurately is an important technical challenge and an excellent economical opportunity. Method The set of features proposed in this paper to code textural information is based on statistical modeling of second order textural measures extracted from co-occurrence matrices. To cope with both joint and marginal non-Gaussianity of second order textural measures, higher order moments are used. These statistical moments are taken from the two-dimensional color-scale feature space, where two different scales are considered. Second and higher order moments of textural measures are computed from the co-occurrence matrices computed from images synthesized by the inverse wavelet transform of the wavelet transform containing only the selected scales for the three color channels. The dimensionality of the data is reduced by using Principal Component Analysis. Results The proposed textural features are then used as the input of a classifier based on artificial neural networks. Classification performances of 93.1% specificity and 93.9% sensitivity are achieved on real data. These promising results open the path towards a deeper study regarding the applicability of this algorithm in computer aided diagnosis systems to assist physicians in their clinical practice.
The Brera Multi-scale Wavelet Chandra Survey. I. Serendipitous source catalogue
Romano, P; Mignani, R P; Moretti, A; Mottini, M; Panzera, M R; Tagliaferri, G
2008-01-01
We present the BMW-Chandra source catalogue drawn from essentially all Chandra ACIS-I pointed observations with an exposure time in excess of 10ks public as of March 2003 (136 observations). Using the wavelet detection algorithm developed by Lazzati et al. (1999) and Campana et al. (1999), which can characterise both point-like and extended sources, we identified 21325 sources. Among them, 16758 are serendipitous, i.e. not associated with the targets of the pointings, and do not require a non-automated analysis. This makes our catalogue the largest compilation of Chandra sources to date. The 0.5--10 keV absorption corrected fluxes of these sources range from ~3E-16 to 9E-12 erg cm^-2 s^-1 with a median of 7E-15 erg cm^-2 s^-1. The catalogue consists of count rates and relative errors in three energy bands (total, 0.5-7keV; soft, 0.5-2keV; and hard, 2-7keV), and source positions relative to the highest signal-to-noise detection among the three bands. The wavelet algorithm also provides an estimate of the exten...
Wavelet-based Characterization of Small-scale Solar Emission Features at Low Radio Frequencies
Suresh, A.; Sharma, R.; Oberoi, D.; Das, S. B.; Pankratius, V.; Timar, B.; Lonsdale, C. J.; Bowman, J. D.; Briggs, F.; Cappallo, R. J.; Corey, B. E.; Deshpande, A. A.; Emrich, D.; Goeke, R.; Greenhill, L. J.; Hazelton, B. J.; Johnston-Hollitt, M.; Kaplan, D. L.; Kasper, J. C.; Kratzenberg, E.; Lynch, M. J.; McWhirter, S. R.; Mitchell, D. A.; Morales, M. F.; Morgan, E.; Ord, S. M.; Prabu, T.; Rogers, A. E. E.; Roshi, A.; Udaya Shankar, N.; Srivani, K. S.; Subrahmanyan, R.; Tingay, S. J.; Waterson, M.; Wayth, R. B.; Webster, R. L.; Whitney, A. R.; Williams, A.; Williams, C. L.
2017-07-01
Low radio frequency solar observations using the Murchison Widefield Array have recently revealed the presence of numerous weak short-lived narrowband emission features, even during moderately quiet solar conditions. These nonthermal features occur at rates of many thousands per hour in the 30.72 MHz observing bandwidth, and hence necessarily require an automated approach for their detection and characterization. Here, we employ continuous wavelet transform using a mother Ricker wavelet for feature detection from the dynamic spectrum. We establish the efficacy of this approach and present the first statistically robust characterization of the properties of these features. In particular, we examine distributions of their peak flux densities, spectral spans, temporal spans, and peak frequencies. We can reliably detect features weaker than 1 SFU, making them, to the best of our knowledge, the weakest bursts reported in literature. The distribution of their peak flux densities follows a power law with an index of -2.23 in the 12-155 SFU range, implying that they can provide an energetically significant contribution to coronal and chromospheric heating. These features typically last for 1-2 s and possess bandwidths of about 4-5 MHz. Their occurrence rate remains fairly flat in the 140-210 MHz frequency range. At the time resolution of the data, they appear as stationary bursts, exhibiting no perceptible frequency drift. These features also appear to ride on a broadband background continuum, hinting at the likelihood of them being weak type-I bursts.
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
Chaudhury, Kunal Narayan
2009-01-01
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for constructing 2D directional-selective complex...
Wavelet based free-form deformations for nonrigid registration
W. Sun (William); W.J. Niessen (Wiro); S.K. Klein (Stefan)
2014-01-01
textabstractIn nonrigid registration, deformations may take place on the coarse and fine scales. For the conventional B-splines based free-form deformation (FFD) registration, these coarse- and fine-scale deformations are all represented by basis functions of a single scale. Meanwhile, wavelets have
Functional Scaling of Musculoskeletal Models
DEFF Research Database (Denmark)
Lund, Morten Enemark; Andersen, Michael Skipper; de Zee, Mark;
The validity of the predictions from musculoskeletal models depends largely on how well the morphology of the model matches that of the patient. To address this problem, we present a novel method to scale a cadaver-based musculoskeletal model to match both the segment lengths and joint parameters...... orientations are then used to morph/scale a cadaver based musculoskeletal model using a set of radial basis functions (RBFs). Using the functional joint axes to scale musculoskeletal models provides a better fit to the marker data, and allows for representation of patients with considerable difference in bone...... geometry, without the need for MR/CT scans. However, more validation activities are needed to better understand the effect of morphing musculoskeletal models based on functional joint parameters....
Ye, Linlin; Yang, Dan; Wang, Xu
2014-06-01
A de-noising method for electrocardiogram (ECG) based on ensemble empirical mode decomposition (EEMD) and wavelet threshold de-noising theory is proposed in our school. We decomposed noised ECG signals with the proposed method using the EEMD and calculated a series of intrinsic mode functions (IMFs). Then we selected IMFs and reconstructed them to realize the de-noising for ECG. The processed ECG signals were filtered again with wavelet transform using improved threshold function. In the experiments, MIT-BIH ECG database was used for evaluating the performance of the proposed method, contrasting with de-noising method based on EEMD and wavelet transform with improved threshold function alone in parameters of signal to noise ratio (SNR) and mean square error (MSE). The results showed that the ECG waveforms de-noised with the proposed method were smooth and the amplitudes of ECG features did not attenuate. In conclusion, the method discussed in this paper can realize the ECG denoising and meanwhile keep the characteristics of original ECG signal.
Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory
Natarajan, Bhaarathi; Casida, Mark E; Deutsch, Thierry; Burchak, Olga N; Philouze, Christian; Balakirev, Maxim Y
2011-01-01
Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BigDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program deMon2k for the calculation of electronic absorption spectra of N2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BigDFT than for deMon2k. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BigDFT, while all virtual orbitals are included in TD-DFT calculations in deMon2k. As a reality check, we report the x-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidaz...
Relations Between Wavelet Network and Feedforward Neural Network
Institute of Scientific and Technical Information of China (English)
刘志刚; 何正友; 钱清泉
2002-01-01
A comparison of construction forms and base functions is made between feedforward neural network and wavelet network. The relations between them are studied from the constructions of wavelet functions or dilation functions in wavelet network by different activation functions in feedforward neural network. It is concluded that some wavelet function is equal to the linear combination of several neurons in feedforward neural network.
Doppler radar fall activity detection using the wavelet transform.
Su, Bo Yu; Ho, K C; Rantz, Marilyn J; Skubic, Marjorie
2015-03-01
We propose in this paper the use of Wavelet transform (WT) to detect human falls using a ceiling mounted Doppler range control radar. The radar senses any motions from falls as well as nonfalls due to the Doppler effect. The WT is very effective in distinguishing the falls from other activities, making it a promising technique for radar fall detection in nonobtrusive inhome elder care applications. The proposed radar fall detector consists of two stages. The prescreen stage uses the coefficients of wavelet decomposition at a given scale to identify the time locations in which fall activities may have occurred. The classification stage extracts the time-frequency content from the wavelet coefficients at many scales to form a feature vector for fall versus nonfall classification. The selection of different wavelet functions is examined to achieve better performance. Experimental results using the data from the laboratory and real inhome environments validate the promising and robust performance of the proposed detector.
Wavelets in scientific computing
DEFF Research Database (Denmark)
Nielsen, Ole Møller
1998-01-01
such a function well. These properties of wavelets have lead to some very successful applications within the field of signal processing. This dissertation revolves around the role of wavelets in scientific computing and it falls into three parts: Part I gives an exposition of the theory of orthogonal, compactly...... is an investigation of the potential for using the special properties of wavelets for solving partial differential equations numerically. Several approaches are identified and two of them are described in detail. The algorithms developed are applied to the nonlinear Schrödinger equation and Burgers' equation...
Battle, G A
1999-01-01
WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the F 4 3 quantum field theory is presented. It is due to Battle and
Institute of Scientific and Technical Information of China (English)
吴凡; 祝国瑞
2001-01-01
With the development of GIS application ceaselessly, a mass of multi-scale geospatial data need to be analyzed and represented because users require different detailed spatial data to dealwith different problems and output maps at different scales. It has become one of the key problemsto applied GIS. The logic relations have to be established between spatial data sets at differentscales so that one representation of spatial data can be transferred to another completely. The completeness refers that spatial precision and characteristics and a high information density that adaptsto relevant abstract detail must be preserved,and the consistency of spatial semantics and spatialrelations have to be maintained simultaneously.In addition, the deriving of new spatial data setsshould be bi-directional on some constraint in GIS, from fine-scale to broad-scale and vice versa.Automatic generalization of geographical information is the core content of multi-scale representation of spatial data, but the scale-dependent generalization methods are far from abundance becauseof its extreme complicacy.Most existing algorithms about automatic generalization do not relate toscale directly or accurately, not forecast and control the generalized effects, and cannot assess theholistic consistency of the generalized results. The rational and quantitative methods and criterionsof measuring the extent of generalization have not still been sought out. Wavelet analysis is a newbranch of mathematics burgeoning at the end of 1980s. It has double meanings simultaneously onprofundity of theory and extent of application. Because it has good local character at both time orspace and frequency field simultaneously, and sample interval of signal can be adjusted automatically with different frequency components, any details of function, such as a sign or image etc., canbe analyzed at any scales by using wavelet analysis. Therefore, wavelet analysis suggests a new solution to the problems mentioned above
Directory of Open Access Journals (Sweden)
G. Ouillon
1995-01-01
Full Text Available The classical method of statistical physics deduces the macroscopic behaviour of a system from the organization and interactions of its microscopical constituents. This kind of problem can often be solved using procedures deduced from the Renormalization Group Theory, but in some cases, the basic microscopic rail are unknown and one has to deal only with the intrinsic geometry. The wavelet analysis concept appears to be particularly adapted to this kind of situation as it highlights details of a set at a given analyzed scale. As fractures and faults generally define highly anisotropic fields, we defined a new renormalization procedure based on the use of anisotropic wavelets. This approach consists of finding an optimum filter will maximizes wavelet coefficients at each point of the fie] Its intrinsic definition allows us to compute a rose diagram of the main structural directions present in t field at every scale. Scaling properties are determine using a multifractal box-counting analysis improved take account of samples with irregular geometry and finite size. In addition, we present histograms of fault length distribution. Our main observation is that different geometries and scaling laws hold for different rang of scales, separated by boundaries that correlate well with thicknesses of lithological units that constitute the continental crust. At scales involving the deformation of the crystalline crust, we find that faulting displays some singularities similar to those commonly observed in Diffusion- Limited Aggregation processes.
A wavelet phase filter for emission tomography
Energy Technology Data Exchange (ETDEWEB)
Olsen, E.T.; Lin, B. [Illinois Inst. of Tech., Chicago, IL (United States). Dept. of Mathematics
1995-07-01
The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, the authors explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, they show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on [0, 2{pi}). They then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.
Wavelet applied to computer vision in astrophysics
Bijaoui, Albert; Slezak, Eric; Traina, Myriam
2004-02-01
Multiscale analyses can be provided by application wavelet transforms. For image processing purposes, we applied algorithms which imply a quasi isotropic vision. For a uniform noisy image, a wavelet coefficient W has a probability density function (PDF) p(W) which depends on the noise statistic. The PDF was determined for many statistical noises: Gauss, Poission, Rayleigh, exponential. For CCD observations, the Anscombe transform was generalized to a mixed Gasus+Poisson noise. From the discrete wavelet transform a set of significant wavelet coefficients (SSWC)is obtained. Many applications have been derived like denoising and deconvolution. Our main application is the decomposition of the image into objects, i.e the vision. At each scale an image labelling is performed in the SSWC. An interscale graph linking the fields of significant pixels is then obtained. The objects are identified using this graph. The wavelet coefficients of the tree related to a given object allow one to reconstruct its image by a classical inverse method. This vision model has been applied to astronomical images, improving the analysis of complex structures.
Joint Time-Frequency And Wavelet Analysis - An Introduction
Directory of Open Access Journals (Sweden)
Majkowski Andrzej
2014-12-01
Full Text Available A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency. The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.
Scaling Equation for Invariant Measure
Institute of Scientific and Technical Information of China (English)
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Digital Watermarking in Wavelet Transform Domain
Directory of Open Access Journals (Sweden)
D. Levicky
2001-06-01
Full Text Available This paper presents a technique for the digital watermarking ofstill images based on the wavelet transform. The watermark (binaryimage is embedded into original image in its wavelet domain. Theoriginal unmarked image is required for watermark extraction. Themethod of embedding of digital watermarks in wavelet transform domainwas analyzed and verified on grey scale static images.
Avci, Derya; Leblebicioglu, Mehmet Kemal; Poyraz, Mustafa; Dogantekin, Esin
2014-02-01
So far, analysis and classification of urine cells number has become an important topic for medical diagnosis of some diseases. Therefore, in this study, we suggest a new technique based on Adaptive Discrete Wavelet Entropy Energy and Neural Network Classifier (ADWEENN) for Recognition of Urine Cells from Microscopic Images Independent of Rotation and Scaling. Some digital image processing methods such as noise reduction, contrast enhancement, segmentation, and morphological process are used for feature extraction stage of this ADWEENN in this study. Nowadays, the image processing and pattern recognition topics have come into prominence. The image processing concludes operation and design of systems that recognize patterns in data sets. In the past years, very difficulty in classification of microscopic images was the deficiency of enough methods to characterize. Lately, it is seen that, multi-resolution image analysis methods such as Gabor filters, discrete wavelet decompositions are superior to other classic methods for analysis of these microscopic images. In this study, the structure of the ADWEENN method composes of four stages. These are preprocessing stage, feature extraction stage, classification stage and testing stage. The Discrete Wavelet Transform (DWT) and adaptive wavelet entropy and energy is used for adaptive feature extraction in feature extraction stage to strengthen the premium features of the Artificial Neural Network (ANN) classifier in this study. Efficiency of the developed ADWEENN method was tested showing that an avarage of 97.58% recognition succes was obtained.
Directory of Open Access Journals (Sweden)
Noor Kamal Al-Qazzaz
2015-11-01
Full Text Available We performed a comparative study to select the efficient mother wavelet (MWT basis functions that optimally represent the signal characteristics of the electrical activity of the human brain during a working memory (WM task recorded through electro-encephalography (EEG. Nineteen EEG electrodes were placed on the scalp following the 10–20 system. These electrodes were then grouped into five recording regions corresponding to the scalp area of the cerebral cortex. Sixty-second WM task data were recorded from ten control subjects. Forty-five MWT basis functions from orthogonal families were investigated. These functions included Daubechies (db1–db20, Symlets (sym1–sym20, and Coiflets (coif1–coif5. Using ANOVA, we determined the MWT basis functions with the most significant differences in the ability of the five scalp regions to maximize their cross-correlation with the EEG signals. The best results were obtained using “sym9” across the five scalp regions. Therefore, the most compatible MWT with the EEG signals should be selected to achieve wavelet denoising, decomposition, reconstruction, and sub-band feature extraction. This study provides a reference of the selection of efficient MWT basis functions.
Magrini, Luciano A.; Domingues, Margarete O.; Mendes, Odim
2017-02-01
The presence of gaps is quite common in signals related to space science phenomena. Usually, this presence prevents the direct use of standard time-scale analysis because this analysis needs equally spaced data; it is affected by the time series borders (boundaries), and gaps can cause an increase of internal borders. Numerical approximations can be used to estimate the records whose entries are gaps. However, their use has limitations. In many practical cases, these approximations cannot faithfully reproduce the original signal behaviour. Alternatively, in this work, we compare an adapted wavelet technique (gaped wavelet transform), based on the continuous wavelet transform with Morlet wavelet analysing function, with two other standard approximation methods, namely, spline and Hermite cubic polynomials. This wavelet method does not require an approximation of the data on the gap positions, but it adapts the analysing wavelet function to deal with the gaps. To perform our comparisons, we use 120 magnetic field time series from a well-known space geophysical phenomena and we select and classify their gaps. Then, we analyse the influence of these methods in two time-scale tools. As conclusions, we observe that when the gaps are small (very few points sequentially missing), all the methods work well. However, with large gaps, the adapted wavelet method presents a better performance in the time-scale representation. Nevertheless, the cubic Hermite polynomial approximation is also an option when a reconstruction of the data is also needed, with the price of having a worse time-scale representation than the adapted wavelet method.
Magrini, Luciano A.; Domingues, Margarete O.; Mendes, Odim
2017-04-01
The presence of gaps is quite common in signals related to space science phenomena. Usually, this presence prevents the direct use of standard time-scale analysis because this analysis needs equally spaced data; it is affected by the time series borders (boundaries), and gaps can cause an increase of internal borders. Numerical approximations can be used to estimate the records whose entries are gaps. However, their use has limitations. In many practical cases, these approximations cannot faithfully reproduce the original signal behaviour. Alternatively, in this work, we compare an adapted wavelet technique (gaped wavelet transform), based on the continuous wavelet transform with Morlet wavelet analysing function, with two other standard approximation methods, namely, spline and Hermite cubic polynomials. This wavelet method does not require an approximation of the data on the gap positions, but it adapts the analysing wavelet function to deal with the gaps. To perform our comparisons, we use 120 magnetic field time series from a well-known space geophysical phenomena and we select and classify their gaps. Then, we analyse the influence of these methods in two time-scale tools. As conclusions, we observe that when the gaps are small (very few points sequentially missing), all the methods work well. However, with large gaps, the adapted wavelet method presents a better performance in the time-scale representation. Nevertheless, the cubic Hermite polynomial approximation is also an option when a reconstruction of the data is also needed, with the price of having a worse time-scale representation than the adapted wavelet method.
Institute of Scientific and Technical Information of China (English)
Zhou Xiaohui; Wang Gang; Wang Baoqin
2011-01-01
The purpose of this paper is to construct an orthogonal Armlet multi-wavelets with multiplicity r and dilation factor a.Firstly,the definition of Armlets with dilation factor a is proposed in this paper.Based on the Two-scale Similar Transform (TST),the notion of the Para-unitary A-scale Similar Transform (PAST) is introduced,and we also give the transform on the all two-scale matrix symbols of the multi-wavelets with dilation a.Then we show that the PAST and the transform on the matrix symbols of the multi-wavelets keep the orthogonality of the multi-wavelets system.We discuss the condition that a- 1 multi-wavelets corresponding to the multi-scaling functions are all Armlets.After performing the PAST and the transform on the matrix symbols of the multi-wavelets,the multi-scaling function can be balanced and the corresponding multi-wavelets can be Armlets at the same time.The construction of Armlets with high order is also discussed.At last,by a given example,we can conclude that the algorithm is feasible and efficient.
Linear Phase Perfect Reconstruction Filters and Wavelets with Even Symmetry
Monzon, Lucas
2011-01-01
Perfect reconstruction filter banks can be used to generate a variety of wavelet bases. Using IIR linear phase filters one can obtain symmetry properties for the wavelet and scaling functions. In this paper we describe all possible IIR linear phase filters generating symmetric wavelets with any prescribed number of vanishing moments. In analogy with the well known FIR case, we construct and study a new family of wavelets obtained by considering maximal number of vanishing moments for each fixed order of the IIR filter. Explicit expressions for the coefficients of numerator, denominator, zeroes, and poles are presented. This new parameterization allows one to design linear phase quadrature mirror filters with many other properties of interest such as filters that have any preassigned set of zeroes in the stopband or that satisfy an almost interpolating property. Using Beylkin's approach, it is indicated how to implement these IIR filters not as recursive filters but as FIR filters.
Chan, Y T
1995-01-01
Since the study of wavelets is a relatively new area, much of the research coming from mathematicians, most of the literature uses terminology, concepts and proofs that may, at times, be difficult and intimidating for the engineer. Wavelet Basics has therefore been written as an introductory book for scientists and engineers. The mathematical presentation has been kept simple, the concepts being presented in elaborate detail in a terminology that engineers will find familiar. Difficult ideas are illustrated with examples which will also aid in the development of an intuitive insight. Chapter 1 reviews the basics of signal transformation and discusses the concepts of duals and frames. Chapter 2 introduces the wavelet transform, contrasts it with the short-time Fourier transform and clarifies the names of the different types of wavelet transforms. Chapter 3 links multiresolution analysis, orthonormal wavelets and the design of digital filters. Chapter 4 gives a tour d'horizon of topics of current interest: wave...
Directory of Open Access Journals (Sweden)
Jian-feng Zhao
2017-01-01
Full Text Available This paper presents a three-dimensional autonomous chaotic system with high fraction dimension. It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. Based on the continuous chaos and the discrete wavelet function map, an image encryption algorithm is put forward. The key space is formed by the initial state variables, parameters, and orders of the system. Every pixel value is included in secret key, so as to improve antiattack capability of the algorithm. The obtained simulation results and extensive security analyses demonstrate the high level of security of the algorithm and show its robustness against various types of attacks.
Plesniak, Daniel H.; Bulusu, Kartik V.; Plesniak, Michael W.
2012-11-01
Interpretation of complex flow patterns observed in this study of a model curved artery required characterization of multiple, low-circulation secondary flow structures that were observed during the late systolic deceleration and diastolic phases under physiological inflow conditions. Phase-locked, planar vorticity PIV data were acquired at various cross-sectional locations of the 180-degree bent tube model. High circulation, deformed Dean- and Lyne-type vortices were observed during early stages of deceleration, while several smaller scale, highly deformed, low-circulation vortical patterns appeared in the core and near-wall regions during late systolic deceleration and diastolic phases. Due to the multiplicity of vortical scales and shapes, anisotropic 2D Ricker wavelets were used for coherent structure detection in a continuous wavelet transform algorithm (PIVlet 1.2). Our bio-inspired study is geared towards understanding whether optimizing the shape of the wavelet kernel will enable better resolution of several low-circulation, multi-scale secondary flow morphologies and whether new insights into the dynamics of arterial secondary flow structures can accordingly be gained. Supported by the National Science Foundation, Grant No. CBET-0828903 and GW Center for Biomimetics and Bioinspired Engineering (COBRE).
Institute of Scientific and Technical Information of China (English)
HAN Jian; JIANG Nan
2008-01-01
Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel.Mean and fluctuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction.At hypersonic speeds,the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode.Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in the frequency range of the second mode.Nonlinear interactions both of the second mode disturbance and the first mode disturbance axe demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.
Institute of Scientific and Technical Information of China (English)
LIU Qi-peng; FENG Quan-ke; XIONG Wei
2004-01-01
Fault diagnosis is confronted with two problems; how to "measure" the growth of a fault and how to predict the remaining useful lifetime of such a failing component or machine.This paper attempts to solve these two problems by proposing a model of fault prognosis using wavelet basis neural network.Gaussian radial basis functions and Mexican hat wavelet frames are used us scaling functions and wavelets,respectively.The centers of the basis functions are calculated using a dyadic expansion scheme and a k-means clustering algorithm.
A wavelet based approach to measure and manage contagion at different time scales
Berger, Theo
2015-10-01
We decompose financial return series of US stocks into different time scales with respect to different market regimes. First, we examine dependence structure of decomposed financial return series and analyze the impact of the current financial crisis on contagion and changing interdependencies as well as upper and lower tail dependence for different time scales. Second, we demonstrate to which extent the information of different time scales can be used in the context of portfolio management. As a result, minimizing the variance of short-run noise outperforms a portfolio that minimizes the variance of the return series.
Directory of Open Access Journals (Sweden)
Francisco de Assis Salviano de Sousa
2009-03-01
Full Text Available The variations of the rainfall in a region of the Mundaú river watershed, at state of Alagoas, Brazil, had been studied using the rainfall anomaly index (RAI and the Wavelet Analysis. This method involves transformation of a one-dimensional series in a time space and frequency, allowing determining the dominant scales of variability and its secular variations. The results had shown that the precipitation variability in the two regions is defined by located secular multi-scales in certain intervals of time. However, on inter-annual variability to the ENSO cycle and the decadal variability of the scales had influenced in the local pluviometric variability.
Relativistic Hydrodynamics with Wavelets
DeBuhr, Jackson; Anderson, Matthew; Neilsen, David; Hirschmann, Eric W
2015-01-01
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of astrophysical compact objects. Because of the many physical length scales present when simulating such mergers, these methods must be highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge throughout the computational domain across many temporal scales. While this has been historically accomplished with adaptive mesh refinement (AMR) based methods, alternatives based on wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. This work presents a new method for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulati...
The berkeley wavelet transform: a biologically inspired orthogonal wavelet transform.
Willmore, Ben; Prenger, Ryan J; Wu, Michael C-K; Gallant, Jack L
2008-06-01
We describe the Berkeley wavelet transform (BWT), a two-dimensional triadic wavelet transform. The BWT comprises four pairs of mother wavelets at four orientations. Within each pair, one wavelet has odd symmetry, and the other has even symmetry. By translation and scaling of the whole set (plus a single constant term), the wavelets form a complete, orthonormal basis in two dimensions. The BWT shares many characteristics with the receptive fields of neurons in mammalian primary visual cortex (V1). Like these receptive fields, BWT wavelets are localized in space, tuned in spatial frequency and orientation, and form a set that is approximately scale invariant. The wavelets also have spatial frequency and orientation bandwidths that are comparable with biological values. Although the classical Gabor wavelet model is a more accurate description of the receptive fields of individual V1 neurons, the BWT has some interesting advantages. It is a complete, orthonormal basis and is therefore inexpensive to compute, manipulate, and invert. These properties make the BWT useful in situations where computational power or experimental data are limited, such as estimation of the spatiotemporal receptive fields of neurons.
Complex Wavelet Transform-Based Face Recognition
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available Complex approximately analytic wavelets provide a local multiscale description of images with good directional selectivity and invariance to shifts and in-plane rotations. Similar to Gabor wavelets, they are insensitive to illumination variations and facial expression changes. The complex wavelet transform is, however, less redundant and computationally efficient. In this paper, we first construct complex approximately analytic wavelets in the single-tree context, which possess Gabor-like characteristics. We, then, investigate the recently developed dual-tree complex wavelet transform (DT-CWT and the single-tree complex wavelet transform (ST-CWT for the face recognition problem. Extensive experiments are carried out on standard databases. The resulting complex wavelet-based feature vectors are as discriminating as the Gabor wavelet-derived features and at the same time are of lower dimension when compared with that of Gabor wavelets. In all experiments, on two well-known databases, namely, FERET and ORL databases, complex wavelets equaled or surpassed the performance of Gabor wavelets in recognition rate when equal number of orientations and scales is used. These findings indicate that complex wavelets can provide a successful alternative to Gabor wavelets for face recognition.
Directional spin wavelets on the sphere
McEwen, Jason D; Büttner, Martin; Peiris, Hiranya V; Wiaux, Yves
2015-01-01
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the sphere that is able to probe the directional intensity of spin signals. Furthermore, directional spin scale-discretised wavelets support the exact synthesis of a signal on the sphere from its wavelet coefficients and satisfy excellent localisation and uncorrelation properties. Consequently, directional spin scale-discretised wavelets are likely to be of use in a wide range of applications and in particular for the analysis of the polarisation of the cosmic microwave background (CMB). We develop new algorithms to compute (scalar and spin) forward and inverse wavelet transforms exactly and efficiently for very large data-sets containing tens of millions of samples on the sphere. By leveraging a novel sampling theorem on the rotation group developed in a companion article, only hal...
Institute of Scientific and Technical Information of China (English)
Xiang Jiawei; He Zhengjia; Chen Xuefeng
2006-01-01
Based on B-spline wavelet on the interval (BSWI), two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based lements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.
Exact reconstruction with directional wavelets on the sphere
Wiaux, Y.; McEwen, J. D.; Vandergheynst, P.; Blanc, O.
2008-08-01
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.
SILC: a new Planck internal linear combination CMB temperature map using directional wavelets
Rogers, Keir K.; Peiris, Hiranya V.; Leistedt, Boris; McEwen, Jason D.; Pontzen, Andrew
2016-08-01
We present new clean maps of the cosmic microwave background (CMB) temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretized wavelets - scale-discretized, directional wavelet ILC or Scale-discretised, directional wavelet Internal Linear Combination (SILC). Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological background signal, SILC can additionally use morphological information in the foregrounds and CMB to better localize the cleaning algorithm. We test the method on Planck data and simulations, demonstrating consistency with existing component separation algorithms, and discuss how to optimize the use of morphological information by varying the number of directional wavelets as a function of spatial scale. We find that combining the use of directional and axisymmetric wavelets depending on scale could yield higher quality CMB temperature maps. Our results set the stage for the application of SILC to polarization anisotropies through an extension to spin wavelets.
THEORY AND APPLICATION OF WAVELET ANALYSIS INSTRUMENT LIBRARY
Institute of Scientific and Technical Information of China (English)
BO Lin; QIN Shuren; LIU Xiaofeng
2006-01-01
Some new theory and algorithms on wavelet analysis are proposed, including continuous wavelet transform (CWT), discrete wavelet transform (DWT), wavelet package transform (WPT),wavelet denosing and mother wavelet selection, etc. Using the component-based hierarchy mode, the platform for virtual instrument (Ⅵ) is constructed, and the functions such as data sampling, data analysis and data present, etc are provided. Subsequently, the wavelet analysis library is designed and developed. The library consists of expert system, experienced database, development platform and abundant wavelet analysis functional module, which together implement general and special wavelet analysis in the field of mechanical engineering, energy source, transportation and biomedicine, etc.Finally, the wavelet analysis virtual instrument library is applied to detect fault called engine knock.Experimental result indicates that the wavelet analysis virtual instrument library can efficiently solve the engineering problem such as detecting engine knock.
Institute of Scientific and Technical Information of China (English)
OU Xiaojuan; ZHOU Wei
2007-01-01
Global positioning system (GPS)common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients.Suppose that the GPS common-view observation data has the 1/f fractal characteristic,the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data.When 0＜H＜1,the 1/f fractal characteristic of the GPS clock difference data iS a Gaussian zero-mean and non-stationary stochastic process.Thus,the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients.Furthermore,the discrete clock difierence can be estimated.The single-channel and multi-channel common-view observation data were processed respectively.Comparisons were made between the results obtained and the Circular T data.Simulation results show that the algorithm discussed in this paper is both feasible and effective.
A Remark on the Mallat Pyramidal Algorithm of Wavelet Analysis
Institute of Scientific and Technical Information of China (English)
无
1997-01-01
The exact relationships between the lenthgs of scale sequences and wavelet sequences in the Mallat pyramidal algorithm for computing wavelet trans-form coefficients are obtained,and the maximum possible scale of arbitrary discrete signal is derived.
Wavelet-fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Wavelet-Based Frequency Response Function: Comparative Study of Input Excitation
Directory of Open Access Journals (Sweden)
K. Dziedziech
2014-01-01
Full Text Available Time-variant systems can be found in many areas of engineering. It is widely accepted that the classical Fourier-based methods are not suitable for the analysis and identification of such systems. The time-variant frequency response function—based on the continuous wavelet transform—is used in this paper for the analysis of time-variant systems. The focus is on the comparative study of various broadband input excitations. The performance of the method is tested using simulated data from a simple MDOF system and experimental data from a frame-like structure.
Representation of 1/f signal with wavelet bases
Institute of Scientific and Technical Information of China (English)
刘峰; 刘贵忠; 张茁生
2000-01-01
The representation of 1/f signal with wavelet transformation is explored. It is shown that a class of 1/f signal can be represented via wavelet synthetic formula and that a statistically self-similar property of signals may be characterized by the correlation functions of wavelet coefficients in the wavelet domain.
Spherical 3D Isotropic Wavelets
Lanusse, F; Starck, J -L
2011-01-01
Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis in is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the Fourier-Bessel decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. 2006. We also present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large...
A multiresolution analysis for tensor-product splines using weighted spline wavelets
Kapl, Mario; Jüttler, Bert
2009-09-01
We construct biorthogonal spline wavelets for periodic splines which extend the notion of "lazy" wavelets for linear functions (where the wavelets are simply a subset of the scaling functions) to splines of higher degree. We then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight function. Using the lifted wavelets we define a multiresolution analysis of tensor-product spline functions and apply it to image compression of black-and-white images. By performing-as a model problem-image compression with black-and-white images, we demonstrate that the use of a weight function allows to adapt the norm to the specific problem.
Wavelet subdivision methods gems for rendering curves and surfaces
Chui, Charles
2010-01-01
OVERVIEW Curve representation and drawing Free-form parametric curves From subdivision to basis functions Wavelet subdivision and editing Surface subdivision BASIS FUNCTIONS FOR CURVE REPRESENTATION Refinability and scaling functions Generation of smooth basis functions Cardinal B-splines Stable bases for integer-shift spaces Splines and polynomial reproduction CURVE SUBDIVISION SCHEMES Subdivision matrices and stencils B-spline subdivision schemes Closed curve rendering Open curve rendering BASIS FUNCTIONS GENERATED BY SUBDIVISION MATRICES Subdivision operators The up-sampling convolution ope
Institute of Scientific and Technical Information of China (English)
冯德山; 杨道学; 王珣
2016-01-01
应用迭代插值方法构造了插值小波尺度函数,并将该尺度函数的导数用于离散Maxwell方程组的空间微分,使用四阶Runge Kutta(four order Runge Kutta, RK4)算法计算时间导数,导出了插值小波尺度法的探地雷达(ground penetrating radar, GPR)正演公式,与常规的基于中心差分的时域有限差分算法(finite difference time domain, FDTD)相比,插值小波尺度算法提高了GPR波动方程的空间与时间离散精度。首先,采用具有解析解的层状模型,分别将FDTD算法及插值小波尺度法应用于层状模型正演,单道雷达数据与解析解拟合表明：相同的网格剖分方式,插值小波尺度法比FDTD具有更高的精度。然后,将辅助微分方程完全匹配层(auxiliary differential equation perfecting matched layer, ADE-PML)边界条件应用到插值小波尺度法GPR正演中,在均匀介质模型中对比了FDTD-CPML(坐标伸缩完全匹配层), FDTD-RK4ADE-PML、插值小波尺度RK4ADE-PML的反射误差,结果表明：插值小波尺度RK4ADE-PML吸收效果优于另外两种条件下的吸收边界。最后,应用加载UPML(各向异性完全匹配层)的FDTD和RK4ADE-PML的插值小波尺度法开展了二维GPR模型的正演,展示了RK4ADE-PML对倏逝波的良好吸收效果。%Ground penetrating radar (GPR) forward is one of the geophysical research directions. Through the forward of geological model, the database of radar model can be enriched and the characteristics of typical geological radar echo images can be understood, which in turn can guide the data interpretation of GPR measured profile, thereby improving the GPR data interpretation level. In this article, the interpolating wavelet scale function by using iterative interpolation method is presented, and the derivative of scale function is used in spatial differentiation of discrete Maxwell equations. The forward modeling formula of GPR based on the interpolation wavelet scale method is derived by
Directory of Open Access Journals (Sweden)
Kohei Arai
2013-08-01
Full Text Available Method for El Nino/Southern Oscillation: ENSO by means of wavelet based data compression with appropriate support length of base function is proposed. Through the experiments with observed southern oscillation index, the proposed method is validated. Also a method for determination of appropriate support length is proposed and is validated.
SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets
Rogers, Keir K; Leistedt, Boris; McEwen, Jason D; Pontzen, Andrew
2016-01-01
We present new clean maps of the CMB temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretised wavelets --- Scale-discretised, directional wavelet ILC or SILC. Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological background signal, SILC can additionally use morphological information in the foregrounds and CMB to better localise the cleaning algorithm. We test the method on Planck data and simulations, demonstrating consistency with existing component separation algorithms, and discuss how to optimise the use of morphological information by varying the number of directional wavelets as a function of spatial scale. We find that combining t...
Morlet Wavelets in Quantum Mechanics
Directory of Open Access Journals (Sweden)
John Ashmead
2012-11-01
Full Text Available Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or δ function decomposition. Morlet wavelets in particular are well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. But to take full advantage of Morlet wavelets we need to supply an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We construct both here.Quanta 2012; 1: 58–70.
Wavelet Based Image Denoising Technique
Directory of Open Access Journals (Sweden)
Sachin D Ruikar
2011-03-01
Full Text Available This paper proposes different approaches of wavelet based image denoising methods. The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. Wavelet algorithms are useful tool for signal processing such as image compression and denoising. Multi wavelets can be considered as an extension of scalar wavelets. The main aim is to modify the wavelet coefficients in the new basis, the noise can be removed from the data. In this paper, we extend the existing technique and providing a comprehensive evaluation of the proposed method. Results based on different noise, such as Gaussian, Poissonâ€™s, Salt and Pepper, and Speckle performed in this paper. A signal to noise ratio as a measure of the quality of denoising was preferred.
Liu, Xueyong; An, Haizhong; Huang, Shupei; Wen, Shaobo
2017-01-01
Aiming to investigate the evolution of mean and volatility spillovers between oil and stock markets in the time and frequency dimensions, we employed WTI crude oil prices, the S&P 500 (USA) index and the MICEX index (Russia) for the period Jan. 2003-Dec. 2014 as sample data. We first applied a wavelet-based GARCH-BEKK method to examine the spillover features in frequency dimension. To consider the evolution of spillover effects in time dimension at multiple-scales, we then divided the full sample period into three sub-periods, pre-crisis period, crisis period, and post-crisis period. The results indicate that spillover effects vary across wavelet scales in terms of strength and direction. By analysis the time-varying linkage, we found the different evolution features of spillover effects between the Oil-US stock market and Oil-Russia stock market. The spillover relationship between oil and US stock market is shifting to short-term while the spillover relationship between oil and Russia stock market is changing to all time scales. That result implies that the linkage between oil and US stock market is weakening in the long-term, and the linkage between oil and Russia stock market is getting close in all time scales. This may explain the phenomenon that the US stock index and the Russia stock index showed the opposite trend with the falling of oil price in the post-crisis period.
Denoising and robust nonlinear wavelet analysis
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-03-01
In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transform, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the 'S+WAVELETS' object-oriented toolkit for wavelet analysis.
Directory of Open Access Journals (Sweden)
Kohei Arai
2013-03-01
Full Text Available Human has a duty to preserve the nature. One of the examples is preserving the ornamental plant. Huge economic value of plant trading, escalating esthetical value of one space and medicine efficacy that contained in a plant are some positive values from this plant. However, only few people know about its medicine efficacy. Considering the easiness to obtain and the medicine efficacy, this plant should be an initial treatment of a simple disease or option towards chemical based medicines. In order to let people get acquaint, we need a system that can proper identify this plant. Therefore, we propose to build a system based on Redundant Discrete Wavelet Transformation (RDWT through its leaf. Since its character is translation invariant that able to produce some robust features to identify ornamental plant. This system was successfully resulting 95.83% of correct classification rate.
Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena
Lombardini, Richard; Acevedo, Ramiro; Kuczala, Alexander; Keys, Kerry P.; Goodrich, Carl P.; Johnson, Bruce R.
2016-01-01
An orthogonal wavelet basis is characterized by its approximation order, which relates to the ability of the basis to represent general smooth functions on a given scale. It is known, though perhaps not widely known, that there are ways of exceeding the approximation order, i.e., achieving higher-order error in the discretized wavelet transform and its inverse. The focus here is on the development of a practical formulation to accomplish this first for 1D smooth functions, then for 1D functions with discontinuities and then for multidimensional (here 2D) functions with discontinuities. It is shown how to transcend both the wavelet approximation order and the 2D Gibbs phenomenon in representing electromagnetic fields at discontinuous dielectric interfaces that do not simply follow the wavelet-basis grid.
Institute of Scientific and Technical Information of China (English)
孙文昌; 周性伟
2000-01-01
For the non-band-limited function ψ, a sufficient condition is presented under whichis a frame for L2(R). The stability of these frames is studied. For the wavelets frequently used in signal processing, some concrete results are given.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
For the non-band-limited function ψ, a sufficient condition is presented under which{√sjψ(sj·-kb)} is a frame for L2(R). The stability of these frames is studied. For the wavelets frequently used in signal processing, some concrete results are given.
Energy Technology Data Exchange (ETDEWEB)
Chauvin, C
2005-11-15
This thesis is devoted to the definition and the implementation of a multi-resolution method to determine the fundamental state of a system composed of nuclei and electrons. In this work, we are interested in the Density Functional Theory (DFT), which allows to express the Hamiltonian operator with the electronic density only, by a Coulomb potential and a non-linear potential. This operator acts on orbitals, which are solutions of the so-called Kohn-Sham equations. Their resolution needs to express orbitals and density on a set of functions owing both physical and numerical properties, as explained in the second chapter. One can hardly satisfy these two properties simultaneously, that is why we are interested in orthogonal and bi-orthogonal wavelets basis, whose properties of interpolation are presented in the third chapter. We present in the fourth chapter three dimensional solvers for the Coulomb's potential, using not only the preconditioning property of wavelets, but also a multigrid algorithm. Determining this potential allows us to solve the self-consistent Kohn-Sham equations, by an algorithm presented in chapter five. The originality of our method consists in the construction of the stiffness matrix, combining a Galerkin formulation and a collocation scheme. We analyse the approximation properties of this method in case of linear Hamiltonian, such as harmonic oscillator and hydrogen, and present convergence results of the DFT for small electrons. Finally we show how orbital compression reduces considerably the number of coefficients to keep, while preserving a good accuracy of the fundamental energy. (author)
Spherical 3D isotropic wavelets
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
Optimization of wavelet- and curvelet-based denoising algorithms by multivariate SURE and GCV
Mortezanejad, R.; Gholami, A.
2016-06-01
One of the most crucial challenges in seismic data processing is the reduction of noise in the data or improving the signal-to-noise ratio (SNR). Wavelet- and curvelet-based denoising algorithms have become popular to address random noise attenuation for seismic sections. Wavelet basis, thresholding function, and threshold value are three key factors of such algorithms, having a profound effect on the quality of the denoised section. Therefore, given a signal, it is necessary to optimize the denoising operator over these factors to achieve the best performance. In this paper a general denoising algorithm is developed as a multi-variant (variable) filter which performs in multi-scale transform domains (e.g. wavelet and curvelet). In the wavelet domain this general filter is a function of the type of wavelet, characterized by its smoothness, thresholding rule, and threshold value, while in the curvelet domain it is only a function of thresholding rule and threshold value. Also, two methods, Stein’s unbiased risk estimate (SURE) and generalized cross validation (GCV), evaluated using a Monte Carlo technique, are utilized to optimize the algorithm in both wavelet and curvelet domains for a given seismic signal. The best wavelet function is selected from a family of fractional B-spline wavelets. The optimum thresholding rule is selected from general thresholding functions which contain the most well known thresholding functions, and the threshold value is chosen from a set of possible values. The results obtained from numerical tests show high performance of the proposed method in both wavelet and curvelet domains in comparison to conventional methods when denoising seismic data.
Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames.
Pad, Pedram; Uhlmann, Virginie; Unser, Michael
2016-05-01
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones.
Entangled Husimi distribution and Complex Wavelet transformation
Hu, Li-yun
2009-01-01
Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.
Bakhouche, A.; Doghmane, N.
2008-06-01
In this paper, a new adaptive watermarking algorithm is proposed for still image based on the wavelet transform. The two major applications for watermarking are protecting copyrights and authenticating photographs. Our robust watermarking [3] [22] is used for copyright protection owners. The main reason for protecting copyrights is to prevent image piracy when the provider distributes the image on the Internet. Embed watermark in low frequency band is most resistant to JPEG compression, blurring, adding Gaussian noise, rescaling, rotation, cropping and sharpening but embedding in high frequency is most resistant to histogram equalization, intensity adjustment and gamma correction. In this paper, we extend the idea to embed the same watermark in two bands (LL and HH bands or LH and HL bands) at the second level of Discrete Wavelet Transform (DWT) decomposition. Our generalization includes all the four bands (LL, HL, LH, and HH) by modifying coefficients of the all four bands in order to compromise between acceptable imperceptibility level and attacks' resistance.
Natural frequencies and damping estimation based on continuous wavelet transform
Institute of Scientific and Technical Information of China (English)
DAI Yu; SUN He-yi; LI Hui-peng; TANG Wen-yan
2008-01-01
The continuous wavelet transform (CWT) based method was improved for estimating the natural fre-quencies and damping ratios of a structural system in this paper. The appropriate scale of CWT was selected by means of the least squares method to identify the systems with closely spaced modes. The important issues relat-ed to estimation accuracy such as mode separation and end effect, were also investigated. These issues were as-sociated with the parameter selection of wavelet function based on the fitting error of least squares. The efficien-cy of the method was confirmed by applying it to a simulated 3dof damped system with two close modes.
Søgaard, Andreas
For the LHC Run 2 and beyond, experiments are pushing both the energy and the intensity frontier so the need for robust and efficient pile-up mitigation tools becomes ever more pressing. Several methods exist, relying on uniformity of pile-up, local correlations of charged to neutral particles, and parton shower shapes, all in $y − \\phi$ space. Wavelets are presented as tools for pile-up removal, utilising their ability to encode position and frequency information simultaneously. This allows for the separation of individual hadron collision events by angular scale and thus for subtracting of soft, diffuse/wide-angle contributions while retaining the hard, small-angle components from the hard event. Wavelet methods may utilise the same assumptions as existing methods, the difference being the underlying, novel representation. Several wavelet methods are proposed and their effect studied in simple toy simulation under conditions relevant for the LHC Run 2. One full pile-up mitigation tool (‘wavelet analysis...
Wavelet transform of neural spike trains
Kim, Youngtae; Jung, Min Whan; Kim, Yunbok
2000-02-01
Wavelet transform of neural spike trains recorded with a tetrode in the rat primary somatosensory cortex is described. Continuous wavelet transform (CWT) of the spike train clearly shows singularities hidden in the noisy or chaotic spike trains. A multiresolution analysis of the spike train is also carried out using discrete wavelet transform (DWT) for denoising and approximating at different time scales. Results suggest that this multiscale shape analysis can be a useful tool for classifying the spike trains.
Generalized b-spline subdivision-surface wavelets and lossless compression
Energy Technology Data Exchange (ETDEWEB)
Bertram, M; Duchaineau, M A; Hamann, B; Joy, K I
1999-11-24
We present a new construction of wavelets on arbitrary two-manifold topology for geometry compression. The constructed wavelets generalize symmetric tensor product wavelets with associated B-spline scaling functions to irregular polygonal base mesh domains. The wavelets and scaling functions are tensor products almost everywhere, except in the neighborhoods of some extraordinary points (points of valence unequal four) in the base mesh that defines the topology. The compression of arbitrary polygonal meshes representing isosurfaces of scalar-valued trivariate functions is a primary application. The main contribution of this paper is the generalization of lifted symmetric tensor product B-spline wavelets to two-manifold geometries. Surfaces composed of B-spline patches can easily be converted to this scheme. We present a lossless compression method for geometries with or without associated functions like color, texture, or normals. The new wavelet transform is highly efficient and can represent surfaces at any level of resolution with high degrees of continuity, except at a finite number of extraordinary points in the base mesh. In the neighborhoods of these points detail can be added to the surface to approximate any degree of continuity.
Implementing wavelet transform with SAW elements
Institute of Scientific and Technical Information of China (English)
LU; Wenke(卢文科); ZHU; Changchun(朱长纯); LIU; Junhua(刘君华); LIU; Qinghong(刘清洪)
2003-01-01
In the design of the finger-overlap envelope according to the envelope of wavelet function, it is concluded that the pulse-response function of the interdigital transducer (IDT) for surface acoustic wave (SAW) is identical to the wavelet function. SAW type of the wavelet-transform element is manufactured. A new method of using two wavelet-transform elements to manufacture the reconstruction element of the wavelet transform is proposed. The sources of the element error are analyzed, and the methods for reducing the error are put forward. SAW type of the wavelet transformation element and its reconstruction element have the following three characteristics: (i) the implementing methods of the wavelet transform element and its reconstruction element are simple, and free of complicated mathematical algorithms of the wavelet transform; (ii) because one of SAW element is fast, the response velocities of SAW type of the wavelet transform element and its reconstruction element are also fast; (iii) the costs of the wavelet transform element and its reconstruction element are low, so the elements may be manufactured in a large quantity.
Scaling-violation phenomena and fractality in the human posture control systems
Thurner, S; Hanel, R; Ehrenberger, K
2000-01-01
By analyzing the movements of quiet standing persons by means of wavelet statistics, we observe multiple scaling regions in the underlying body dynamics. The use of the wavelet-variance function opens the possibility to relate scaling violations to different modes of posture control. We show that scaling behavior becomes close to perfect, when correctional movements are dominated by the vestibular system.
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Directory of Open Access Journals (Sweden)
Catarino Ana
2013-01-01
Full Text Available Abstract Background Autism Spectrum Conditions (ASC are a set of pervasive neurodevelopmental conditions characterized by a wide range of lifelong signs and symptoms. Recent explanatory models of autism propose abnormal neural connectivity and are supported by studies showing decreased interhemispheric coherence in individuals with ASC. The first aim of this study was to test the hypothesis of reduced interhemispheric coherence in ASC, and secondly to investigate specific effects of task performance on interhemispheric coherence in ASC. Methods We analyzed electroencephalography (EEG data from 15 participants with ASC and 15 typical controls, using Wavelet Transform Coherence (WTC to calculate interhemispheric coherence during face and chair matching tasks, for EEG frequencies from 5 to 40 Hz and during the first 400 ms post-stimulus onset. Results Results demonstrate a reduction of interhemispheric coherence in the ASC group, relative to the control group, in both tasks and for all electrode pairs studied. For both tasks, group differences were generally observed after around 150 ms and at frequencies lower than 13 Hz. Regarding within-group task comparisons, while the control group presented differences in interhemispheric coherence between faces and chairs tasks at various electrode pairs (FT7-FT8, TP7-TP8, P7-P8, such differences were only seen for one electrode pair in the ASC group (T7-T8. No significant differences in EEG power spectra were observed between groups. Conclusions Interhemispheric coherence is reduced in people with ASC, in a time and frequency specific manner, during visual perception and categorization of both social and inanimate stimuli and this reduction in coherence is widely dispersed across the brain. Results of within-group task comparisons may reflect an impairment in task differentiation in people with ASC relative to typically developing individuals. Overall, the results of this research support the value of WTC
Institute of Scientific and Technical Information of China (English)
王鲜芳; 朱晓霞; 吴瑞红; 郑延斌
2012-01-01
To solve the problem that some parameters are difficult to be measured on-line in the process of waste water disposal, a soft measurement modeling method is presented base on multi-scale wavelet least square support vector machine in this Paper. Mexican-hat wavelet function is used as the support vector kernel function, and further the Multi-scale Wavelet Least square Support Vector Regression (MW-LSSVR) algorithm is presented. Build an advanced model with above SVR and characteristics between BOD&COD, predicting BOD&COD of drainage that had been treated. Through using this method in practical sewage disposal process, the result shows that this modeling method has higher precision and faster learning speed of BOD model, can make accurate predictions, can replace online measuring instrument in some expensive, provide control operation basis to the sewage treatment plant workers, and has a certain practical value.%针对污水处理中某些生物参数难以在线测量的情况,本文提出了一种基于小波核的多尺度最小二乘小波支持向量机软测量建模方法.首先,选取墨西哥草帽小波函数作为最小二乘支持向量机的核函数,进而设计出多尺度小波最小二乘支持向量回归机(MW-LSSVR).然后利用该支持向量机和出水水质参数特性建立混合软测量模型,实现对出水BOD浓度、COD浓度在线预测.通过在实际污水处理过程的应用,结果表明本建模方法具有较高的预测精度和较快的模型学习速度,能对BOD的做出准确的预测,一定程度上可以替代某些昂贵的在线测量仪表,给污水处理厂工作人员提供了控制操作依据,具有一定的实际应用价值.
Fault Identification of Gearbox Degradation with Optimized Wavelet Neural Network
Directory of Open Access Journals (Sweden)
Hanxin Chen
2013-01-01
Full Text Available A novel intelligent method based on wavelet neural network (WNN was proposed to identify the gear crack degradation in gearbox in this paper. The wavelet packet analysis (WPA is applied to extract the fault feature of the vibration signal, which is collected by two acceleration sensors mounted on the gearbox along the vertical and horizontal direction. The back-propagation (BP algorithm is studied and applied to optimize the scale and translation parameters of the Morlet wavelet function, the weight coefficients, threshold values in WNN structure. Four different gear crack damage levels under three different loads and three various motor speeds are presented to obtain the different gear fault modes and gear crack degradation in the experimental system. The results show the feasibility and effectiveness of the proposed method by the identification and classification of the four gear modes and degradation.
Pautomatic Sea Target Detection Based on Wavelet Transform
Institute of Scientific and Technical Information of China (English)
PEI Li-li; LUO Hai-bo
2009-01-01
An effective automatic target detection algorithm based on wavelet transform, which takes advantage of the localization and the orientation of wavelet analysis, is proposed. The algorithm detects the target in the vertical component of the wavelet transformation of the image. After mutual energy combination and sea clutter suppression through spatial weighting and thresholding, the target is located through maximum energy determination and its size is indicated through similarity measurement function of two overlapping windows. Experiment results show that the target can be detected by the algorithm in a single image frame and the better efficiency can be obtained also under the complicated backgrounds of existing the disturbances of cloud layer and fish scale light.
Application of wavelet transform in runoff sequence analysis
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
A wavelet transform is applied to runoff analysis to obtain the composition of the runoff sequence and to forecast future runoff. An observed runoff sequence is firstly decomposed and reconstructed by wavelet transform and its expanding tendency is derived. Then, the runoff sequence is forecasted by the back propagation artificial neural networks (BPANN) and by a wavelet transform combined with BPANN. The earlier researches seldom involve the problem of how to choose wavelet function, which is important and cannot be ignored when the wavelet transform is used. With application of the developed approach to the analysis of runoff sequence, several kinds of wavelet functions have been tested.
WAVELET KERNEL SUPPORT VECTOR MACHINES FOR SPARSE APPROXIMATION
Institute of Scientific and Technical Information of China (English)
Tong Yubing; Yang Dongkai; Zhang Qishan
2006-01-01
Wavelet, a powerful tool for signal processing, can be used to approximate the target function. For enhancing the sparse property of wavelet approximation, a new algorithm was proposed by using wavelet kernel Support Vector Machines (SVM), which can converge to minimum error with better sparsity. Here, wavelet functions would be firstly used to construct the admitted kernel for SVM according to Mercy theory; then new SVM with this kernel can be used to approximate the target funciton with better sparsity than wavelet approxiamtion itself. The results obtained by our simulation experiment show the feasibility and validity of wavelet kernel support vector machines.
Wavelet and wavelet packet compression of electrocardiograms.
Hilton, M L
1997-05-01
Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECG's are clinically useful.
Vaudor, Lise; Piegay, Herve; Wawrzyniak, Vincent; Spitoni, Marie
2016-04-01
The form and functioning of a geomorphic system result from processes operating at various spatial and temporal scales. Longitudinal channel characteristics thus exhibit complex patterns which vary according to the scale of study, might be periodic or segmented, and are generally blurred by noise. Describing the intricate, multiscale structure of such signals, and identifying at which scales the patterns are dominant and over which sub-reach, could help determine at which scales they should be investigated, and provide insights into the main controlling factors. Wavelet transforms aim at describing data at multiple scales (either in time or space), and are now exploited in geophysics for the analysis of nonstationary series of data. They provide a consistent, non-arbitrary, and multiscale description of a signal's variations and help explore potential causalities. Nevertheless, their use in fluvial geomorphology, notably to study longitudinal patterns, is hindered by a lack of user-friendly tools to help understand, implement, and interpret them. We have developed a free application, The Wavelet ToolKat, designed to facilitate the use of wavelet transforms on temporal or spatial series. We illustrate its usefulness describing longitudinal channel curvature and slope of three freely meandering rivers in the Amazon basin (the Purus, Juruá and Madre de Dios rivers), using topographic data generated from NASA's Shuttle Radar Topography Mission (SRTM) in 2000. Three types of wavelet transforms are used, with different purposes. Continuous Wavelet Transforms are used to identify in a non-arbitrary way the dominant scales and locations at which channel curvature and slope vary. Cross-wavelet transforms, and wavelet coherence and phase are used to identify scales and locations exhibiting significant channel curvature and slope co-variations. Maximal Overlap Discrete Wavelet Transforms decompose data into their variations at a series of scales and are used to provide
National Research Council Canada - National Science Library
Elsanabary, Mohamed Helmy; Gan, Thian Yew; Mwale, Davison
2014-01-01
This study employed the wavelet empirical orthogonal function ( WEOF ) analysis to analyse the nonstationary variability of rainfall in Ethiopia and global sea surface temperature ( SST ) for 1900–1998...
Physical wavelets and their sources: real physics in complex spacetime
Energy Technology Data Exchange (ETDEWEB)
Kaiser, Gerald [Center for Signals and Waves, 1921 Kings Road, Glen Allen, VA 23059 (United States)
2003-08-01
A thorough review of acoustic and electromagnetic wavelets is given, including a first account of recent progress in understanding their sources. These physical wavelets, introduced in 1994, are families of 'small' solutions of the wave and Maxwell equations generated from a single member by group operations including translations, Lorentz transformations, and scaling. They are parametrized by complex spacetime points z = x - iy, where x gives the centre of their region of origin and y gives the extension and orientation of this region in spacetime. They are thus pulsed beams whose origin, direction and focus are all governed by z and which give, by superposition, 'wavelet representations' of acoustic and electromagnetic waves. Recently this idea has been developed substantially by the rigorous understanding of the source distributions required to launch and absorb the wavelets, defined as extended delta functions. The unexpected simplicity and complex structure of the sources in the Fourier domain suggests their potential use in the construction of fast algorithms for the analysis and synthesis of acoustic and electromagnetic waves. The review begins with a brief account of the physical wavelets associated with massive (Klein-Gordon and Dirac) fields, which are relativistic coherent states. (topical review)
On the Differentiation Matrix for Daubechies-Based Wavelets on an Interval
1993-12-01
projection matrix D. If we let .’ denote the vector of the scaling function coefficients sk, for k = 0, ... , d - 1, then 1) maps from the scaling...80, NASA CR-191557. [8] Y. Meyer, "Ondelettes sur I’nteralle", Revista Matematica Iberoamericana 7, 1992, pp 115-133. [9] G. Strang, "Wavelets and
Wavelet Transform and its Application to CBIR
Directory of Open Access Journals (Sweden)
Mr. V. K. Magar
2013-07-01
Full Text Available Wavelet filter bank, based on the lifting scheme framework. The lifting scheme there are two linear filters denoted Adapt a multidimensional P (prediction and U (update are defined as Neville filters of order N and Ñ, respectively. We are applying the Haar wavelet transform {&} wavelet decomposition of the image then we enter the Neville filter order {&} optimization the Neville filter. Lifting scheme on quincunx grids perform wavelet decomposition of 2-D signal (image and corresponding reconstruction tools for image as well as a function for computation of moments. The wavelet schemes rely on the lifting scheme use the splitting of rectangular grid into quincunx grid. The proposed methods apply the genetic algorithm wide range of problems, from optimization problem inductive concept learning, scheduling, and layout problem. In this project we did comparison between separable wavelet and nonseparable wavelet. We calculate the retrieval rate of separable and nonseparable.Retrieval rate is more means maximum features can be extracted. This method is applied to content-based image retrieval (CBIR an image signature is derived from this new adaptive non-separable wavelet transform. In CBIR we are used Texture feature for retrieving the image. We used 260 image databases. There are 5 classes. Images are scanned through its particular characteristics now some degree of freedom is given to the algorithm to find the image from its weight so term non-separable lifting is used and through the wavelet transformation Image primal and dual wavelet is taken into consideration for the application
Rai, H. M.; Trivedi, A.; Chatterjee, K.; Shukla, S.
2014-01-01
This paper employed the Daubechies wavelet transform (WT) for R-peak detection and radial basis function neural network (RBFNN) to classify the electrocardiogram (ECG) signals. Five types of ECG beats: normal beat, paced beat, left bundle branch block (LBBB) beat, right bundle branch block (RBBB) beat and premature ventricular contraction (PVC) were classified. 500 QRS complexes were arbitrarily extracted from 26 records in Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database, which are available on Physionet website. Each and every QRS complex was represented by 21 points from p1 to p21 and these QRS complexes of each record were categorized according to types of beats. The system performance was computed using four types of parameter evaluation metrics: sensitivity, positive predictivity, specificity and classification error rate. The experimental result shows that the average values of sensitivity, positive predictivity, specificity and classification error rate are 99.8%, 99.60%, 99.90% and 0.12%, respectively with RBFNN classifier. The overall accuracy achieved for back propagation neural network (BPNN), multilayered perceptron (MLP), support vector machine (SVM) and RBFNN classifiers are 97.2%, 98.8%, 99% and 99.6%, respectively. The accuracy levels and processing time of RBFNN is higher than or comparable with BPNN, MLP and SVM classifiers.
The Discrete, Orthogonal Wavelet Transform, A Protective Approach.
1995-09-01
completely determined by the collection of functions onto which it projects. The wavelet transform projects onto a set of functions which satisfy a...simple linear relationship between different levels of dilation. The properties of the wavelet transform are determined by the coefficients of this linear...relationship. This thesis examines the connections between the wavelet transform properties and the linear relationship coefficients. (AN)
Scale-Free Brain Functional Networks
Eguíluz, Victor M.; Chialvo, Dante R.; Cecchi, Guillermo A.; Baliki, Marwan; Apkarian, A. Vania
2005-01-01
Functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites. Analysis of the resulting networks in different tasks shows that (a)the distribution of functional connections, and the probability of finding a link versus distance are both scale-free, (b)the characteristic path length is small and comparable with those of equivalent random networks, and (c)the clustering coefficient is orders of magnitude larger than those of equivalent random networks. All these properties, typical of scale-free small-world networks, reflect important functional information about brain states.
Chevrot, Sébastien; Martin, Roland; Komatitsch, Dimitri
2012-12-01
Wavelets are extremely powerful to compress the information contained in finite-frequency sensitivity kernels and tomographic models. This interesting property opens the perspective of reducing the size of global tomographic inverse problems by one to two orders of magnitude. However, introducing wavelets into global tomographic problems raises the problem of computing fast wavelet transforms in spherical geometry. Using a Cartesian cubed sphere mapping, which grids the surface of the sphere with six blocks or 'chunks', we define a new algorithm to implement fast wavelet transforms with the lifting scheme. This algorithm is simple and flexible, and can handle any family of discrete orthogonal or bi-orthogonal wavelets. Since wavelet coefficients are local in space and scale, aliasing effects resulting from a parametrization with global functions such as spherical harmonics are avoided. The sparsity of tomographic models expanded in wavelet bases implies that it is possible to exploit the power of compressed sensing to retrieve Earth's internal structures optimally. This approach involves minimizing a combination of a ℓ2 norm for data residuals and a ℓ1 norm for model wavelet coefficients, which can be achieved through relatively minor modifications of the algorithms that are currently used to solve the tomographic inverse problem.
Energy Technology Data Exchange (ETDEWEB)
Kingsbury, J Ng and N G [Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)
2004-02-06
This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar
Vibration analysis of composite pipes using the finite element method with B-spline wavelets
Energy Technology Data Exchange (ETDEWEB)
Oke, Wasiu A.; Khulief, Yehia A. [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia)
2016-02-15
A finite element formulation using the B-spline wavelets on the interval is developed for modeling the free vibrations of composite pipes. The composite FRP pipe element is treated as a beam element. The finite pipe element is constructed in the wavelet space and then transformed to the physical space. Detailed expressions of the mass and stiffness matrices are derived for the composite pipe using the Bspline scaling and wavelet functions. Both Euler-Bernoulli and Timoshenko beam theories are considered. The generalized eigenvalue problem is formulated and solved to obtain the modal characteristics of the composite pipe. The developed wavelet-based finite element discretization scheme utilizes significantly less elements compared to the conventional finite element method for modeling composite pipes. Numerical solutions are obtained to demonstrate the accuracy of the developed element, which is verified by comparisons with some available results in the literature.
Directory of Open Access Journals (Sweden)
P. C. Stoy
2013-02-01
Full Text Available Earth system processes exhibit complex patterns across time, as do the models that seek to replicate these processes. Model output may or may not be significantly related to observations at different times and on different frequencies. Conventional model diagnostics provide an aggregate view of model-data agreement, but usually do not identify the time and frequency patterns of model misfit, leaving unclear the steps required to improve model response to environmental drivers that vary on characteristic frequencies. Wavelet coherence can quantify the times and frequencies at which models and measurements are significantly different. We applied wavelet coherence to interpret the predictions of twenty ecosystem models from the North American Carbon Program (NACP Site-Level Interim Synthesis when confronted with eddy covariance-measured net ecosystem exchange (NEE from ten ecosystems with multiple years of available data. Models were grouped into classes with similar approaches for incorporating phenology, the calculation of NEE, and the inclusion of foliar nitrogen (N. Models with prescribed, rather than prognostic, phenology often fit NEE observations better on annual to interannual time scales in grassland, wetland and agricultural ecosystems. Models that calculate NEE as net primary productivity (NPP minus heterotrophic respiration (HR rather than gross ecosystem productivity (GPP minus ecosystem respiration (ER fit better on annual time scales in grassland and wetland ecosystems, but models that calculate NEE as GPP – ER were superior on monthly to seasonal time scales in two coniferous forests. Models that incorporated foliar nitrogen (N data were successful at capturing NEE variability on interannual (multiple year time scales at Howland Forest, Maine. Combined with previous findings, our results suggest that the mechanisms driving daily and annual NEE variability tend to be correctly simulated, but the magnitude of these fluxes is often
Directory of Open Access Journals (Sweden)
Abdallah Bengueddoudj
2017-05-01
Full Text Available In this paper, we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform (2D-SMCWT. The fusion of the detail 2D-SMCWT coefficients is performed via a Bayesian Maximum a Posteriori (MAP approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients. For the approximation coefficients, a new fusion rule based on the Principal Component Analysis (PCA is applied. We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method. The obtained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics. Robustness of the proposed method is further tested against different types of noise. The plots of fusion metrics establish the accuracy of the proposed fusion method.
Optical Wavelet Signals Processing and Multiplexing
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2005-12-01
We present compact integrable architectures to perform the discrete wavelet transform (DWT) and the wavelet packet (WP) decomposition of an optical digital signal, and we show that the combined use of planar lightwave circuits (PLC) technology and multiresolution analysis (MRA) can add flexibility to current multiple access optical networks. We furnish the design guidelines to synthesize wavelet filters as two-port lattice-form planar devices, and we give some examples of optical signal denoising and compression/decompression techniques in the wavelet domain. Finally, we present a fully optical wavelet packet division multiplexing (WPDM) scheme where data signals are waveform-coded onto wavelet atom functions for transmission, and numerically evaluate its performances.
Wavelet transform analysis of transient signals: the seismogram and the electrocardiogram
Energy Technology Data Exchange (ETDEWEB)
Anant, K.S.
1997-06-01
In this dissertation I quantitatively demonstrate how the wavelet transform can be an effective mathematical tool for the analysis of transient signals. The two key signal processing applications of the wavelet transform, namely feature identification and representation (i.e., compression), are shown by solving important problems involving the seismogram and the electrocardiogram. The seismic feature identification problem involved locating in time the P and S phase arrivals. Locating these arrivals accurately (particularly the S phase) has been a constant issue in seismic signal processing. In Chapter 3, I show that the wavelet transform can be used to locate both the P as well as the S phase using only information from single station three-component seismograms. This is accomplished by using the basis function (wave-let) of the wavelet transform as a matching filter and by processing information across scales of the wavelet domain decomposition. The `pick` time results are quite promising as compared to analyst picks. The representation application involved the compression of the electrocardiogram which is a recording of the electrical activity of the heart. Compression of the electrocardiogram is an important problem in biomedical signal processing due to transmission and storage limitations. In Chapter 4, I develop an electrocardiogram compression method that applies vector quantization to the wavelet transform coefficients. The best compression results were obtained by using orthogonal wavelets, due to their ability to represent a signal efficiently. Throughout this thesis the importance of choosing wavelets based on the problem at hand is stressed. In Chapter 5, I introduce a wavelet design method that uses linear prediction in order to design wavelets that are geared to the signal or feature being analyzed. The use of these designed wavelets in a test feature identification application led to positive results. The methods developed in this thesis; the
Wavelets centered on a knot sequence: piecewise polynomial wavelets on a quasi-crystal lattice
Atkinson, Bruce W; Geronimo, Jeffrey S; Hardin, Douglas P
2011-01-01
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. As an application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\\tau$-integers where $\\tau$ is the golden-mean. The resulting spaces then generate a multiresolution analysis of $L^2(\\mathbf{R})$ with scaling factor $\\tau$.
Multi-scale coding of genomic information: From DNA sequence to genome structure and function
Energy Technology Data Exchange (ETDEWEB)
Arneodo, Alain, E-mail: alain.arneodo@ens-lyon.f [Universite de Lyon, F-69000 Lyon (France); Laboratoire Joliot-Curie and Laboratoire de Physique, CNRS, Ecole Normale Superieure de Lyon, F-69007 Lyon (France); Vaillant, Cedric, E-mail: cedric.vaillant@ens-lyon.f [Universite de Lyon, F-69000 Lyon (France); Laboratoire Joliot-Curie and Laboratoire de Physique, CNRS, Ecole Normale Superieure de Lyon, F-69007 Lyon (France); Audit, Benjamin, E-mail: benjamin.audit@ens-lyon.f [Universite de Lyon, F-69000 Lyon (France); Laboratoire Joliot-Curie and Laboratoire de Physique, CNRS, Ecole Normale Superieure de Lyon, F-69007 Lyon (France); Argoul, Francoise, E-mail: francoise.argoul@ens-lyon.f [Universite de Lyon, F-69000 Lyon (France); Laboratoire Joliot-Curie and Laboratoire de Physique, CNRS, Ecole Normale Superieure de Lyon, F-69007 Lyon (France); D' Aubenton-Carafa, Yves, E-mail: daubenton@cgm.cnrs-gif.f [Centre de Genetique Moleculaire, CNRS, Allee de la Terrasse, 91198 Gif-sur-Yvette (France); Thermes, Claude, E-mail: claude.thermes@cgm.cnrs-gif.f [Centre de Genetique Moleculaire, CNRS, Allee de la Terrasse, 91198 Gif-sur-Yvette (France)
2011-02-15
Understanding how chromatin is spatially and dynamically organized in the nucleus of eukaryotic cells and how this affects genome functions is one of the main challenges of cell biology. Since the different orders of packaging in the hierarchical organization of DNA condition the accessibility of DNA sequence elements to trans-acting factors that control the transcription and replication processes, there is actually a wealth of structural and dynamical information to learn in the primary DNA sequence. In this review, we show that when using concepts, methodologies, numerical and experimental techniques coming from statistical mechanics and nonlinear physics combined with wavelet-based multi-scale signal processing, we are able to decipher the multi-scale sequence encoding of chromatin condensation-decondensation mechanisms that play a fundamental role in regulating many molecular processes involved in nuclear functions.
Patel, Ameera X; Bullmore, Edward T
2016-11-15
Connectome mapping using techniques such as functional magnetic resonance imaging (fMRI) has become a focus of systems neuroscience. There remain many statistical challenges in analysis of functional connectivity and network architecture from BOLD fMRI multivariate time series. One key statistic for any time series is its (effective) degrees of freedom, df, which will generally be less than the number of time points (or nominal degrees of freedom, N). If we know the df, then probabilistic inference on other fMRI statistics, such as the correlation between two voxel or regional time series, is feasible. However, we currently lack good estimators of df in fMRI time series, especially after the degrees of freedom of the "raw" data have been modified substantially by denoising algorithms for head movement. Here, we used a wavelet-based method both to denoise fMRI data and to estimate the (effective) df of the denoised process. We show that seed voxel correlations corrected for locally variable df could be tested for false positive connectivity with better control over Type I error and greater specificity of anatomical mapping than probabilistic connectivity maps using the nominal degrees of freedom. We also show that wavelet despiked statistics can be used to estimate all pairwise correlations between a set of regional nodes, assign a P value to each edge, and then iteratively add edges to the graph in order of increasing P. These probabilistically thresholded graphs are likely more robust to regional variation in head movement effects than comparable graphs constructed by thresholding correlations. Finally, we show that time-windowed estimates of df can be used for probabilistic connectivity testing or dynamic network analysis so that apparent changes in the functional connectome are appropriately corrected for the effects of transient noise bursts. Wavelet despiking is both an algorithm for fMRI time series denoising and an estimator of the (effective) df of denoised
Perceptually Lossless Wavelet Compression
Watson, Andrew B.; Yang, Gloria Y.; Solomon, Joshua A.; Villasenor, John
1996-01-01
The Discrete Wavelet Transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter, which we call DWT uniform quantization noise. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2(exp -1), where r is display visual resolution in pixels/degree, and L is the wavelet level. Amplitude thresholds increase rapidly with spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from low-pass to horizontal/vertical to diagonal. We propose a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a 'perceptually lossless' quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.
Correlation functions in theories with Lifshitz scaling
Keranen, Ville; Szepietowski, Phillip; Thorlacius, Larus
2016-01-01
The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time correlation functions of scaling operators in the generalised quantum Lifshitz model are given by a d-dimensional higher-derivative conformal field theory. Autocorrelation functions in the generalised quantum Lifshitz model in any number of dimensions can on the other hand be expressed in terms of autocorrelation functions of a two-dimensional conformal field theory. This also holds for autocorrelation functions in a strongly coupled Lifshitz field theory with a holographic dual of Einstein-Maxwell-dilaton type. The map to a two-dimensional conformal field theory extends to autocorrelation functions in thermal states and out- of-equilbrium states preserving symmetry under spatial translations and rotations in both types of Lifshitz models. Furthermore, the spectrum of quasinorma...
Wavelet view on renormalization group
Altaisky, M V
2016-01-01
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier described in {\\em Phys.Rev.D} 81(2010)125003, 88(2013)025015, is finite by construction. The space of scale-dependent functions $\\{ \\phi_a(x) \\}$ is more relevant to physical reality than the space of square-integrable functions $\\mathrm{L}^2(R^d)$, because, due to the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than point. The effective action $\\Gamma_{(A)}$ of our theory turns to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet -- an "aperture function" of a measuring device used to produce the snapshot of a field $\\phi$ at the point $x$ with the resolution $a$. The standard RG results for $\\phi^4$ model are reproduced.
Irregular wavelet frames on L2(Rn)
Institute of Scientific and Technical Information of China (English)
YANG Deyun; ZHOU Xingwei
2005-01-01
In this paper, we present the conditions on dilation parameter {sj }j that ensure a discrete irregular wavelet system {Snj/2ψ(sj·-bk)}j∈(Z),k∈(Z)n to be a frame on L2(Rn),and for the wavelet frame we consider the perturbations of translation parameter b and frame function ψ respectively.
OPTICAL REALIZATION OF WAVELET TRANSFORM WITH A SINGLE LENS
Institute of Scientific and Technical Information of China (English)
王取泉; 熊贵光; 李承芳; 张苏淮; 王琳
2001-01-01
Two optical set-ups to implement wavelet transform with a single lens have been proposed, in which the wavelet filter was placed in front of the imaging lens or on the frequency plane. The general formula of the complex field distribution of the output plane has been deduced. The analysing wavelet functions of the band-pass wavelet filters with double and circular slits have been discussed.
RESEARCH OF WAVELET TRANSFORM INSTRUMENT SYSTEM FOR SIGNAL ANALYSIS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
After brief describing the principle of wavelet transform (WT) of signals, a new signals analysis system based on wavelet transform is introduced. The design and development of the instrument of wavelet transform are described. A number of practical uses of this system demonstrate that wavelet transform system is specially functional in identifying and processing impulse, singular and nonsmooth signals,so that it should be evaluated the most advanced signal analyzing system.
Constructions of Vector-Valued Filters and Vector-Valued Wavelets
Directory of Open Access Journals (Sweden)
Jianxun He
2012-01-01
Full Text Available Let a =(a1,a2,…,am∈ℂm be an m-dimensional vector. Then, it can be identified with an m×m circulant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002, we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.
An improved adaptive wavelet shrinkage for ultrasound despeckling
Indian Academy of Sciences (India)
P Nirmala Devi; R Asokan
2014-08-01
Ultrasound imaging is the most widely used medical diagnostic technique for clinical decision making, due to its ability to make real time imaging for moving structures, low cost and safety. However, its usefulness is degraded by the presence of signal dependent speckle noise. Several wavelet-based denoising schemes have been reported in the literature for the removal of speckle noise. This study proposes a new and improved adaptive wavelet shrinkage in the translational invariant domain. It exploits the knowledge of the correlation of the wavelet coefficients within and across the resolution scales. A preliminary coefficient classification representing useful image information and noise is performed with a novel inter-scale dependency measure. The spatial context adaptation of the wavelet coefficients within a subband is achieved by a local spatial adaptivity indicator, determined by using a truncation threshold. A weighted signal variance is estimated based on this measure and used in the determination of a subband adaptive threshold. The proposed thresholding function aims to reduce the fixed bias of the soft thresholding approach. Experiments conducted with the proposed filter are compared with the existing filtering algorithms in terms of Peak-Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Structural Similarity IndexMeasure (SSIM), Equivalent Number of Looks (ENL) and Edge Preservation Index (EPI). A comparison of the results shows that the proposed filter achieves an improvement in terms of quantitative measures and in terms of visual quality of the images.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new me- thod of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
郑建斌; 张红权; 高鸿
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new method of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Energy Technology Data Exchange (ETDEWEB)
Zahra, Noor e; Sevindir, Huliya A.; Aslan, Zafar; Siddiqi, A. H. [Sharda University, SET, Department of Electronics and Communication, Knowledge Park 3rd, Gr. Noida (India); University of Kocaeli, Department of Mathematics, 41380 Kocaeli (Turkey); Istanbul Aydin University, Department of Computer Engineering, 34295 Istanbul (Turkey); Sharda University, SET, Department of Mathematics, 32-34 Knowledge Park 3rd, Greater Noida (India)
2012-07-17
The aim of this study is to provide emerging applications of wavelet methods to medical signals and images, such as electrocardiogram, electroencephalogram, functional magnetic resonance imaging, computer tomography, X-ray and mammography. Interpretation of these signals and images are quite important. Nowadays wavelet methods have a significant impact on the science of medical imaging and the diagnosis of disease and screening protocols. Based on our initial investigations, future directions include neurosurgical planning and improved assessment of risk for individual patients, improved assessment and strategies for the treatment of chronic pain, improved seizure localization, and improved understanding of the physiology of neurological disorders. We look ahead to these and other emerging applications as the benefits of this technology become incorporated into current and future patient care. In this chapter by applying Fourier transform and wavelet transform, analysis and denoising of one of the important biomedical signals like EEG is carried out. The presence of rhythm, template matching, and correlation is discussed by various method. Energy of EEG signal is used to detect seizure in an epileptic patient. We have also performed denoising of EEG signals by SWT.
LOWER BOUNDS FOR FINITE WAVELET AND GABOR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Ole Christensen; Alexander M. Lindner
2001-01-01
Given ψ∈L2(R) and a finite sequence {(ar,λy)}τ∈r R+ XR consitiag of distinct points, the correspond wavelet system is the set of functions { )}τ∈r·We prove that for a dense set of functions ψ∈ ing L2(R) the wavelet system corresponding to any choice of {(aγ,λγ)}τ∈r is linearly independent, and we derive explicite estimates for the corresponding lower (frame) bounds. In particular, this puts restrictions on the choice of a scaling function in the theory for multiresolution analysis. We also obtain estimates for the lower bound for Gabor systems {e g(x－λr) }τ∈r for functions g in a dense subset of L2(R).
Campana, S; Panzera, M R; Tagliaferri, G; Campana, Sergio; Lazzati, Davide; Panzera, Maria Rosa; Tagliaferri, Gianpiero
1999-01-01
The wavelet detection algorithm (WDA) described in the accompanying paper by Lazzati et al. is made suited for a fast and efficient analysis of images taken with the High Resolution Imager (HRI) instrument on board the ROSAT satellite. An extensive testing is carried out on the detection pipeline: HRI fields with different exposure times are simulated and analysed in the same fashion as the real data. Positions are recovered with few arcsecond errors, whereas fluxes are within a factor of two from their input values in more than 90% of the cases in the deepest images. At variance with the ``sliding-box'' detection algorithms, the WDA provides also a reliable description of the source extension, allowing for a complete search of e.g. supernova remnant or cluster of galaxies in the HRI fields. A completeness analysis on simulated fields shows that for the deepest exposures considered (~120 ks) a limiting flux of the algorithm on real HRI fields selected for their crowding and/or presence of extended or bright s...
Characterization of nonlinear ultrasonic effects using the dynamic wavelet fingerprint technique
Lv, Hongtao; Jiao, Jingpin; Meng, Xiangji; He, Cunfu; Wu, Bin
2017-02-01
An improved dynamic wavelet fingerprint (DWFP) technique was developed to characterize nonlinear ultrasonic effects. The white area in the fingerprint was used as the nonlinear feature to quantify the degree of damage. The performance of different wavelet functions, the effect of scale factor and white subslice ratio on the nonlinear feature extraction were investigated, and the optimal wavelet function, scale factor and white subslice ratio for maximum damage sensitivity were determined. The proposed DWFP method was applied to the analysis of experimental signals obtained from nonlinear ultrasonic harmonic and wave-mixing experiments. It was demonstrated that the proposed DWFP method can be used to effectively extract nonlinear features from the experimental signals. Moreover, the proposed nonlinear fingerprint coefficient was sensitive to micro cracks and correlated well with the degree of damage.
A robust method for estimating the multifractal wavelet spectrum in geophysical images
Nicolis, Orietta; Porro, Francesco
2013-04-01
The description of natural phenomena by an analysis of the statistical scaling laws is always a popular topic. Many studies aim to identify the fractal feature by estimating the self-similar parameter H, considered constant at different scales of observation. However, most real world data exhibit a multifractal structure, that is, the self-similarity parameter varies erratically with time. The multifractal spectrum provide an efficient tool for characterizing the scaling and singularity structures in signals and images, proving useful in numerous applications such as fluid dynamics, internet network traffic, finance, image analysis, texture synthesis, meteorology, and geophysics. In recent years, the multifractal formalism has been implemented with wavelets. The advantages of using the wavelet-based multifractal spectrum are: the availability of fast algorithms for wavelet transform, the locality of wavelet representations in both time and scale, and intrinsic dyadic self-similarity of basis functions. In this work we propose a robust Wavelet-based Multifractal Spectrum Estimator for the analysis of geophysical signals and satellite images. Finally, a simulation study and examples are considered to test the performances of the estimator.
Functional Materials Produced On An Industrial Scale
Directory of Open Access Journals (Sweden)
Barska Justyna
2015-08-01
Full Text Available The article presents a wide range of applications of functional materials and a scale of their current industrial production. These are the materials which have specific characteristics, thanks to which they became virtually indispensable in certain constructional solutions. Their basic characteristics, properties, methods of production and use as smart materials were described.
Wavelet Representation of Contour Sets
Energy Technology Data Exchange (ETDEWEB)
Bertram, M; Laney, D E; Duchaineau, M A; Hansen, C D; Hamann, B; Joy, K I
2001-07-19
We present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contoum and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields.
Low-power Analog VLSI Implementation of Wavelet Transform
Institute of Scientific and Technical Information of China (English)
ZHANG Jiang-hong
2009-01-01
For applications requiring low-power, low-voltage and real-time, a novel analog VLSI implementation of continuous Marr wavelet transform based on CMOS log-domain integrator is proposed.Mart wavelet is approximated by a parameterized class of function and with Levenbery-Marquardt nonlinear least square method,the optimum parameters of this function are obtained.The circuits of implementating Mart wavelet transform are composed of analog filter whose impulse response is the required wavelet.The filter design is based on IFLF structure with CMOS log-domain integrators as the main building blocks.SPICE simulations indicate an excellent approximations of ideal wavelet.
Higher-density dyadic wavelet transform and its application
Qin, Yi; Tang, Baoping; Wang, Jiaxu
2010-04-01
This paper proposes a higher-density dyadic wavelet transform with two generators, whose corresponding wavelet filters are band-pass and high-pass. The wavelet coefficients at each scale in this case have the same length as the signal. This leads to a new redundant dyadic wavelet transform, which is strictly shift invariant and further increases the sampling in the time dimension. We describe the definition of higher-density dyadic wavelet transform, and discuss the condition of perfect reconstruction of the signal from its wavelet coefficients. The fast implementation algorithm for the proposed transform is given as well. Compared with the higher-density discrete wavelet transform, the proposed transform is shift invariant. Applications into signal denoising indicate that the proposed wavelet transform has better denoising performance than other commonly used wavelet transforms. In the end, various typical wavelet transforms are applied to analyze the vibration signals of two faulty roller bearings, the results show that the proposed wavelet transform can more effectively extract the fault characteristics of the roller bearings than the other wavelet transforms.
Ng, J.; Kingsbury, N. G.
2004-02-01
This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar
The Clinical Functional Impairment Scale Development.
Sandler, Adrian; Wright, Mary Ellen; Denslow, Sheri
2017-10-01
The purpose of the project was to review content validity and assess the span of responses for the newly developed Clinical Functional Impairment Scale (CFIS). A cross-sectional, content validity process using focus groups of developmental, behavioral pediatric clinicians was conducted. After qualitative analysis of the focus group data, adjustments were made in the CFIS based on the recommendations of the content experts. A survey was conducted of clinicians participating in the online Society of Developmental and Behavioral Pediatrics Discussion Board. Clinicians reviewed 2 case studies and used the CFIS to score severity and interval change of predetermined functional impairments. The amount of spread in the answers was assessed by calculating the index of dispersion. Qualitative analysis of the focus groups resulted in adjustment to the CFIS to 20 functional impairments, with a 5-point Likert scale of severity and a 7-point Likert scale of interval change. Ninety-four clinicians participated in the survey. The index of dispersion ranged from 0.49 to 0.88. The interval ratings of severity and interval change had lower dispersion ranges. The CFIS uses a mutual prioritization by the family and clinician of the child's functional impairments. The study demonstrated that the clinicians' ratings of the case studies were more variable in the initial symptom severity score than their ratings of symptom severity and interval change in symptoms. Further testing of the CFIS is planned using face-to-face clinical encounters and including parent/caregiver ratings of severity and interval change.
Infrared Image Small Target Detection Based on Bi-orthogonal Wavelet and Morphology
Institute of Scientific and Technical Information of China (English)
CHI Jian-nan; ZHANG Zhao-hui; WANG Dong-shu; HAO Yan-shuang
2007-01-01
An image multi-scale edge detection method based on anti-symmetrical bi-orthogonal wavelet is given in theory. Convolution operation property and function as a differential operator are analyzed,which anti-symmetrical bi-orthogonal wavelet transform have. An algorithm for wavelet reconstruction in which multi-scale edge can be detected is put forward. Based on it, a detection method for small target in infrared image with sea or sky background based on the anti-symmetrical bi-orthogonal wavelet and morphology is proposed. The small target detection is considered as a process in which structural background is removed, correlative background is suppressed, and noise is restrained. In this approach, the multi-scale edge is extracted by means of the anti-symmetrical bi-orthogonal wavelet decomposition. Then, module maximum chains formed by complicated background of clouds, sea wave and sea-sky-line are removed, and the image background becomes smoother. Finally, the morphology based edge detection method is used to get small target and restrain undulate background and noise. Experiment results show that the approach can suppress clutter background and detect the small target effectively.
Investigation of cosmic ray penetration with wavelet cross-correlation analysis
Yang, Rui-zhi
2016-01-01
Aims. We use Fermi and Planck data to calculate the cross correlation between gamma ray signal and gas distribution in different scales in giant molecular clouds (GMC). Then we investigate the cosmic rays (CRs) penetration in GMCs with these informations. Methods.We use the wavelet technique to decompose both the gamma ray and dust opacity maps in different scales, then we calculate the wavelet cross correlation functions in these scales. We also define wavelet response as an analog to the impulsive response in Fourier transform and calculate that in different scales down to Fermi angular resolution. Results. The gamma ray maps above 2 GeV show strong correlation with the dust opacity maps, the correlation coefficient is larger than 0.9 above a scale of 0.4 degree.The derived wavelet response is uniform in different scales. Conclusions. We argue that the CR above 10 GeV can penetrate the giant molecular cloud freely and the CRs distributions in the same energy range are uniform down to parsec scale.
Numerical solution of Helmholtz equation of barotropic atmosphere using wavelets
Institute of Scientific and Technical Information of China (English)
Wang Ping; Dai Xin-Gang
2004-01-01
The numerical solution of the Helmholtz equation for barotropic atmosphere is estimated by use of the waveletGalerkin method. The solution involves the decomposition of a circulant matrix consisting up of 2-term connection coefficients of wavelet scaling functions. Three matrix decompositions, i.e. fast Fourier transformation (FFT), Jacobian and QR decomposition methods, are tested numerically. The Jacobian method has the smallest matrix-reconstruction error with the best orthogonality while the FFT method causes the biggest errors. Numerical result reveals that the numerical solution of the equation is very sensitive to the decomposition methods, and the QR and Jacobian decomposition methods, whose errors are of the order of 10-3, much smaller than that with the FFT method, are more suitable to the numerical solution of the equation. With the two methods the solutions are also proved to have much higher accuracy than the iteration solution with the finite difference approximation. In addition, the wavelet numerical method is very useful for the solution of a climate model in low resolution. The solution accuracy of the equation may significantly increase with the order of Daubechies wavelet.
A CMOS Morlet Wavelet Generator
Directory of Open Access Journals (Sweden)
A. I. Bautista-Castillo
2017-04-01
Full Text Available The design and characterization of a CMOS circuit for Morlet wavelet generation is introduced. With the proposed Morlet wavelet circuit, it is possible to reach a~low power consumption, improve standard deviation (σ control and also have a small form factor. A prototype in a double poly, three metal layers, 0.5 µm CMOS process from MOSIS foundry was carried out in order to verify the functionality of the proposal. However, the design methodology can be extended to different CMOS processes. According to the performance exhibited by the circuit, may be useful in many different signal processing tasks such as nonlinear time-variant systems.
Design of compactly supported wavelet to match singularities in medical images
Fung, Carrson C.; Shi, Pengcheng
2002-11-01
Analysis and understanding of medical images has important clinical values for patient diagnosis and treatment, as well as technical implications for computer vision and pattern recognition. One of the most fundamental issues is the detection of object boundaries or singularities, which is often the basis for further processes such as organ/tissue recognition, image registration, motion analysis, measurement of anatomical and physiological parameters, etc. The focus of this work involved taking a correlation based approach toward edge detection, by exploiting some of desirable properties of wavelet analysis. This leads to the possibility of constructing a bank of detectors, consisting of multiple wavelet basis functions of different scales which are optimal for specific types of edges, in order to optimally detect all the edges in an image. Our work involved developing a set of wavelet functions which matches the shape of the ramp and pulse edges. The matching algorithm used focuses on matching the edges in the frequency domain. It was proven that this technique could create matching wavelets applicable at all scales. Results have shown that matching wavelets can be obtained for the pulse edge while the ramp edge requires another matching algorithm.
3D steerable wavelets in practice.
Chenouard, Nicolas; Unser, Michael
2012-11-01
We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible (tight frame) and its elementary constituents (Riesz wavelets) can be efficiently rotated in any 3D direction by forming appropriate linear combinations. Moreover, the basis functions at a given location can be linearly combined to design custom (and adaptive) steerable wavelets. The features of the proposed method are illustrated with the processing and analysis of 3D biomedical data. In particular, we show how those wavelets can be used to characterize directional patterns and to detect edges by means of a 3D monogenic analysis. We also propose a new inverse-problem formalism along with an optimization algorithm for reconstructing 3D images from a sparse set of wavelet-domain edges. The scheme results in high-quality image reconstructions which demonstrate the feature-reduction ability of the steerable wavelets as well as their potential for solving inverse problems.
Denoising and robust non-linear wavelet analysis
Bruce, Andrew G.; Donoho, David L.; Gao, Hong-Ye; Martin, R. D.
1994-04-01
In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistance wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transforms, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the S+Wavelets object-oriented toolkit for wavelet analysis.
RESEARCH OF PROBLEMS ON REALIZING DIRECT ALGORITHM OF WAVELET TRANSFORM
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Direct algorithm of wavelet transform (WT) is the numerical algorithm obtained from the integral formula of WT by directly digitization.Some problems on realizing the algorithm are studied.Some conclusions on the direct algorithm of discrete wavelet transform (DWT), such as discrete convolution operation formula of wavelet coefficients and wavelet components, sampling principle and technology to wavelets, deciding method for scale range of wavelets, measures to solve edge effect problem, etc, are obtained.The realization of direct algorithm of continuous wavelet transform (CWT) is also studied.The computing cost of direct algorithm and Mallat algorithm of DWT are still studied, and the computing formulae are obtained.These works are beneficial to deeply understand WT and Mallat algorithm.Examples in the end show that direct algorithm can also be applied widely.
Energy Technology Data Exchange (ETDEWEB)
Szu, H.; Hsu, C. [Univ. of Southwestern Louisiana, Lafayette, LA (United States)
1996-12-31
Human sensors systems (HSS) may be approximately described as an adaptive or self-learning version of the Wavelet Transforms (WT) that are capable to learn from several input-output associative pairs of suitable transform mother wavelets. Such an Adaptive WT (AWT) is a redundant combination of mother wavelets to either represent or classify inputs.
Wavelet Neural Network Based Traffic Prediction for Next Generation Network
Institute of Scientific and Technical Information of China (English)
Zhao Qigang; Li Qunzhan; He Zhengyou
2005-01-01
By using netflow traffic collecting technology, some traffic data for analysis are collected from a next generation network (NGN) operator. To build a wavelet basis neural network (NN), the Sigmoid function is replaced with the wavelet in NN. Then the wavelet multiresolution analysis method is used to decompose the traffic signal, and the decomposed component sequences are employed to train the NN. By using the methods, an NGN traffic prediction model is built to predict one day's traffic. The experimental results show that the traffic prediction method of wavelet NN is more accurate than that without using wavelet in the NGN traffic forecasting.
OPEN-LOOP FOG SIGNAL TESTING AND WAVELET ELIMINATING NOISE
Institute of Scientific and Technical Information of China (English)
ZHUYun-zhao; WANGShun-ring; MIAOLing-juan; WANGBo
2005-01-01
An open-loop fiber optic gyro (FOG) testing system is designed. The noise characteristic of open-loop fiber optic gyro signals is analyzed. The wavelet eliminating noise method is discussed and compared with other methods, such as smoothing and low-pass filter methods. Results indicate that the wavelet eliminating noise method can satisfy the measuring demand of the FOG weak output signal with noise disturbing. The wavelet analysis method can efficiently eliminate the noise and reserve the information of the signal. The eliminating noise effect of using different wavelet base functions is compared. The effectiveness of multiresolution wavelet analyses of eliminating noise is proved by experimental results.
Directory of Open Access Journals (Sweden)
Shuihua Wang
2015-08-01
Full Text Available Fruit classification is quite difficult because of the various categories and similar shapes and features of fruit. In this work, we proposed two novel machine-learning based classification methods. The developed system consists of wavelet entropy (WE, principal component analysis (PCA, feedforward neural network (FNN trained by fitness-scaled chaotic artificial bee colony (FSCABC and biogeography-based optimization (BBO, respectively. The K-fold stratified cross validation (SCV was utilized for statistical analysis. The classification performance for 1653 fruit images from 18 categories showed that the proposed “WE + PCA + FSCABC-FNN” and “WE + PCA + BBO-FNN” methods achieve the same accuracy of 89.5%, higher than state-of-the-art approaches: “(CH + MP + US + PCA + GA-FNN ” of 84.8%, “(CH + MP + US + PCA + PSO-FNN” of 87.9%, “(CH + MP + US + PCA + ABC-FNN” of 85.4%, “(CH + MP + US + PCA + kSVM” of 88.2%, and “(CH + MP + US + PCA + FSCABC-FNN” of 89.1%. Besides, our methods used only 12 features, less than the number of features used by other methods. Therefore, the proposed methods are effective for fruit classification.
Perturbation of Wavelet and Gabor Frames
Institute of Scientific and Technical Information of China (English)
Ivana Carrizo; Sergio Favier
2003-01-01
In this work two aspects of theory of frames are presented: a side necessary condition on irregular wavelet frames is obtained, another perturbation of wavelet and Gabor frames is considered. Specifically,we present the results obtained on frame stability when one disturbs the mother of wavelet frame, or the parameter of dilatation, and in Gabor frames when the generating function or the parameter of translation are perturbed. In all cases we work without demanding compactness of the support, neither on the generating function, nor on its Fourier transform.
Directory of Open Access Journals (Sweden)
Jikai Chen
2016-12-01
Full Text Available In a power system, the analysis of transient signals is the theoretical basis of fault diagnosis and transient protection theory. Shannon wavelet entropy (SWE and Shannon wavelet packet entropy (SWPE are powerful mathematics tools for transient signal analysis. Combined with the recent achievements regarding SWE and SWPE, their applications are summarized in feature extraction of transient signals and transient fault recognition. For wavelet aliasing at adjacent scale of wavelet decomposition, the impact of wavelet aliasing is analyzed for feature extraction accuracy of SWE and SWPE, and their differences are compared. Meanwhile, the analyses mentioned are verified by partial discharge (PD feature extraction of power cable. Finally, some new ideas and further researches are proposed in the wavelet entropy mechanism, operation speed and how to overcome wavelet aliasing.
Singh, Ram Chandra; Bhatla, Rajeev
2012-07-01
This paper deals with the meteorological applications of wavelets and fuzzy logics and a hybrid of wavelets and fuzzy logics. The wavelet transform has emerged over recent years as a powerful time-frequency analysis and signal coding tool favoured for the interrogation of complex non-stationary signals. It has been shown that the wavelet transform is a flexible time-frequency decomposition tool which can form the basis of useful time series analysis. It is expected to see an increased amount of research and technology development work in the coming years employing wavelets for various scientific and engineering applications.
利用小波多尺度积实现裂纹缺陷的边缘检测%Edge detection of crack defect based on wavelet multi-scale multiplication.
Institute of Scientific and Technical Information of China (English)
贾超; 王耀坤; 邢晶晶
2011-01-01
A new image edge detection algorithm which is based on wavelet transform is concerned with doing multi-scale wavelet decomposition to the image with multi-scale of edge information and the modulus maximum value of wavelet transform, and then making a multiplication of consecutive scale wavelet coefficient to enhance edge and achieving the final image edge with double threshold to remove noise components. The result of test indicates that this algorithm solves problems of edge noise and the bad edge, and ensures the accuracy of edge continuation and positioning. The algorithm with double threshold is superior to a single threshold and can be used effectively in framing member detection.%提出了一种基于小波变换的图像边缘检测方法,即利用边缘信息的多尺度特性和小波变换模极大值对图像进行多尺度分解,将相邻尺度的小渡系数相乘增强边缘,再通过双阈值去噪的方法,得到最终的图像边缘.实验结果表明该方法很好地解决了噪声和坏边的问题,边缘连续的同时又保证了边缘定位的准确性,采用双阈值的算法明显优于采用单阈值,可以有效用于结构件的检测.
Dyadic Bivariate Wavelet Multipliers in L2(R2)
Institute of Scientific and Technical Information of China (English)
Zhong Yan LI; Xian Liang SHI
2011-01-01
The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation (where A is any expansive matrix with integer entries and |detA|＝2)wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium(1998)and Li Z.,et al.(2010).But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation.matrix with the absolute value of determinant not 2 in L2(R2).In this paper,we choose 2I2＝(0202)as the dilation matrix and consider the 2I2-dilation multivariate wavelet Ψ＝{ψ1,ψ2,ψ3}(which is called a dyadic bivariate wavelet)multipliers.Here we call a measurable function family f＝{f1,f2,f3}a dyadic bivariate wavelet multiplier if Ψ1＝{F-1(f1ψ1),F-1(f2ψ2),F-1(f3ψ3)} is a dyadic bivariate wavelet for any dyadic bivariate wavelet Ψ={ψ1,ψ2,ψ3},where(f)and,F-1 denote the Fourier transform and the inverse transform of function f respectively.We study dyadic bivariate wavelet multipliers,and give some conditions for dyadic bivariate wavelet multipliers.We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.
van den Berg, J. C.
2004-03-01
A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guérin and M. Holschneider.
Interplay between functional connectivity and scale-free dynamics in intrinsic fMRI networks.
Ciuciu, Philippe; Abry, Patrice; He, Biyu J
2014-07-15
Studies employing functional connectivity-type analyses have established that spontaneous fluctuations in functional magnetic resonance imaging (fMRI) signals are organized within large-scale brain networks. Meanwhile, fMRI signals have been shown to exhibit 1/f-type power spectra - a hallmark of scale-free dynamics. We studied the interplay between functional connectivity and scale-free dynamics in fMRI signals, utilizing the fractal connectivity framework - a multivariate extension of the univariate fractional Gaussian noise model, which relies on a wavelet formulation for robust parameter estimation. We applied this framework to fMRI data acquired from healthy young adults at rest and while performing a visual detection task. First, we found that scale-invariance existed beyond univariate dynamics, being present also in bivariate cross-temporal dynamics. Second, we observed that frequencies within the scale-free range do not contribute evenly to inter-regional connectivity, with a systematically stronger contribution of the lowest frequencies, both at rest and during task. Third, in addition to a decrease of the Hurst exponent and inter-regional correlations, task performance modified cross-temporal dynamics, inducing a larger contribution of the highest frequencies within the scale-free range to global correlation. Lastly, we found that across individuals, a weaker task modulation of the frequency contribution to inter-regional connectivity was associated with better task performance manifesting as shorter and less variable reaction times. These findings bring together two related fields that have hitherto been studied separately - resting-state networks and scale-free dynamics, and show that scale-free dynamics of human brain activity manifest in cross-regional interactions as well.
Performance Evaluation of Wavelet Based on Human Visual System
Institute of Scientific and Technical Information of China (English)
胡海平; 莫玉龙
2002-01-01
We have constructed a compactly supported biorthogonal wavelet that approximates the modulation transfer function(MTF) of human visual system in the frequency domain.In this paper,we evaluate performance of the constructed wavelet,and compare it with the widely used Daubechies9-7,Daubechies 9-3 and GBCW-9-7 wavelets.The result shows that coding performance of the constructed wavelet is better than Daubechies9-3,and is competitive with Daubechies 9-7 and GBCW-9-7 wavelets.Like Dauechies 9-3 wavelet,the filter coefficients of the constructed waveklet are all dyadic fractions,and the tap is less than Daubechies 9-7 and GBOW 9-7,It has an attractive feature in the realization of discrete wavelet transform.
Polynomial Representations for a Wavelet Model of Interest Rates
Directory of Open Access Journals (Sweden)
Dennis G. Llemit
2015-12-01
Full Text Available In this paper, we approximate a non – polynomial function which promises to be an essential tool in interest rates forecasting in the Philippines. We provide two numerical schemes in order to generate polynomial functions that approximate a new wavelet which is a modification of Morlet and Mexican Hat wavelets. The first is the Polynomial Least Squares method which approximates the underlying wavelet according to desired numerical errors. The second is the Chebyshev Polynomial approximation which generates the required function through a sequence of recursive and orthogonal polynomial functions. We seek to determine the lowest order polynomial representations of this wavelet corresponding to a set of error thresholds.
Automatic Identification of Axis Orbit Based on Both Wavelet Moment Invariants and Neural Network
Institute of Scientific and Technical Information of China (English)
FuXiang-qian; LiuGuang-lin; JiangJing; LiYou-ping
2003-01-01
Axis orbit is an important characteristic to be used in the condition monitoring and diagnosis system of rotating machine. The wavelet moment has the invariant to the translation, scaling and rotation. A method, which uses a neural network based on Radial Basis Function (RBF) and wavelet moment invariants to identify the orbit of shaft centerline of rotating machine is discussed in this paper. The principle and its application procedure of the method are introduced in detail. It gives simulation results of automatic identification for three typical axis orbits. It is proved that the method is effective and practicable.
Automatic Identification of Axis Orbit Based on Both Wavelet Moment Invariants and Neural Network
Institute of Scientific and Technical Information of China (English)
Fu Xiang-qian; Liu Guang-lin; Jiang Jing; Li You-ping
2003-01-01
Axis orbit is an important characteristic to be used in the condition monitoring and diagnosis system of rota-ting machine. The wavelet moment has the invariant to the translation, scaling and rotation. A method, which uses a neural network based on Radial Basis Function (RBF) and wavelet moment invariants to identify the orbit of shaft centerline of rotating machine is discussed in this paper. The principle and its application procedure of the method are intro-duced in detail. It gives simulation results of automatic identi-fication for three typical axis orbits. It is proved that the method is effective and practicable.
Shukla, K K
2013-01-01
Due to its inherent time-scale locality characteristics, the discrete wavelet transform (DWT) has received considerable attention in signal/image processing. Wavelet transforms have excellent energy compaction characteristics and can provide perfect reconstruction. The shifting (translation) and scaling (dilation) are unique to wavelets. Orthogonality of wavelets with respect to dilations leads to multigrid representation. As the computation of DWT involves filtering, an efficient filtering process is essential in DWT hardware implementation. In the multistage DWT, coefficients are calculated
Likert and Guttman scaling of visual function rating scale questionnaires.
Massof, Robert W
2004-12-01
To test the assumptions underlying Likert scoring of visual function questionnaires. Questionnaires were administered to 284 low-vision subjects by telephone. Each subject was administered two of four questionnaires: ADVS, NEI VFQ-25 plus supplement, expanded VAQ, and VF-14. Z-scores for cumulative frequency of using each rating category across subjects are not linear with rating category rank and items are not the same difficulty for any of the questionnaires. Guttmann coefficients of reproducibility ranged from 57% for the ADVS to 51% for the NEI VFQ-25. Cronbach alphas ranged from 0.92 for the VF-14 to 0.96 for the NEI VFQ; however, inter-item consistency coefficients ranged from 0.24 for the VAQ to 0.45 for the NEI VFQ. Likert scores were significantly correlated between instruments, ranging from 0.66 for NEI VFQ vs ADVS to 0.90 for the VF-14 vs. ADVS. The rating scales of all four questionnaires fail to satisfy Likert's assumptions. Also, ratings are probabilistic, rather than deterministic, which means that the Likert model is not valid for these questionnaires. However, Likert scores for all four instruments are intercorrelated, suggesting that they are monotonic with the latent subject trait distributed in the low vision sample.
Optimization of wavelet decomposition for image compression and feature preservation.
Lo, Shih-Chung B; Li, Huai; Freedman, Matthew T
2003-09-01
A neural-network-based framework has been developed to search for an optimal wavelet kernel that can be used for a specific image processing task. In this paper, a linear convolution neural network was employed to seek a wavelet that minimizes errors and maximizes compression efficiency for an image or a defined image pattern such as microcalcifications in mammograms and bone in computed tomography (CT) head images. We have used this method to evaluate the performance of tap-4 wavelets on mammograms, CTs, magnetic resonance images, and Lena images. We found that the Daubechies wavelet or those wavelets with similar filtering characteristics can produce the highest compression efficiency with the smallest mean-square-error for many image patterns including general image textures as well as microcalcifications in digital mammograms. However, the Haar wavelet produces the best results on sharp edges and low-noise smooth areas. We also found that a special wavelet whose low-pass filter coefficients are 0.32252136, 0.85258927, 1.38458542, and -0.14548269) produces the best preservation outcomes in all tested microcalcification features including the peak signal-to-noise ratio, the contrast and the figure of merit in the wavelet lossy compression scheme. Having analyzed the spectrum of the wavelet filters, we can find the compression outcomes and feature preservation characteristics as a function of wavelets. This newly developed optimization approach can be generalized to other image analysis applications where a wavelet decomposition is employed.
POLY-SCALE REFINABLE FUNCTION AND THEIR PROPERTIES
Institute of Scientific and Technical Information of China (English)
YANG Shou-zhi
2006-01-01
Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function φ of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.
Institute of Scientific and Technical Information of China (English)
ZHANG Wei-min; CAO Xiao-qun; XIAO Qin-nong; SONG Jun-qiang; ZHU Xiao-qian; WANG Shu-chang
2010-01-01
Background error covariance plays an important role in any variational data assimilation system,because it determines how information from observations is spread in model space and between different model variables.In this paper,the use of orthogonal wavelets in representation of background error covariance over a limited area is studied.Based on the WRF model and its 3D-VAR system,an algorithm using orthogonal wavelets to model background error covariance is developed.Because each wavelet function contains information on both position and scale,using a diagonal correlation matrix in wavelet space gives the possibility to represent some anisotropic and inhomogeneous characteristics of background error covariance.The experiments show that local correlation functions are better modeled than spectral methods.The formulation of wavelet background error covariance is tested with the typhoon Kaemi (2006).The results of experiments indicate that the subsequent forecasts of typhoon Kaemi's track and intensity are significantly improved by the new method.
On the efficacy of the wavelet decomposition for high frequency vibration analyses
Zhang, S.; Cheng, L.
2016-10-01
This paper reports the extraordinary ability of the wavelet decomposition for vibration analyses under the framework of Rayleigh-Ritz method. Using a beam as an example, Daubechies wavelet scale functions are used as admissible functions for decomposing the flexural displacement of the structure, along with the artificial springs at the boundary, to predict vibration of an Euler-Bernoulli beam in an extremely large frequency range. It is shown that the use of wavelet basis allows reaching very high frequencies, typically covering more than 1000 modes using conventional computational facility within the available numerical dynamics of the computers with no particular care needed for round-off errors. As a side benefit, the use of spring boundary also allows handling any elastic boundary conditions through a dynamic contribution in the Hamiltonian of the beam. The wavelet decomposed approach combines the flexibility of the global methods and the accuracy of local methods by inheriting the versatility of the Rayleigh-Ritz approach and the superior fitting ability of the wavelets. Numerical results on both free and forced vibrations are given, in excellent agreement with predictions of classical methods.
Abibullaev, Berdakh; An, Jinung
2012-12-01
Recent advances in neuroimaging demonstrate the potential of functional near-infrared spectroscopy (fNIRS) for use in brain-computer interfaces (BCIs). fNIRS uses light in the near-infrared range to measure brain surface haemoglobin concentrations and thus determine human neural activity. Our primary goal in this study is to analyse brain haemodynamic responses for application in a BCI. Specifically, we develop an efficient signal processing algorithm to extract important mental-task-relevant neural features and obtain the best possible classification performance. We recorded brain haemodynamic responses due to frontal cortex brain activity from nine subjects using a 19-channel fNIRS system. Our algorithm is based on continuous wavelet transforms (CWTs) for multi-scale decomposition and a soft thresholding algorithm for de-noising. We adopted three machine learning algorithms and compared their performance. Good performance can be achieved by using the de-noised wavelet coefficients as input features for the classifier. Moreover, the classifier performance varied depending on the type of mother wavelet used for wavelet decomposition. Our quantitative results showed that CWTs can be used efficiently to extract important brain haemodynamic features at multiple frequencies if an appropriate mother wavelet function is chosen. The best classification results were obtained by a specific combination of input feature type and classifier.
Lu, Zhao; Sun, Jing; Butts, Kenneth
2014-05-01
Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.
Directory of Open Access Journals (Sweden)
Hannu Olkkonen
2013-01-01
Full Text Available In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG. Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.
Design of Steerable Wavelets to Detect Multifold Junctions.
Püspöki, Zsuzsanna; Uhlmann, Virginie; Vonesch, Cédric; Unser, Michael
2016-02-01
We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern analysis. The goal of this paper is to build optimal junction detectors based on 2D steerable wavelets that are polar-separable in the Fourier domain. The approaches we develop are general and can be used for the detection of arbitrary symmetric and asymmetric junctions. The backbone of our construction is a multiscale pyramid with a radial wavelet function where the directional components are represented by circular harmonics and encoded in a shaping matrix. We are able to detect M -fold junctions in different scales and orientations. We provide experimental results on both simulated and real data to demonstrate the effectiveness of the algorithm.
Wavelet Analysis for Acoustic Phased Array
Kozlov, Inna; Zlotnick, Zvi
2003-03-01
Wavelet spectrum analysis is known to be one of the most powerful tools for exploring quasistationary signals. In this paper we use wavelet technique to develop a new Direction Finding (DF) Algorithm for the Acoustic Phased Array (APA) systems. Utilising multi-scale analysis of libraries of wavelets allows us to work with frequency bands instead of individual frequency of an acoustic source. These frequency bands could be regarded as features extracted from quasistationary signals emitted by a noisy object. For detection, tracing and identification of a sound source in a noisy environment we develop smart algorithm. The essential part of this algorithm is a special interacting procedure of the above-mentioned DF-algorithm and the wavelet-based Identification (ID) algorithm developed in [4]. Significant improvement of the basic properties of a receiving APA pattern is achieved.
Discrete multiscale wavelet shrinkage and integrodifferential equations
Didas, S.; Steidl, G.; Weickert, J.
2008-04-01
We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.
Wang, Zhanyong; Lu, Feng; He, Hong-di; Lu, Qing-Chang; Wang, Dongsheng; Peng, Zhong-Ren
2015-03-01
At road intersections, vehicles frequently stop with idling engines during the red-light period and speed up rapidly in the green-light period, which generates higher velocity fluctuation and thus higher emission rates. Additionally, the frequent changes of wind direction further add the highly variable dispersion of pollutants at the street scale. It is, therefore, very difficult to estimate the distribution of pollutant concentrations using conventional deterministic causal models. For this reason, a hybrid model combining wavelet neural network and genetic algorithm (GA-WNN) is proposed for predicting 5-min series of carbon monoxide (CO) and fine particulate matter (PM2.5) concentrations in proximity to an intersection. The proposed model is examined based on the measured data under two situations. As the measured pollutant concentrations are found to be dependent on the distance to the intersection, the model is evaluated in three locations respectively, i.e. 110 m, 330 m and 500 m. Due to the different variation of pollutant concentrations on varied time, the model is also evaluated in peak and off-peak traffic time periods separately. Additionally, the proposed model, together with the back-propagation neural network (BPNN), is examined with the measured data in these situations. The proposed model is found to perform better in predictability and precision for both CO and PM2.5 than BPNN does, implying that the hybrid model can be an effective tool to improve the accuracy of estimating pollutants' distribution pattern at intersections. The outputs of these findings demonstrate the potential of the proposed model to be applicable to forecast the distribution pattern of air pollution in real-time in proximity to road intersection.
Multiuser detector based on wavelet networks
Institute of Scientific and Technical Information of China (English)
王伶; 焦李成; 陶海红; 刘芳
2004-01-01
Multiple access interference (MAI) and near-far problem are two major obstacles in DS-CDMA systems.Combining wavelet neural networks and two matched filters, the novel multiuser detector, which is based on multiple variable function estimation wavelet networks over single path asynchronous channel and space-time channel respectively is presented. Excellent localization characteristics of wavelet functions in both time and frequency domains allowed hierarchical multiple resolution learning of input-output data mapping. The mathematic frame of the neural networks and error back ward propagation algorithm are introduced. The complexity of the multiuser detector only depends on that of wavelet networks. With numerical simulations and performance analysis, it indicates that the multiuser detector has excellent performance in eliminating MAI and near-far resistance.
Skopina, Maria; Protasov, Vladimir
2016-01-01
This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult. Another important feature of wavelet is ...
Hramov, Alexander E; Makarov, Valeri A; Pavlov, Alexey N; Sitnikova, Evgenia
2015-01-01
This book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade. Chapters 1 and 2 introduce and review the relevant foundations of neurophysics and wavelet theory, respectively, pointing on one hand to the various current challenges in neuroscience and introducing on the other the mathematical techniques of the wavelet transform in its two variants (discrete and continuous) as a powerful and versatile tool for investigating the relevant neuronal dynamics. Chapter 3 then analyzes results from examining individual neuron dynamics and intracellular processes. The principles for recognizing neuronal spikes from extracellular recordings and the advantages of using wavelets to address these issues are described and combined with approaches based on wavelet neural ...
A Physical Interpretation of The Poisson Wavelet Transform of Potential Fields
Hornby, P.; Horowitz, F. G.; Boschetti, F.
Hornby et al. (1999) derive a Cartesian coordinate wavelet specialised for potential fields from the horizontal gradient of the Green's function for the vertical acceleration due to a point mass. In this framework, the wavelet transform of a potential field at some height z0 is given by the simple expression: - W [f0] (s, -) = (z/z0) -fz (-) x x where f0 is the original potential field on a plane, the wavelet scale s = z/z0, and - denotes the vectorial 2D horizontal gradient. It has been shown in Appendix B of Hornby et al. (1999) that the inverse of this wavelet transform (the IWT) is given by: f0 (-) = 4 ds - x s (- - x ) , - [f0] (s, -) u - W u d-u s 2 0 2 - Here, s is the wavelet basis function proportional to the field due to the horizontal gradient of a point source at depth (i.e. proportional to the field due to a mass dipole at depth), and (, ) denotes a 2D inner product. 2 - Now, because the function s is both the analysing and the synthesising wavelet for - this problem, there is an interesting physical interpretation of the function W. The wavelet transform itself is proportional to a mass dipole source distribution -- one that exactly generates the observed field f0. - Even though the form of the components of the dipole strength W is suggestive of probability amplitudes, it would be more correct to interpret the maxima of the hori- zontal gradients of the field at a given height as the points of greatest edge density in a particular IWT source model -- which provides a physical basis for traditional tech- niques such as those of Cordell and Grauch. The divergence of the dipole distribution (a vector field) is, by Gauss' theorem, a valid density distribution. The PDE satisfied by this density distribution can be deduced. From this PDE we can in turn deduce a variational term that leads to this equation, and hence infer the prior hypothesis being expressed. While the solution so obtained is not itself of great practical interest, it is interesting to
CW-THz image contrast enhancement using wavelet transform and Retinex
Chen, Lin; Zhang, Min; Hu, Qi-fan; Huang, Ying-Xue; Liang, Hua-Wei
2015-10-01
To enhance continuous wave terahertz (CW-THz) scanning images contrast and denoising, a method based on wavelet transform and Retinex theory was proposed. In this paper, the factors affecting the quality of CW-THz images were analysed. Second, an approach of combination of the discrete wavelet transform (DWT) and a designed nonlinear function in wavelet domain for the purpose of contrast enhancing was applied. Then, we combine the Retinex algorithm for further contrast enhancement. To evaluate the effectiveness of the proposed method in qualitative and quantitative, it was compared with the adaptive histogram equalization method, the homomorphic filtering method and the SSR(Single-Scale-Retinex) method. Experimental results demonstrated that the presented algorithm can effectively enhance the contrast of CW-THZ image and obtain better visual effect.
Wavelet analysis on paleomagnetic (and computer simulated VGP time series
Directory of Open Access Journals (Sweden)
A. Siniscalchi
2003-06-01
Full Text Available We present Continuous Wavelet Transform (CWT data analysis of Virtual Geomagnetic Pole (VGP latitude time series. The analyzed time series are sedimentary paleomagnetic and geodynamo simulated data. Two mother wavelets (the Morlet function and the first derivative of a Gaussian function are used in order to detect features related to the spectral content as well as polarity excursions and reversals. By means of the Morlet wavelet, we estimate both the global spectrum and the time evolution of the spectral content of the paleomagnetic data series. Some peaks corresponding to the orbital components are revealed by the spectra and the local analysis helped disclose their statistical significance. Even if this feature could be an indication of orbital influence on geodynamo, other interpretations are possible. In particular, we note a correspondence of local spectral peaks with the appearance of the excursions in the series. The comparison among the paleomagnetic and simulated spectra shows a similarity in the high frequency region indicating that their degree of regularity is analogous. By means of Gaussian first derivative wavelet, reversals and excursions of polarity were sought. The analysis was performed first on the simulated data, to have a guide in understanding the features present in the more complex paleomagnetic data. Various excursions and reversals have been identified, despite of the prevalent normality of the series and its inherent noise. The found relative chronology of the paleomagnetic data reversals was compared with a coeval global polarity time scale (Channel et al., 1995. The relative lengths of polarity stability intervals are found similar, but a general shift appears between the two scales, that could be due to the datation uncertainties of the Hauterivian/Barremian boundary.
Partially coherent imaging and spatial coherence wavelets
Castaneda, R
2003-01-01
A description of spatially partially coherent imaging based on the propagation of second order spatial coherence wavelets and marginal power spectra (Wigner distribution functions) is presented. In this dynamics, the spatial coherence wavelets will be affected by the system through its elementary transfer function. The consistency of the model with the both extreme cases of full coherent and incoherent imaging was proved. In the last case we obtained the classical concept of optical transfer function as a simple integral of the elementary transfer function. Furthermore, the elementary incoherent response function was introduced as the Fourier transform of the elementary transfer function. It describes the propagation of spatial coherence wavelets form each object point to each image point through a specific point on the pupil planes. The point spread function of the system was obtained by a simple integral of the elementary incoherent response function.
Borisov, A A; Bruevich, V V; Rozgacheva, I K; Shimanovskaya, E V
2015-01-01
We applied the method of continuous wavelet-transform to high-quality time-frequency analysis to the sets of observations of relative sunspot numbers. Wavelet analysis of these data reveals the following pattern: at the same time there are several activity cycles whose periods vary widely from the quasi biennial up to the centennial period. These relatively low-frequency periodic variations of the solar activity gradually change the values of periods of different cycles in time. This phenomenon can be observed in every cycle of activity.
The Discrete Wavelet Transform
1991-06-01
focuses on bringing together two separately motivated implementations of the wavelet transform , the algorithm a trous and Mallat’s multiresolution...decomposition. These algorithms are special cases of a single filter bank structure, the discrete wavelet transform , the behavior of which is governed by...nonorthogonal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, we show that the commonly used Lagrange a trous
Making electromagnetic wavelets
Energy Technology Data Exchange (ETDEWEB)
Kaiser, Gerald [Center for Signals and Waves, 3803 Tonkawa Trail no. 2, Austin, TX 78756-3915 (United States)
2004-06-04
Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.
Four-band compactly supported orthogonal symmetric interpolating scaling function
Institute of Scientific and Technical Information of China (English)
水鹏朗; 保铮
2001-01-01
An efficient method is proposed to design 4-band scaling functions w ith the following five advantages: compact support, orthogonality, symmetry, regularity, and interpolation; and a family of such scaling functions with the shortest support is given.
Wavelet Transform of Fixed Pattern Noise in Focal Plane Arrays
1994-02-01
AD-A276 963 1111111111 I NAWCWPNS TP 8185 Wavelet Transform of Fixed Pattern Noise in Focal Plane Arrays OTIC by ELECTE Dr. Gary Hewer MAR 151994 and...REPORT TYPE AND DATES COVERED IFebruary 1994 Final; 199 ,L TTLE ND SBTILE LFUNDNG UBER Wavelet Transform of Fixed Pattern Noise in Focal Plane Arrays...nonlinearity 71,(w) = sgn(w)(IwI-t). with threshold t to each empirical sample value w in the wavelet transform d scales. After thresholding the wavelet
Watermarking on 3D mesh based on spherical wavelet transform
Institute of Scientific and Technical Information of China (English)
金剑秋; 戴敏雅; 鲍虎军; 彭群生
2004-01-01
In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.
Institute of Scientific and Technical Information of China (English)
崔世林; 田斐; 李德华
2012-01-01
只需要一幅调制图像的光栅投影测量方法主要有傅里叶变换轮廓术(FTP)、小波变换轮廓术(WTP)等.采用基于指数尺度间隔的连续小波变换与重构方法,提取调制图像的瞬时相位.针对指数尺度间隔连续小波变换,指出了足够大的噪声能够改变小波变换脊的位置,并且该脊向上移动的概率最大.因此,为了重构载频信号,选择脊及其紧邻的较大的那个尺度所对应的小波系数,采用灰度图像阈值分割中最大类间方差法(OTSU),剔除掉幅值较小的系数；针对斑点噪声的影响,对OTSU算法的结果进行了修正;使用修正后的系数集合重构载频信号,并计算该信号的瞬时相位.理论分析和实验结果表明算法有效且具有稳健性.%The methods which only need one modulated pattern for fringe projection measurement mainly have Fourier transform profilometry, wavelet transform profilometry, and so on. The continuous complex Morlet wavelet based on exponent scale interval and reconstruction is used to retrieve the instantaneous phase of fringe pattern. For the continuous wavelet transform, the great enough noise can change the position of wavelet transform ridge, the probability that the ridge moves up with the influence of noise is greatest. So, the wavelet coefficients corresponding to the ridge and the closest larger scale are chosen, and the maximum between-class variance methord (OTSU) is used to prevent the interference caused by low frequency components) in order to overcome the speckle noise, the result of OTSU is modified and at last, the modified result is used to reconstruct the analytic carrier-frequency signal, and compute the intantaneous phase of the signal. The theoretical analysis and experimental results illustrate that the method is valid and robust.
Andre, Julia; Kiremidjian, Anne; Liao, Yizheng; Georgakis, Christos; Rajagopal, Ram
2016-04-01
Ice accretion on cables of bridge structures poses serious risk to the structure as well as to vehicular traffic when the ice falls onto the road. Detection of ice formation, quantification of the amount of ice accumulated, and prediction of icefalls will increase the safety and serviceability of the structure. In this paper, an ice accretion detection algorithm is presented based on the Continuous Wavelet Transform (CWT). In the proposed algorithm, the acceleration signals obtained from bridge cables are transformed using wavelet method. The damage sensitive features (DSFs) are defined as a function of the wavelet energy at specific wavelet scales. It is found that as ice accretes on the cables, the mass of cable increases, thus changing the wavelet energies. Hence, the DSFs can be used to track the change of cables mass. To validate the proposed algorithm, we use the data collected from a laboratory experiment conducted at the Technical University of Denmark (DTU). In this experiment, a cable was placed in a wind tunnel as ice volume grew progressively. Several accelerometers were installed at various locations along the testing cable to collect vibration signals.
Directory of Open Access Journals (Sweden)
Sayadi Omid
2007-01-01
Full Text Available We present a new modified wavelet transform, called the multiadaptive bionic wavelet transform (MABWT, that can be applied to ECG signals in order to remove noise from them under a wide range of variations for noise. By using the definition of bionic wavelet transform and adaptively determining both the center frequency of each scale together with the -function, the problem of desired signal decomposition is solved. Applying a new proposed thresholding rule works successfully in denoising the ECG. Moreover by using the multiadaptation scheme, lowpass noisy interference effects on the baseline of ECG will be removed as a direct task. The method was extensively clinically tested with real and simulated ECG signals which showed high performance of noise reduction, comparable to those of wavelet transform (WT. Quantitative evaluation of the proposed algorithm shows that the average SNR improvement of MABWT is 1.82 dB more than the WT-based results, for the best case. Also the procedure has largely proved advantageous over wavelet-based methods for baseline wandering cancellation, including both DC components and baseline drifts.
Wiaux, Y.; Jacques, L.; Vandergheynst, P.
2005-12-01
Wavelets on the sphere are reintroduced and further developed on both the theoretical and the algorithmic grounds. A specific application to cosmology is also discussed. First, a new practical approach to the wavelet filtering of signals on the sphere is developed. Translations and rotations of the filters are naturally implemented through three-dimensional rotations of the group SO(3), and a unitary, radial, and conformal dilation operator is required. The resulting formalism is unique. A correspondence principle is also established, stating that the inverse stereographic projection of a wavelet on the plane (i.e., Euclidean wavelet) also uniquely leads to a wavelet on the sphere (i.e., spherical wavelet). It simplifies the construction of wavelets on the sphere and allows the transfer onto the sphere of properties of wavelets on the plane, such as directionality and steerability. Second, an exact fast algorithm is developed for the directional correlation on the sphere of band-limited signals of band limit L and steerable (wavelet) filters, on 2L×2L equi-angular grids in the coordinates (θ,φ). On the one hand, the algorithm is based on a technique of separation of variables in the Wigner D-functions, basis functions for the harmonic analysis on the rotation group SO(3). The asymptotic complexity of the algorithm is correspondingly reduced from O(L5) to O(L4). On the other hand, the filter steerability and the use of the Driscoll and Healy fast scalar spherical harmonics transform further reduce the algorithm complexity to a simple O(L2log22L). Finally, we consider the perspective of the wavelet analysis of the cosmic microwave background (CMB) temperature and polarization anisotropies on the sphere of the sky. The notions of directionality and steerability are important tools for the identification of local directional features in the wavelet coefficients of the signal, and for their interpretation in cosmology. In this context, computation times for the exact
Wavelet analysis of epileptic spikes
Latka, M; Kozik, A; West, B J; Latka, Miroslaw; Was, Ziemowit; Kozik, Andrzej; West, Bruce J.
2003-01-01
Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous, pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.
Wavelet analysis of epileptic spikes
Latka, Miroslaw; Was, Ziemowit; Kozik, Andrzej; West, Bruce J.
2003-05-01
Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.
Electric Equipment Diagnosis based on Wavelet Analysis
Directory of Open Access Journals (Sweden)
Stavitsky Sergey A.
2016-01-01
Full Text Available Due to electric equipment development and complication it is necessary to have a precise and intense diagnosis. Nowadays there are two basic ways of diagnosis: analog signal processing and digital signal processing. The latter is more preferable. The basic ways of digital signal processing (Fourier transform and Fast Fourier transform include one of the modern methods based on wavelet transform. This research is dedicated to analyzing characteristic features and advantages of wavelet transform. This article shows the ways of using wavelet analysis and the process of test signal converting. In order to carry out this analysis, computer software Mathcad was used and 2D wavelet spectrum for a complex function was created.
Nonparametric Transient Classification using Adaptive Wavelets
Varughese, Melvin M; Stephanou, Michael; Bassett, Bruce A
2015-01-01
Classifying transients based on multi band light curves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. Here we present a nonparametric classifier that uses the transient's light curve measurements to predict its class given training data. It implements two novel components: the first is the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients. The second novelty is the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The ranked classifier is simple and quick to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant, hence they do not need the light curves to be aligned to extract features. Further, BAGIDIS is nonparametric so it can be used for blind ...
Application of spline wavelet transform in differential of electroanalytical signal
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Investigating characteristics of spline wavelet, we found that if the two-order spline function, the derivative function of the three-order B spline function, is used as the wavelet base function, the spline wavelet transform has both the property of denoising and that of differential. As a result, the relation between the spline wavelet transform and the differential was studied in theory. Experimental results show that the spline wavelet transform can well be applied to the differential of the electroanalytical signal. Compared with other kinds of wavelet transform, the spline wavelet trans-form has a characteristic of differential. Compared with the digital differential and simulative differential with electronic circuit, the spline wavelet transform not only can carry out denoising and differential for a signal, but also has the ad-vantages of simple operation and small quantity of calcula-tion, because step length, RC constant and other kinds of parameters need not be selected. Compared with Alexander Kai-man Leung's differential method, the differential method with spline wavelet transform has the characteristic that the differential order is not dependent on the number of data points in the original signal.
Multi-focus image fusion algorithm based on adaptive PCNN and wavelet transform
Wu, Zhi-guo; Wang, Ming-jia; Han, Guang-liang
2011-08-01
Being an efficient method of information fusion, image fusion has been used in many fields such as machine vision, medical diagnosis, military applications and remote sensing. In this paper, Pulse Coupled Neural Network (PCNN) is introduced in this research field for its interesting properties in image processing, including segmentation, target recognition et al. and a novel algorithm based on PCNN and Wavelet Transform for Multi-focus image fusion is proposed. First, the two original images are decomposed by wavelet transform. Then, based on the PCNN, a fusion rule in the Wavelet domain is given. This algorithm uses the wavelet coefficient in each frequency domain as the linking strength, so that its value can be chosen adaptively. Wavelet coefficients map to the range of image gray-scale. The output threshold function attenuates to minimum gray over time. Then all pixels of image get the ignition. So, the output of PCNN in each iteration time is ignition wavelet coefficients of threshold strength in different time. At this moment, the sequences of ignition of wavelet coefficients represent ignition timing of each neuron. The ignition timing of PCNN in each neuron is mapped to corresponding image gray-scale range, which is a picture of ignition timing mapping. Then it can judge the targets in the neuron are obvious features or not obvious. The fusion coefficients are decided by the compare-selection operator with the firing time gradient maps and the fusion image is reconstructed by wavelet inverse transform. Furthermore, by this algorithm, the threshold adjusting constant is estimated by appointed iteration number. Furthermore, In order to sufficient reflect order of the firing time, the threshold adjusting constant αΘ is estimated by appointed iteration number. So after the iteration achieved, each of the wavelet coefficient is activated. In order to verify the effectiveness of proposed rules, the experiments upon Multi-focus image are done. Moreover
Wavelet methods in (financial) time-series processing
Struzik, Z.R.
2000-01-01
We briefly describe the major advantages of using the wavelet transform for the processing of financial time series on the example of the S&P index. In particular, we show how to uncover local the scaling (correlation) characteristics of the S&P index with the wavelet based effective H'older expone
Invariant wavelet transform-based automatic target recognition
Sadovnik, Lev S.; Rashkovskiy, Oleg; Tebelev, Igor
1995-03-01
The authors' previous work (SPIE Vol. 2237) on scale-, rotation- and shift-invariant wavelet transform is extended to accommodate multiple objects in the scene and a nonuniform background. After background elimination and segmentation, a set of windows each containing a single object are analyzed based on an invariant wavelet feature extraction algorithm and neural network-based classifier.
Wavelet Analyses and Applications
Bordeianu, Cristian C.; Landau, Rubin H.; Paez, Manuel J.
2009-01-01
It is shown how a modern extension of Fourier analysis known as wavelet analysis is applied to signals containing multiscale information. First, a continuous wavelet transform is used to analyse the spectrum of a nonstationary signal (one whose form changes in time). The spectral analysis of such a signal gives the strength of the signal in each…
1994-07-29
Douglas (MDA). This has been extended to the use of local SVD methods and the use of wavelet packets to provide a controlled sparsening. The goal is to be...possibilities for segmenting, compression and denoising signals and one of us (GVW) is using these wavelets to study edge sets with Prof. B. Jawerth. The
Sato, Haruo; Fehler, Michael C.
2016-10-01
The envelope broadening and the peak delay of the S-wavelet of a small earthquake with increasing travel distance are results of scattering by random velocity inhomogeneities in the earth medium. As a simple mathematical model, Sato proposed a new stochastic synthesis of the scalar wavelet envelope in 3-D von Kármán type random media when the centre wavenumber of the wavelet is in the power-law spectral range of the random velocity fluctuation. The essential idea is to split the random medium spectrum into two components using the centre wavenumber as a reference: the long-scale (low-wavenumber spectral) component produces the peak delay and the envelope broadening by multiple scattering around the forward direction; the short-scale (high-wavenumber spectral) component attenuates wave amplitude by wide angle scattering. The former is calculated by the Markov approximation based on the parabolic approximation and the latter is calculated by the Born approximation. Here, we extend the theory for the envelope synthesis of a wavelet in 2-D random media, which makes it easy to compare with finite difference (FD) simulation results. The synthetic wavelet envelope is analytically written by using the random medium parameters in the angular frequency domain. For the case that the power spectral density function of the random velocity fluctuation has a steep roll-off at large wavenumbers, the envelope broadening is small and frequency independent, and scattering attenuation is weak. For the case of a small roll-off, however, the envelope broadening is large and increases with frequency, and the scattering attenuation is strong and increases with frequency. As a preliminary study, we compare synthetic wavelet envelopes with the average of FD simulation wavelet envelopes in 50 synthesized random media, which are characterized by the RMS fractional velocity fluctuation ε = 0.05, correlation scale a = 5 km and the background wave velocity V0 = 4 km s-1. We use the radiation
A CHARACTERIZATION OF N-DIMENSIONAL DAUBECHIES TYPE TENSOR PRODUCT WAVELET
Institute of Scientific and Technical Information of China (English)
李登峰; 彭思龙
2001-01-01
In this paper, we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form.We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form. This helps us to explicate the difficulty of constructing the non-separable variate wavelet basis and to hint how to construct non-separable variate wavelet basis.
Implementation of functional assessment scales in geriatric practice
DEFF Research Database (Denmark)
Poulsen, Ingrid; Hesselbo, Bjørn; Pietersen, Inge
2005-01-01
A study was undertaken to evaluate the feasibility of functional assessment scales regarding completion rate and ability to document functional changes in geriatric rehabilitation patients.......A study was undertaken to evaluate the feasibility of functional assessment scales regarding completion rate and ability to document functional changes in geriatric rehabilitation patients....
Wavelet transform for Fresnel-transformed mother wavelets
Institute of Scientific and Technical Information of China (English)
Liu Shu-Guang; Chen Jun-Hua; Fan Hong-Yi
2011-01-01
In this paper,we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation.This motivation can let the mother-wavelet-state itself vary from |ψ〉 to Fr,s(+)｜ψ),except for variation within the family of dilations and translations.The Parseval's equality,admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed.By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform,we obtain some mother wavelets.A comparison between the newly found mother wavelets is presented.
Cheng, Li-Fang; Chen, Tung-Chien; Chen, Liang-Gee
2012-01-01
Most of the abnormal cardiac events such as myocardial ischemia, acute myocardial infarction (AMI) and fatal arrhythmia can be diagnosed through continuous electrocardiogram (ECG) analysis. According to recent clinical research, early detection and alarming of such cardiac events can reduce the time delay to the hospital, and the clinical outcomes of these individuals can be greatly improved. Therefore, it would be helpful if there is a long-term ECG monitoring system with the ability to identify abnormal cardiac events and provide realtime warning for the users. The combination of the wireless body area sensor network (BASN) and the on-sensor ECG processor is a possible solution for this application. In this paper, we aim to design and implement a digital signal processor that is suitable for continuous ECG monitoring and alarming based on the continuous wavelet transform (CWT) through the proposed architectures--using both programmable RISC processor and application specific integrated circuits (ASIC) for performance optimization. According to the implementation results, the power consumption of the proposed processor integrated with an ASIC for CWT computation is only 79.4 mW. Compared with the single-RISC processor, about 91.6% of the power reduction is achieved.
Synthesis of Vibration Waves Based on Wavelet Technology
Directory of Open Access Journals (Sweden)
L.H. Zou
2012-01-01
Full Text Available A novel method to generate time series of vibration waves is proposed in the paper. Considering the frequency band energy as the criterion, synthesis formulas for fluctuating wind pressure and earthquake ground motion are developed in terms of Daubechies wavelet and Harr wavelet respectively. The wavelet reconstruction method is applicable to both stationary and non-stationary process simulation. Theoretically, for non-stationary (such as seismic process synthesis, it has a better non-stationarity in time-frequency domain than the traditional trigonometric series. Influence of wavelet delamination number and wavelet function type is also analyzed. Numerical results show that the synthesis of vibration waves based on wavelet reconstruction method contains main components of vibration, and can reflect the main properties of practical vibrations.
Fast Adaptive Wavelet for Remote Sensing Image Compression
Institute of Scientific and Technical Information of China (English)
Bo Li; Run-Hai Jiao; Yuan-Cheng Li
2007-01-01
Remote sensing images are hard to achieve high compression ratio because of their rich texture. By analyzing the influence of wavelet properties on image compression, this paper proposes wavelet construction rules and builds a new biorthogonal wavelet construction model with parameters. The model parameters are optimized by using genetic algorithm and adopting energy compaction as the optimization object function. In addition, in order to resolve the computation complexity problem of online construction, according to the image classification rule proposed in this paper we construct wavelets for different classes of images and implement the fast adaptive wavelet selection algorithm (FAWS). Experimental results show wavelet bases of FAWS gain better compression performance than Daubechies9/7.
Spatial Verification Using Wavelet Transforms: A Review
Weniger, Michael; Friederichs, Petra
2016-01-01
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet transforms offer an effective framework to decompose spatial data into separate (and possibly orthogonal) scales and directions. Most wavelet based spatial verification techniques have been developed or refined in the last decade and concentrate on assessing forecast performance (i.e. forecast skill or forecast error) on distinct physical scales. Particularly during the last five years, a significant growth in meteorological applications could be observed. However, a comparison with other scientific fields such as feature detection, image fusion, texture analysis, or facial and biometric recognition, shows that there is still a considerable, currently unused potential to derive useful diagnostic information. In order to tab the full potential of wavelet analysis, we revise the stat...
A Multiscale Wavelet Solver with O( n) Complexity
Williams, John R.; Amaratunga, Kevin
1995-11-01
In this paper, we use the biorthogonal wavelets recently constructed by Dahlke and Weinreich to implement a highly efficient procedure for solving a certain class of one-dimensional problems, (∂21/∂x21)u = f,I ɛ Z, I > 0. For these problems, the discrete biorthogonal wavelet transform allows us to set up a system of wavelet-Galerkin equations in which the scales are uncoupled, so that a true multiscale solution procedure may be formulated. We prove that the resulting stiffness matrix is in fact an almost perfectly diagonal matrix (the original aim of the construction was to achieve a block diagonal structure) and we show that this leads to an algorithm whose cost is O(n). We also present numerical results which demonstrate that the multiscale biorthogonal wavelet algorithm is superior to the more conventional single scale orthogonal wavelet approach both in terms of speed and in terms of convergence.
The principle of second generation wavelet for milling cutter breakage detection
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Performance degradation or failure of manufacturing equipment will badly influence machining quality.Because of discontinuousness of the milling process,dynamic signals produced in the milling process become non-stationary.This paper indicates that the essence of SGW(second generation wavelet) transform in non-stationary signal processing is the mathematics principle of inner product transform of a dynamic signal with basis functions.Namely,by means of the inner product operation of a signal with basis functions containing scale function and wavelet function,signal decomposition and reconstruction are obtained.Acoustic emission signals generated in the milling processes of a CNC machine were analyzed by using the basis functions of SGW which are oscillation,decay and compact support.The features of end milling cutter breakage have been extracted,and the influences on machining surface quality have been identified effectively,which provide scientific bases for fault diagnosis,error tracing and quality control.
The principle of second generation wavelet for milling cutter breakage detection
Institute of Scientific and Technical Information of China (English)
HE ZhengJia; CAO HongRui; LI Zhen; ZI YanYang; CHEN XueFeng
2009-01-01
Performance degradation or failure of manufacturing equipment will badly influence machining quality.Because of discontinuousness of the milling process, dynamic signals produced in the milling process become non-stationary. This paper indicates that the essence of SGW (second generation wavelet)transform in non-stationary signal processing is the mathematics principle of inner product transform of a dynamic signal with basis functions. Namely, by means of the inner product operation of a signal with basis functions containing scale function and wavelet function, signal decomposition and recon-struction are obtained. Acoustic emission signals generated in the milling processes of a CNC machine were analyzed by using the basis functions of SGW which are oscillation, decay and compact support.The features of end milling cutter breakage have been extracted, and the influences on machining surface quality have been identified effectively, which provide scientific bases for fault diagnosis, error tracing and quality control.
Characteristics and realization of the second generation surface acoustic wave's wavelet device
Institute of Scientific and Technical Information of China (English)
Wen Changbao; Zhu Changchun; Lu Wenke; Liu Qinghong; Liu Junhua
2006-01-01
To overcome the bulk acoustic wave (BAW), the triple transit signals and the discontinuous frequency band in the first generation surface acoustic wave's (FGSAW's) wavelet device, the full transfer multistrip coupler (MSC) is applied to implement wavelet device, and a novel structure of the second generation surface acoustic wave's (SGSAW's) wavelet device is proposed. In the SGSAW's wavelet device, the BAW is separated and eliminated in different acoustic propagating tracks, and the triple transit signal is suppressed. For arbitrary wavelet scale device, the center frequency is three times the radius of frequency band, which ensures that the frequency band of the SGSAW's wavelet device is continuous, and avoids losing signals caused by the discontinuation of frequency band. Experimental result confirms that the BAW suppression, ripples in band, receiving loss and insertion loss of the SGSAW's wavelet device are remarkably improved compared with those of the FGSAW's wavelet device.
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
Double-density complex wavelet cartoon-texture decomposition
Hewer, Gary A.; Kuo, Wei; Hanson, Grant
2007-09-01
Both the Kingsbury dual-tree and the subsequent Selesnick double-density dual-tree complex wavelet transform approximate an analytic function. The classification of the phase dependency across scales is largely unexplored except by Romberg et al.. Here we characterize the sub-band dependency of the orientation of phase gradients by applying the Helmholtz principle to bivariate histograms to locate meaningful modes. A further characterization using the Earth Mover's Distance with the fundamental Rudin-Osher-Meyer Banach space decomposition into cartoon and texture elements is presented. Possible applications include image compression and invariant descriptor selection for image matching.
ON CONVERGENCE OF WAVELET PACKET EXPANSIONS
Institute of Scientific and Technical Information of China (English)
Morten Nielsen
2002-01-01
It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 ＜q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1＜p＜∞, converges in norm and pointwise almost everywhere.
Fang, Li-Zhi
1998-01-01
Recent advances have shown wavelets to be an effective, and even necessary, mathematical tool for theoretical physics. This book is a timely overview of the progress of this new frontier. It includes an introduction to wavelet analysis, and applications in the fields of high energy physics, astrophysics, cosmology and statistical physics. The topics are selected for the interests of physicists and graduate students of theoretical studies. It emphasizes the need for wavelets in describing and revealing structure in physical problems, which is not easily accomplishing by other methods.
Wavelet analysis in neurodynamics
Pavlov, Aleksei N.; Hramov, Aleksandr E.; Koronovskii, Aleksei A.; Sitnikova, Evgenija Yu; Makarov, Valeri A.; Ovchinnikov, Alexey A.
2012-09-01
Results obtained using continuous and discrete wavelet transforms as applied to problems in neurodynamics are reviewed, with the emphasis on the potential of wavelet analysis for decoding signal information from neural systems and networks. The following areas of application are considered: (1) the microscopic dynamics of single cells and intracellular processes, (2) sensory data processing, (3) the group dynamics of neuronal ensembles, and (4) the macrodynamics of rhythmical brain activity (using multichannel EEG recordings). The detection and classification of various oscillatory patterns of brain electrical activity and the development of continuous wavelet-based brain activity monitoring systems are also discussed as possibilities.
On Generalized Carleson Operators of Periodic Wavelet Packet Expansions
Directory of Open Access Journals (Sweden)
Shyam Lal
2013-01-01
Full Text Available Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.
Real-time modeling of primitive environments through wavelet sensors and Hebbian learning
Vaccaro, James M.; Yaworsky, Paul S.
1999-06-01
Modeling the world through sensory input necessarily provides a unique perspective for the observer. Given a limited perspective, objects and events cannot always be encoded precisely but must involve crude, quick approximations to deal with sensory information in a real- time manner. As an example, when avoiding an oncoming car, a pedestrian needs to identify the fact that a car is approaching before ascertaining the model or color of the vehicle. In our methodology, we use wavelet-based sensors with self-organized learning to encode basic sensory information in real-time. The wavelet-based sensors provide necessary transformations while a rank-based Hebbian learning scheme encodes a self-organized environment through translation, scale and orientation invariant sensors. Such a self-organized environment is made possible by combining wavelet sets which are orthonormal, log-scale with linear orientation and have automatically generated membership functions. In earlier work we used Gabor wavelet filters, rank-based Hebbian learning and an exponential modulation function to encode textural information from images. Many different types of modulation are possible, but based on biological findings the exponential modulation function provided a good approximation of first spike coding of `integrate and fire' neurons. These types of Hebbian encoding schemes (e.g., exponential modulation, etc.) are useful for quick response and learning, provide several advantages over contemporary neural network learning approaches, and have been found to quantize data nonlinearly. By combining wavelets with Hebbian learning we can provide a real-time front-end for modeling an intelligent process, such as the autonomous control of agents in a simulated environment.
Greedy Wavelet Projections are Bounded on BV (Preprint)
2003-10-30
functions of bounded variation on IRd with d ??? 2. Let ????, ?? ??? ??, be a wavelet basis of compactly supported functions normalized in BV, i.e...Wojtaszczyk October 30, 2003 Abstract Let BV = BV(IRd) be the space of functions of bounded variation on IRd with d ≥ 2. Let ψλ, λ ∈ ∆, be a wavelet basis...greedy approximation, functions of bounded variation , thresholding, bounded projections. 1 Introduction The space BV := BV(Ω) of functions of
An inertial range length scale in structure functions
Kerr, R M; Gotoh, T; Kerr, Robert M.; Meneguzzi, Maurice; Gotoh, Toshiyuki
2000-01-01
It is shown using experimental and numerical data that within the traditional inertial subrange defined by where the third order structure function is linear that the higher order structure function scaling exponents for longitudinal and transverse structure functions converge only over larger scales, $r>r_S$, where $r_S$ has scaling intermediate between $\\eta$ and $\\lambda$ as a function of $R_\\lambda$. Below these scales, scaling exponents cannot be determined for any of the structure functions without resorting to procedures such as extended self-similarity (ESS). With ESS, different longitudinal and transverse higher order exponents are obtained that are consistent with earlier results. The relationship of these statistics to derivative and pressure statistics, to turbulent structures and to length scales is discussed.
Multiscale functions, scale dynamics, and applications to partial differential equations
Cresson, Jacky; Pierret, Frédéric
2016-05-01
Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.
Siddiqi, A. H.
2012-07-01
In this chapter, the role of wavelet methods applied to identification and characterization of oil reservoir is elaborated. The market rate of petroleum product is very much related to exploration, drilling and production cost. The main goal of researchers working in oil industry is to develop tools and techniques for minimizing cost of exploration and production. Efforts of researchers working in applications of wavelet methods in different parts of the world to achieve this goal is reviewed. Wavelet based solution of Buckley-Leverett equation modelling reservoir is discussed. Variants of Buckley-Leverett equations including its higher dimension versions are introduced. Wavelet methods for inverse problems associated with Buckley-Leverett equation, which are quite useful for oil recovery, are also explained in this chapter.
Contrast Enhancement of Radiographs Using Shift Invariant Wavelet Transform
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel approach using shift invariant wavelet transform is presented for the contrast enhancement of radiographs. By exploiting cross-scale correlation among wavelet coefficients, edge information of radiographic images is extracted and protected, while noise is smoothed out in the wavelet domain. Radiographs are then reconstructed from the transform coefficients modified at multi-scales by nonlinear enhancement operator. The method can achieve effectively contrast enhancement and edge-preserved denoising simultaneously, yet it is capable of giving visually distinct images and offering considerable benefits in medical diagnosis.
Option pricing from wavelet-filtered financial series
de Almeida, V. T. X.; Moriconi, L.
2012-10-01
We perform wavelet decomposition of high frequency financial time series into large and small time scale components. Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most (≃99.6%) of the wavelet coefficients can be neglected for the purpose of option premium evaluation. The relevance of the hugely compressed information provided by low-pass wavelet-filtering is related to the fact that the non-gaussian statistical structure of the original financial time series is essentially preserved for expiration times which are larger than just one trading day.
Han, Bin
2003-06-01
Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d×d dilation matrix M, we demonstrate in a constructive way that we can construct compactly supported tight M-wavelet frames and orthonormal M-wavelet bases in of exponential decay, which are derived from compactly supported M-refinable functions, such that they can have both arbitrarily high smoothness and any preassigned order of vanishing moments. This paper improves several results in Battle (Comm. Math. Phys. 110 (1987) 601), Bownik (J. Fourier Anal. Appl. 7(2001) 489), Gröchenig and Ron (Proc. Amer. Math. Soc. 126 (1998) 1101), Lemarie (J. Math. Pures Appl. 67 (1988) 227), and Strichartz (Constr. Approx. 9 (1993) 327).
Haar wavelets with applications
Lepik, Ülo
2014-01-01
This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-08
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Wavelet despiking of fractographs
Aubry, Jean-Marie; Saito, Naoki
2000-12-01
Fractographs are elevation maps of the fracture zone of some broken material. The technique employed to create these maps often introduces noise composed of positive or negative 'spikes' that must be removed before further analysis. Since the roughness of these maps contains useful information, it must be preserved. Consequently, conventional denoising techniques cannot be employed. We use continuous and discrete wavelet transforms of these images, and the properties of wavelet coefficients related to pointwise Hoelder regularity, to detect and remove the spikes.
GPS Receiver Performance Inspection by Wavelet Transform
Institute of Scientific and Technical Information of China (English)
Xia Lin-yuan; Liu Jing-nan; Lu Liang-xi
2003-01-01
As a powerful analysis tool and the result of contemporary mathematics development, wavelet transform has shown its promising application potentials through the research in the paper. Three aspects regarding GPS receiver performance is tackled: cycle slip detection, receiver noise analysis and receiver channel bias inspection. Wavelet decomposition for double differential observation has demonstrated that this multi-level transform can reveal cycle slips as small as 0.5 cycles without any pre-adjustment processes or satellite orbit information, it can therefore be regarded as a 'geometry free' method. Based on property assumption of receiver noise, signal of noise serial is obtained at the high frequency scale in wavelet decomposition layers. This kind of noise influence on GPSb aseline result can be effectively eliminated by reconstruction process during wavelet reconstruction. Through observed data analysis, the transform has detected a kind of receiver channel bias that has not been completely removed by processing unit of GPS receiver during clock offset resetting operation. Thus the wavelet approach can be employed as a kind of system diagnosis in a generalized point of view.
Institute of Scientific and Technical Information of China (English)
LAI Xing-yu; YE Bang-yan; LI Wei-guang; YAN Chun-yan
2007-01-01
Combining information entropy and wavelet analysis with neural network, an adaptive control system and an adaptive control algorithm are presented for machining process based on extended entropy square error (EESE) and wavelet neural network (WNN). Extended entropy square error function is defined and its availability is proved theoretically. Replacing the mean square error criterion of BP algorithm with the EESE criterion, the proposed system is then applied to the on-line control of the cutting force with variable cutting parameters by searching adaptively wavelet base function and self adjusting scaling parameter, translating parameter of the wavelet and neural network weights. Simulation results show that the designed system is of fast response,non-overshoot and it is more effective than the conventional adaptive control of machining process based on the neural network. The suggested algorithm can adaptively adjust the feed rate on-line till achieving a constant cutting force approaching the reference force in varied cutting conditions, thus improving the machining efficiency and protecting the tool.
Improved System Identification Approach Using Wavelet Networks
Institute of Scientific and Technical Information of China (English)
石宏理; 蔡远利; 邱祖廉
2005-01-01
A new approach is proposed to improve the general identification algorithm of multidimensional systems using wavelet networks. The general algorithm involves mapping vector input into its norm to avoid problem of dimensionality in construction multidimensional wavelet basis functions. Thus, the basis functions are spherically symmetric without direction selectivity. In order to restore the direction selectivity, the improved approach weights the input variables before mapping it into a scalar form. The weights can be obtained using universal optimization algorithms. Generally, only local optimal weights are obtained. Even so, performance of identification can be improved.
Predictive depth coding of wavelet transformed images
Lehtinen, Joonas
1999-10-01
In this paper, a new prediction based method, predictive depth coding, for lossy wavelet image compression is presented. It compresses a wavelet pyramid composition by predicting the number of significant bits in each wavelet coefficient quantized by the universal scalar quantization and then by coding the prediction error with arithmetic coding. The adaptively found linear prediction context covers spatial neighbors of the coefficient to be predicted and the corresponding coefficients on lower scale and in the different orientation pyramids. In addition to the number of significant bits, the sign and the bits of non-zero coefficients are coded. The compression method is tested with a standard set of images and the results are compared with SFQ, SPIHT, EZW and context based algorithms. Even though the algorithm is very simple and it does not require any extra memory, the compression results are relatively good.
Institute of Scientific and Technical Information of China (English)
张邻
2015-01-01
多分簇网络是蜂窝通信和移动数据传输的混合产物,多分簇网络流量具有时变耦合特性,传统方法采用功率谱局部特征分析方法进行流量的特征检测,效果不好.提出一种基于小波尺度耦合和粒子群优化分析的多分簇网络变步长检测算法,采用粒子群优化算法进行多分簇网络流量的特征提取和编码分析,采用小波尺度耦合方法变步长检测,引入小波变换,进行流量序列的尺度耦合分析,采用自适应变步长方法去除流量特征的虚假分量.仿真结果表明,采用算法进行网络流量的检测,能有效识别不同尺度下的网络流量特征,在流量预测中,通过变步长自适应控制,使得收敛速度很快,流量准确预测精概率为1,检测性能较好.%Multi cluster network is a mixed product of cellular communications and mobile data transmission, multi cluster network traffic with time-varying coupling characteristics, traditional methods of the power spectrum local feature analysis method for the detection of flow characteristics, the effect is not good. A step detection algorithm based on wavelet multi-scale coupling and particle group optimization analysis of multi cluster network, the particle swarm optimization algorithm for multi cluster network traffic feature extraction and coding analysis, variable step size detection using wavelet multi-scale coupling method, the introduction of wavelet transform, scale coupling analysis of flow series is conducted, using adap-tive variable step size method to remove false component flow characteristics is proposed in this paper. Simulation results show that the algorithm for the detection of network traffic, it can effectively identify different scale network traffic charac-teristics, in the traffic prediction, the variable step size adaptive control, the convergence speed is very fast and accurate flow forecasting precision with probability 1, it has good detection performance.
Generalized Tree-Based Wavelet Transform
Ram, Idan; Cohen, Israel
2010-01-01
In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in \\cite{gavish2010mwot}, and it is similarly defined via a hierarchical tree, which is assumed to capture the geometry and structure of the input data. It is applied to the data using a multiscale filtering and decimation scheme, which can employ different wavelet filters. We propose a tree construction method which results in efficient representation of the input function in the transform domain. We show that the proposed transform is more efficient than both the 1D and 2D separable wavelet transforms in representing images. We also explore the application of the proposed transform to image denoising, and show that combined with a subimage averaging scheme, it achieves denoising results which are similar to the ones obtained with the K-SVD algorithm.
Combining Wavelet Transform and Hidden Markov Models for ECG Segmentation
Directory of Open Access Journals (Sweden)
Jérôme Boudy
2007-01-01
Full Text Available This work aims at providing new insights on the electrocardiogram (ECG segmentation problem using wavelets. The wavelet transform has been originally combined with a hidden Markov models (HMMs framework in order to carry out beat segmentation and classification. A group of five continuous wavelet functions commonly used in ECG analysis has been implemented and compared using the same framework. All experiments were realized on the QT database, which is composed of a representative number of ambulatory recordings of several individuals and is supplied with manual labels made by a physician. Our main contribution relies on the consistent set of experiments performed. Moreover, the results obtained in terms of beat segmentation and premature ventricular beat (PVC detection are comparable to others works reported in the literature, independently of the type of the wavelet. Finally, through an original concept of combining two wavelet functions in the segmentation stage, we achieve our best performances.
Hermitian hat wavelet design for singularity detection in the Paraguay river-level data analyses
Szu, Harold H.; Hsu, Charles C.; Sa, Leonardo D.; Li, Weigang
1997-04-01
The direct differentiation of a noisy signal ds/dt is known to be inaccurate. Differentiation can be improved by employing the Dirac (delta) -function introduced into a convolution product denoted by (direct product) and then integrated by parts: ds/dt equals ds/dt (direct product) (delta) equals - s (direct product) d(delta) /dt. The Schwartz Gaussian representation of the delta function is then explicitly used in the differentiation. It turns out that such a convolution approach to the first and the second derivatives produces a pair of mother wavelets the combination of which is the complex generalization of the Mexican hat called a Hermitian hat wavelet. It is shown that the Hermitian filter is a single oscillation wavelet having much lower frequency bandwidth than the Mortlet or Gabor wavelet. As a result of Nyquist theorem, a fewer number of grid points would be needed for the discrete convolution operation. Therefore, the singularity characteristic will not be overly smeared and the noise can be smoothed away. The phase plot of the Hermitian wavelet transform in terms of the time scale and frequency domains reveal a bifurcation discontinuity of a noisy cusp singularity at the precise location of the singularity as well as the scale nature of the underlying dynamics. This phase plot is defined as (theta) (t/a) equals tan-1 [(ds/dt)/(-d2s/dt2] equals tan-1 [((d(delta) (t/a)dt) (direct product) s)/((d2(delta) (t/a)/dt2) (direct product) s)] applied to a real world data of the Paraguay river levels.
Applications of Multidimensional Wavelet Filtering in Geosciences
Yuen, D. A.; Vincent, A. P.; Kido, M.
2001-12-01
Today we are facing a severe crisis of being flooded with huge amounts of data being generated by higher-resolution numerical simulations , laboratory instrumentions and satellite observations. Since there is no way one can visualize the full data set, we must extract essential features from the data-set. One way of addressing this problem is to use mathematical filters , such as multidimensional wavelets. We present imaging results in the geosciences based on using multidimensional Gaussian wavelets as a filter. This approach has been applied to a wide-range of problems, which span from the nanoscale in mineral surfaces imaged by atomic force microscopy to hundreds of kilometers in geoidal undulations determined from satellite orbits or small-scale plumes in high Rayleigh number convection. Besides decomposing the field under consideration into various scales , called a scalogram, we have also constructed two-dimensional maps, delineating the spatial distributions of the maximum of the wavelet transformed quantity E-max and the associated local wave-number. We have generalized the application of multidimensional wavelets to quantify in terms of a two-dimensional map the correlation C for two multidimensional fields A and B. We will show a simple 2D isotropic wavelet-like transform for a spherical surface. We have analyzed the transformed geoid data with a band-pass filter in the spherical harmonic domain and have shown the equivalency of the two representations. This spherical wavelet-like filter can be applied also to problems in planetary science, such as the surface topography and geoid of other planetary bodies, like Mars.
Schrödinger like equation for wavelets
Directory of Open Access Journals (Sweden)
A. Zúñiga-Segundo
2016-01-01
Full Text Available An explicit phase space representation of the wave function is build based on a wavelet transformation. The wavelet transformation allows us to understand the relationship between s − ordered Wigner function, (or Wigner function when s = 0, and the Torres-Vega-Frederick’s wave functions. This relationship is necessary to find a general solution of the Schrödinger equation in phase-space.
Modified scaling function projective synchronization of chaotic systems
Xu, Yu-Hua; Zhou, Wu-Neng; Fang, Jian-An
2011-09-01
This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.
The use of wavelet transforms in the solution of two-phase flow problems
Energy Technology Data Exchange (ETDEWEB)
Moridis, G.J. [Lawrence Berkeley Lab., CA (United States); Nikolaou, M.; You, Yong [Texas A& M Univ., College Station, TX (United States). Dept. of Chemical Engineering
1994-10-01
In this paper we present the use of wavelets to solve the nonlinear Partial Differential.Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt chance, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigational any spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. We determine that the Chui-Wang, wavelets and a collocation method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. Our results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts.
Wavelet Transform Modulus Maxima-Based Robust Digital Image Watermarking in Wavelet Domain
Institute of Scientific and Technical Information of China (English)
LUO Ting; HONG Fan
2009-01-01
A new robust watermarking approach was proposed in 2D continuous wavelet domain (CWT).The watermark is embedded into the large coefficients in the middle band of wavelet transform modulus maxima (WTMM) of the host image.After possible attacks,the watermark is then detected and extracted by correlation analysis.Compared with other wavelet domain watermarking approaches,the WTMM approach can endow the image with both rotation and shift invariant properties.On the other hand,scale invariance is achieved with the geometric normalization during watermark detection.Case studies involve various attacks such as shifting,lossy compression,scaling,rotation and median filtering on the watermarked image,and the result shows that the approach is robust to these attacks.
Wavelet-Based Techniques for the Gamma-Ray Sky
McDermott, Samuel D; Cholis, Ilias; Lee, Samuel K
2015-01-01
We demonstrate how the image analysis technique of wavelet decomposition can be applied to the gamma-ray sky to separate emission on different angular scales. New structures on scales that differ from the scales of the conventional astrophysical foreground and background uncertainties can be robustly extracted, allowing a model-independent characterization with no presumption of exact signal morphology. As a test case, we generate mock gamma-ray data to demonstrate our ability to extract extended signals without assuming a fixed spatial template. For some point source luminosity functions, our technique also allows us to differentiate a diffuse signal in gamma-rays from dark matter annihilation and extended gamma-ray point source populations in a data-driven way.
Lecture notes on wavelet transforms
Debnath, Lokenath
2017-01-01
This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these ...
Wavelet transformation to determine impedance spectra of lithium-ion rechargeable battery
Hoshi, Yoshinao; Yakabe, Natsuki; Isobe, Koichiro; Saito, Toshiki; Shitanda, Isao; Itagaki, Masayuki
2016-05-01
A new analytical method is proposed to determine the electrochemical impedance of lithium-ion rechargeable batteries (LIRB) from time domain data by wavelet transformation (WT). The WT is a waveform analysis method that can transform data in the time domain to the frequency domain while retaining time information. In this transformation, the frequency domain data are obtained by the convolution integral of a mother wavelet and original time domain data. A complex Morlet mother wavelet (CMMW) is used to obtain the complex number data in the frequency domain. The CMMW is expressed by combining a Gaussian function and sinusoidal term. The theory to select a set of suitable conditions for variables and constants related to the CMMW, i.e., band, scale, and time parameters, is established by determining impedance spectra from wavelet coefficients using input voltage to the equivalent circuit and the output current. The impedance spectrum of LIRB determined by WT agrees well with that measured using a frequency response analyzer.
A NOTE ON FINITE ELEMENT WAVELETS
Institute of Scientific and Technical Information of China (English)
谌秋辉; 陈翰麟
2001-01-01
The refinability and approximation order of finite element multi-scale vector are discussed in [1]. But the coefficients in the conditions of approximation order of finite element multi-scale vector are incorrect there. The main purpose of this note is to make a correction of the error in the main result of [1]. These coefficients are very important for the properties of wavelets, such as vanishing moments and regularity.
Wavelet transform in electrocardiography--data compression.
Provazník, I; Kozumplík, J
1997-06-01
An application of the wavelet transform to electrocardiography is described in the paper. The transform is used as a first stage of a lossy compression algorithm for efficient coding of rest ECG signals. The proposed technique is based on the decomposition of the ECG signal into a set of basic functions covering the time-frequency domain. Thus, non-stationary character of ECG data is considered. Some of the time-frequency signal components are removed because of their low influence to signal characteristics. Resulting components are efficiently coded by quantization, composition into a sequence of coefficients and compression by a run-length coder and a entropic Huffman coder. The proposed wavelet-based compression algorithm can compress data to average code length about 1 bit/sample. The algorithm can be also implemented to a real-time processing system when wavelet transform is computed by fast linear filters described in the paper.
Fingerprint verification based on wavelet subbands
Huang, Ke; Aviyente, Selin
2004-08-01
Fingerprint verification has been deployed in a variety of security applications. Traditional minutiae detection based verification algorithms do not utilize the rich discriminatory texture structure of fingerprint images. Furthermore, minutiae detection requires substantial improvement of image quality and is thus error-prone. In this paper, we propose an algorithm for fingerprint verification using the statistics of subbands from wavelet analysis. One important feature for each frequency subband is the distribution of the wavelet coefficients, which can be modeled with a Generalized Gaussian Density (GGD) function. A fingerprint verification algorithm that combines the GGD parameters from different subbands is proposed to match two fingerprints. The verification algorithm in this paper is tested on a set of 1,200 fingerprint images. Experimental results indicate that wavelet analysis provides useful features for the task of fingerprint verification.
Use of wavelet in specifying optics
Institute of Scientific and Technical Information of China (English)
Zhi Yang; Yifan Dai; Guilin Wang
2007-01-01
Using power spectral density (PSD) function to specify large aperture optical components' quality of laser system is universal. But it cannot provide effective guidance to eliminate certain frequency segment error.In order to solve this problem, two-dimensional discrete wavelet transform (2D-DWT) is used to separate frequency segment error and detect the corresponding region of certain frequency segment error, which is used as feedback to a machining process. The experimental results show that the corresponding region of certain frequency segment can be found and machining can be guided effectively by using wavelet.
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
Wavelet approach to accelerator problems. 1: Polynomial dynamics
Energy Technology Data Exchange (ETDEWEB)
Fedorova, A.; Zeitlin, M. [Russian Academy of Sciences, St. Petersburg (Russian Federation). Inst. of Problems of Mechanical Engineering; Parsa, Z. [Brookhaven National Lab., Upton, NY (United States). Dept. of Physics
1997-05-01
This is the first part of a series of talks in which the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case they have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parameterized by solutions of two reduced algebraical problems, one is nonlinear and the second is some linear problem, which is obtained from one of the next wavelet constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the method of Connection Coefficients. In this paper the authors consider the problem of calculation of orbital motion in storage rings. The key point in the solution of this problem is the use of the methods of wavelet analysis, relatively novel set of mathematical methods, which gives one a possibility to work with well-localized bases in functional spaces and with the general type of operators (including pseudodifferential) in such bases.
On robust kalman filtering with using wavelet analysis
Lobach, V. I.
2013-01-01
One presents a nonlinear filtering algorithm that propagates the entire condi- tional probability density functions. These functions are recursively computed in efficient manner using the discrete wavelet transform. With the multiresolution analysis we can speed up the computation by ignoring the high-frequency details of the probability density function up to a certain level. The level of the wavelet decomposition can be determined at each time step adaptively.
Target recognition by wavelet transform
Li Zheng Dong; He Wu Liang; Pei Chun Lan; Peng Wen; SongChen; Zheng Xiao Dong
2002-01-01
Wavelet transform has an important character of multi-resolution power, which presents pyramid structure, and this character coincides the way by which people distinguish object from coarse to fineness and from large to tiny. In addition to it, wavelet transform benefits to reducing image noise, simplifying calculation, and embodying target image characteristic point. A method of target recognition by wavelet transform is provided
Spatial verification using wavelet transforms: a review
Weniger, Michael; Kapp, Florian; Friederichs, Petra
2017-01-01
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet transforms offer an effective framework to decompose spatial data into separate (and possibly orthogonal) scales and directions. Most wavelet based spatial verification techniques have been developed or refined in the last decade and concentrate on assessing forecast performance (i.e. forecast skill or forecast error) on distinct physical scales. Particularly during the last five years, a significant growth in meteorological applications could be observed. However, a comparison with other scientific fields such as feature detection, image fusion, texture analysis, or facial and biometric recognition, shows that there is still a considerable, currently unused potential to derive useful diagnostic information. In order to tab the full potential of wavelet analysis, we revise the state-of-the art in one- and two-dimensional wavelet analysis and its application with emphasis on spatial verification. We further use a technique developed for texture analysis in the context of high-resolution quantitative precipitation forecasts, which is able to assess structural characteristics of the precipitation fields and allows efficient clustering of ensemble data.
Characterization and simulation of gunfire with wavelets
Energy Technology Data Exchange (ETDEWEB)
Smallwood, D.O.
1998-09-01
Gunfire is used as an example to show how the wavelet transform can be used to characterize and simulate nonstationary random events when an ensemble of events is available. The response of a structure to nearby firing of a high-firing rate gun has been characterized in several ways as a nonstationary random process. The methods all used some form of the discrete fourier transform. The current paper will explore a simpler method to describe the nonstationary random process in terms of a wavelet transform. As was done previously, the gunfire record is broken up into a sequence of transient waveforms each representing the response to the firing of a single round. The wavelet transform is performed on each of these records. The mean and standard deviation of the resulting wavelet coefficients describe the composite characteristics of the entire waveform. It is shown that the distribution of the wavelet coefficients is approximately Gaussian with a nonzero mean and that the standard deviation of the coefficients at different times and levels are approximately independent. The gunfire is simulated by generating realizations of records of a single-round firing by computing the inverse wavelet transform from Gaussian random coefficients with the same mean and standard deviation as those estimated from the previously discussed gunfire record. The individual realizations are then assembled into a realization of a time history of many rounds firing. A second-order correction of the probability density function (pdf) is accomplished with a zero memory nonlinear (ZMNL) function. The method is straightforward, easy to implement, and produces a simulated record very much like the original measured gunfire record.
Image compression with embedded wavelet coding via vector quantization
Katsavounidis, Ioannis; Kuo, C.-C. Jay
1995-09-01
In this research, we improve Shapiro's EZW algorithm by performing the vector quantization (VQ) of the wavelet transform coefficients. The proposed VQ scheme uses different vector dimensions for different wavelet subbands and also different codebook sizes so that more bits are assigned to those subbands that have more energy. Another feature is that the vector codebooks used are tree-structured to maintain the embedding property. Finally, the energy of these vectors is used as a prediction parameter between different scales to improve the performance. We investigate the performance of the proposed method together with the 7 - 9 tap bi-orthogonal wavelet basis, and look into ways to incorporate loseless compression techniques.
Comparative performance of wavelets and JPEG coders at high quality
Algazi, V. Ralph; Estes, Robert R., Jr.
1997-04-01
In recent work, we have examined the performance of wavelet coders using a perceptually relevant image quality metric, the picture quality scale (PQS). In that study, we considered some of the design options available with respect to choice of wavelet basis, quantizer, and method for error- free encoding of the quantized coefficients, including the EZW methodology. A specific combination of these design options provides the best trade off between performance and PQS quality. Here, we extend this comparison by evaluating the performance of JPEG and the previously chosen optimal wavelet scheme, focusing principally on the high quality range.
Conductance calculations with a wavelet basis set
DEFF Research Database (Denmark)
Thygesen, Kristian Sommer; Bollinger, Mikkel; Jacobsen, Karsten Wedel
2003-01-01
. The linear-response conductance is calculated from the Green's function which is represented in terms of a system-independent basis set containing wavelets with compact support. This allows us to rigorously separate the central region from the contacts and to test for convergence in a systematic way...
Novel Fractional Wavelet Transform with Closed-Form Expression
Directory of Open Access Journals (Sweden)
K. O. O. Anoh
2014-01-01
Full Text Available A new wavelet transform (WT is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT. The transform permits the identification of a transformed function based on the fractional rotation in time-frequency plane. The fractional rotation is then used to identify individual fractional daughter wavelets. This study is, for convenience, limited to one-dimension. Approach for discussing two or more dimensions is shown.
Pearlman, William A
2013-01-01
This book explains the stages necessary to create a wavelet compression system for images and describes state-of-the-art systems used in image compression standards and current research. It starts with a high level discussion of the properties of the wavelet transform, especially the decomposition into multi-resolution subbands. It continues with an exposition of the null-zone, uniform quantization used in most subband coding systems and the optimal allocation of bitrate to the different subbands. Then the image compression systems of the FBI Fingerprint Compression Standard and the JPEG2000 S
Wavelets on Planar Tesselations
Energy Technology Data Exchange (ETDEWEB)
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-02-25
We present a new technique for progressive approximation and compression of polygonal objects in images. Our technique uses local parameterizations defined by meshes of convex polygons in the plane. We generalize a tensor product wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tessellation rather than, for example, a uniform rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.
Coherent vorticity extraction in turbulent boundary layers using orthogonal wavelets
Energy Technology Data Exchange (ETDEWEB)
Khujadze, George; Oberlack, Martin [Chair of Fluid Dynamics, Technische Universitaet Darmstadt (Germany); Yen, Romain Nguyen van [Institut fuer Mathematik, Freie Universitaet Berlin (Germany); Schneider, Kai [M2P2-CNRS and CMI, Universite de Provence, Marseille (France); Farge, Marie, E-mail: khujadze@fdy.tu-darmstadt.de [LMD-IPSL-CNRS, Ecole Normale Superieure, Paris (France)
2011-12-22
Turbulent boundary layer data computed by direct numerical simulation are analyzed using orthogonal anisotropic wavelets. The flow fields, originally given on a Chebychev grid, are first interpolated on a locally refined dyadic grid. Then, they are decomposed using a wavelet basis, which accounts for the anisotropy of the flow by using different scales in the wall-normal direction and in the planes parallel to the wall. Thus the vorticity field is decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. It is shown that less than 1% of the coefficients retain the coherent structures of the flow, while the majority of the coefficients corresponds to a structureless, i.e., noise-like background flow. Scale-and direction-dependent statistics in wavelet space quantify the flow properties at different wall distances.
The Cost Function and Scale Economies in Academic Research Libraries.
Liu, Lewis G.
2003-01-01
This empirical research examined scale economies of academic research libraries and developed a total cost function for estimating economies of scale. Suggests that libraries in general, and academic research libraries in particular, are information provision organizations that provide multiproducts and multiservices. Findings indicate that slight…
Petrov, N. P.; Davis, A. B.
2001-12-01
Semi-discrete wavelet transforms are discrete in scale, as in Mallat's multi-resolution analysis, but continuous in position. The number of coefficients and algorithmic complexity then grows only as NlogN where N is the number of points (pixels) in the time-series (image). The redundancy of this representation at each scale has been exploited in denoising and data compression applications but we see it here as an asset when cumulating spatial statistics. Following Arnéodo, the wavelets are normalized in such a way that the scaling exponents of the moments of the coefficients are the same as for structure functions at all orders, at least in nonstationary/stationary-increment signals. We apply 1D and 2D semi-discrete transforms to remote sensing data on cloud structure from a variety of sources: NASA's MODerate Imaging Spectroradiometer (MODIS) on Terra and Thematic Mapper (TM) on LandSat; high-resolution cloud scenes from DOE's Multispectral Thermal Imager (MTI); and an upward-looking mm-radar at one of DOE's climate observation sites supporting the Atmospheric Radiation Measurement (ARM) Program. We show that the scale-dependence of the variance of the wavelet coefficients is always a better discriminator of transition from stationary to nonstationary behavior than conventional methods based on auto-correlation analysis, 2nd-order structure function (a.k.a. the semi-variogram), or spectral analysis. Examples of stationary behavior are (delta-correlated) instrumental noise and large-scale decorrelation of cloudiness; here wavelet coefficients decrease with increasing scale. Examples of nonstationary behavior are the predominant turbulent structure of cloud layers as well as instrumental or physical smoothing in the data; here wavelet coefficients increase with scale. In all of these regimes, we have theoretical expectations and/or empirical evidence of power-law relations for wavelet statistics with respect to scale as is expected in physical (finite-scaling
Wavelets theory, algorithms, and applications
Montefusco, Laura
2014-01-01
Wavelets: Theory, Algorithms, and Applications is the fifth volume in the highly respected series, WAVELET ANALYSIS AND ITS APPLICATIONS. This volume shows why wavelet analysis has become a tool of choice infields ranging from image compression, to signal detection and analysis in electrical engineering and geophysics, to analysis of turbulent or intermittent processes. The 28 papers comprising this volume are organized into seven subject areas: multiresolution analysis, wavelet transforms, tools for time-frequency analysis, wavelets and fractals, numerical methods and algorithms, and applicat
monthly energy consumption forecasting using wavelet analysis and ...
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paper, a wavelet transform and radial basis function neural network based energy forecast model is developed to .... These prop- erties lead to quicker learning in comparison to ..... Machine Learning and Cybernetics,. IEEE Transactions, 8: ...
Elastic wavelets and their application to problems of solitary wave propagation
Directory of Open Access Journals (Sweden)
Cattani, Carlo
2008-03-01
Full Text Available The paper can be referred to that direction in the wavelet theory, which was called by Kaiser "the physical wavelets". He developed the analysis of first two kinds of physical wavelets - electromagnetic (optic and acoustic wavelets. Newland developed the technique of application of harmonic wavelets especially for studying the harmonic vibrations. Recently Cattani and Rushchitsky proposed the 4th kind of physical wavelets - elastic wavelets. This proposal was based on three main elements: 1. Kaiser's idea of constructing the physical wavelets on the base of specially chosen (admissible solutions of wave equations. 2. Developed by one of authors theory of solitary waves (with profiles in the form of Chebyshov-Hermite functions propagated in elastic dispersive media. 3. The theory and practice of using the wavelet "Mexican Hat" system, the mother and farther wavelets (and their Fourier transforms of which are analytically represented as the Chebyshov-Hermite functions of different indexes. An application of elastic wavelets to studying the evolution of solitary waves of different shape during their propagation through composite materials is shown on many examples.
Dyadic Bivariate Fourier Multipliers for Multi-Wavelets in L2(R2)
Institute of Scientific and Technical Information of China (English)
Zhongyan Li∗; Xiaodi Xu
2015-01-01
The single 2 dilation orthogonal wavelet multipliers in one dimensional case and single A-dilation (where A is any expansive matrix with integer entries and|detA|=2) wavelet multipliers in high dimensional case were completely characterized by the Wutam Consortium (1998) and Z. Y. Li, et al. (2010). But there exist no more results on orthogonal multivariate wavelet matrix multipliers corresponding integer expansive dilation matrix with the absolute value of determinant not 2 in L2(R2). In this paper, we choose as the dilation matrix and consider the 2I2-dilation orthogonal multivariate wavelet Y={y1,y2,y3}, (which is called a dyadic bivariate wavelet) multipliers. We call the 3×3 matrix-valued function A(s)=[ fi,j(s)]3×3, where fi,j are measurable functions, a dyadic bivariate matrix Fourier wavelet multiplier if the inverse Fourier transform of A(s)(cy1(s),cy2(s),cy3(s))⊤ = ( b g1(s), b g2(s), b g3(s))⊤ is a dyadic bivariate wavelet whenever (y1,y2,y3) is any dyadic bivariate wavelet. We give some conditions for dyadic matrix bivariate wavelet multipliers. The results extended that of Z. Y. Li and X. L. Shi (2011). As an application, we construct some useful dyadic bivariate wavelets by using dyadic Fourier matrix wavelet multipliers and use them to image denoising.
Identification of Electrooculography Signals Frequency Energy Distribution Using Wavelet Algorithm
Directory of Open Access Journals (Sweden)
W. M. Bukhari
2011-01-01
Full Text Available Problem statement: The time frequency analysis of non-stationary signals has been the considerable research effort in recent years. Wavelet transform is one of the favored tool for the analyzing the biomedical signals. Approach: We describe the identification of Electro-Oculograph (EOG signals of eye movement potentials by using wavelet algorithm which gives a lot of information than FFT. The capability of wavelet transform was to distribute the signal energy with the change of time in different frequency bands. This will showed the characteristic of the signals since energy was an important physical variable in signal analysis. The EOG signals were captured using electrodes placed on the forehead around the eyes to record the eye movements. The wavelet features used to determine the characteristic of eye movement waveform. This technique adopted because it was a non-invasive, inexpensive and accurate. The new technology enhancement has allowed the EOG signals captured using the Neuronal EEG-9200. The recorded data was composed of an eye movement toward four directions, i.e., downward, upward, leftward and rightward. The proposed analysis for each eyes signal is analyzed by using Wavelet Transform (WT with energy algorithm and by comparing the energy distribution with the change of time and frequency of each signal. Results: A wavelet Scalogram was plotted to display the different percentages of energy for each wavelet coefficient towards different movement. Conclusion: From the result, it is proved that the different EOG signals exhibit differences in signals energy with their corresponding scale such as leftward with scale 6 (8- 16Hz, rightward with scale 8 (2-4Hz, downward with scale 9 (1-2Hz and upward with level 7 (4-8Hz. Statistically, the results in this study indicate that there are 93% (averages significance differences in the extracted features of wavelet Scalogram analysis.
Institute of Scientific and Technical Information of China (English)
邵骏
2013-01-01
针对传统水文相关分析的局限性,将交叉小波变换应用于水文时间序列的相关分析.采用交叉小波功率谱和凝聚谱分析伊犁河雅马渡水文站实测年径流量与4个影响因子之间的联合统计特征及其在时频域中的相关关系,揭示其在不同时间和频率尺度上的相关程度和细部特征.研究结果表明,与传统的相关系数只能从总体上考察两个时间序列的相关关系相比,交叉小波变换能够从时域和频率两方面同时考察两者的相关振荡随频率和时间后延的变化细节、局部特征和位相差异,在水文相关分析方面具有较好的应用效果.%As traditional hydrologic correlation analysis can only exhibit the basic relationship of two time series, a new multi-scale correlation analysis method based on cross wavelet transform is presented. This new approach was used to study the associated statistical characteristics and time frequency correlations of the annual runoff at the Ya Madu station with annual rainfall, monthly mean zonal circulation index, monthly mean radial circulation index and solar radio flux. Cross wavelet transform and wavelet coherence for examining the relationships of two series in both the time and frequency domains are discussed in this paper. The results show that this method possesses an ability to distinguish coupling signals and an excellence to describe the distribution of coupling signals in time-frequency space and it provides a new analytic method to hydrological time series correlation analysis.
WAVELET ANALYSIS OF ABNORMAL ECGS
Directory of Open Access Journals (Sweden)
Vasudha Nannaparaju
2014-02-01
Full Text Available Detection of the warning signals by the heart can be diagnosed from ECG. An accurate and reliable diagnosis of ECG is very important however which is cumbersome and at times ambiguous in time domain due to the presence of noise. Study of ECG in wavelet domain using both continuous Wavelet transform (CWT and discrete Wavelet transform (DWT, with well known wavelet as well as a wavelet proposed by the authors for this investigation is found to be useful and yields fairly reliable results. In this study, Wavelet analysis of ECGs of Normal, Hypertensive, Diabetic and Cardiac are carried out. The salient feature of the study is that detection of P and T phases in wavelet domain is feasible which are otherwise feeble or absent in raw ECGs.
Institute of Scientific and Technical Information of China (English)
朱俊敏; 张潇; 王旌阳; 吴粤北
2009-01-01
在数字化时代,音频的转录或录制都会引入噪音,但是历史音频保存和音频资料处理需要纯净的音频信号,因此音频降噪研究有着重要的现实意义.首先介绍了二进小波和奇异性指数,并阐述了尺度跟踪和模极大值重构等理论,在Mallat工作的基础上,提出了一种基于小波滤波的音频降噪方法.该方法首先引入补偿因子削减二进小波变换对系数造成的影响,并计算带噪音频的小波系数和模极大值;然后基于信号和噪声奇异指数不同的特点,结合阈值降噪和尺度跟踪理论,采用层间相关搜索去除噪声的模极大值;最后利用交替投影算法,重建音频信号.用该方法处理带click和hiss噪声的音频信号,跟小波阈值方法和小波包方法相比,能达到较好的听觉效果和信噪比.同时观察信号的波形图及模极大值演示图,发现该方法都表现出优异的降噪效果.%Audio recording or transcription inevitably brings in noise, so audio denoising is crucial for data processing and preservation. There are many existing techniques with respect to audio denoising based on wavelet transformation. An improved algorithm was provided based on three kinds of techniques: dyadic wavelet, scale tracking theory and modulus maximum theory. The novelties of the algorithm lie in the following: the compensation factors is introduced in order to reduce the influence of scale discretization; the interlayer correlation searching is used to eliminate noise according to the modulus maximum; and the original signal is reconstructed by using alternating projection algorithm. As an attempt, the algorithm was adopted to process audio signals with click and hiss noise, and better results were achieved, comparing with the wavelet threshold and wavelet packet algorithms in terms of comfort degree of hearing sense. By inspection with signal oscillograms and by display of modulus maxima it is verified the algorithm reduces
Music Tune Restoration Based on a Mother Wavelet Construction
Fadeev, A. S.; Konovalov, V. I.; Butakova, T. I.; Sobetsky, A. V.
2017-01-01
It is offered to use the mother wavelet function obtained from the local part of an analyzed music signal. Requirements for the constructed function are proposed and the implementation technique and its properties are described. The suggested approach allows construction of mother wavelet families with specified identifying properties. Consequently, this makes possible to identify the basic signal variations of complex music signals including local time-frequency characteristics of the basic one.
Directory of Open Access Journals (Sweden)
Liwei Liu
2014-01-01
Full Text Available Interval wavelet numerical method for nonlinear PDEs can improve the calculation precision compared with the common wavelet. A new interval Shannon wavelet is constructed with the general variational principle. Compared with the existing interval wavelet, both the gradient and the smoothness near the boundary of the approximated function are taken into account. Using the new interval Shannon wavelet, a multiscale interpolation wavelet operator was constructed in this paper, which can transform the nonlinear partial differential equations into matrix differential equations; this can be solved by the coupling technique of the wavelet precise integration method (WPIM and the variational iteration method (VIM. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical results show that this method can decrease the boundary effect greatly and improve the numerical precision in the whole definition domain compared with Yan’s method.
Directory of Open Access Journals (Sweden)
Fenghua Tian
2016-01-01
Full Text Available Cerebral autoregulation represents the physiological mechanisms that keep brain perfusion relatively constant in the face of changes in blood pressure and thus plays an essential role in normal brain function. This study assessed cerebral autoregulation in nine newborns with moderate-to-severe hypoxic–ischemic encephalopathy (HIE. These neonates received hypothermic therapy during the first 72 h of life while mean arterial pressure (MAP and cerebral tissue oxygenation saturation (SctO2 were continuously recorded. Wavelet coherence analysis, which is a time-frequency domain approach, was used to characterize the dynamic relationship between spontaneous oscillations in MAP and SctO2. Wavelet-based metrics of phase, coherence and gain were derived for quantitative evaluation of cerebral autoregulation. We found cerebral autoregulation in neonates with HIE was time-scale-dependent in nature. Specifically, the spontaneous changes in MAP and SctO2 had in-phase coherence at time scales of less than 80 min (<0.0002 Hz in frequency, whereas they showed anti-phase coherence at time scales of around 2.5 h (~0.0001 Hz in frequency. Both the in-phase and anti-phase coherence appeared to be related to worse clinical outcomes. These findings suggest the potential clinical use of wavelet coherence analysis to assess dynamic cerebral autoregulation in neonatal HIE during hypothermia.
Wave Forecasting Using Neuro Wavelet Technique
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Pradnya Dixit
2014-12-01
Full Text Available In the present work a hybrid Neuro-Wavelet Technique is used for forecasting waves up to 6 hr, 12 hr, 18 hr and 24 hr in advance using hourly measured significant wave heights at an NDBC station 41004 near the east coast of USA. The NW Technique is employed by combining two methods, Discrete Wavelet Transform and Artificial Neural Networks. The hourly data of previously measured significant wave heights spanning over 2 years from 2010 and 2011 is used to calibrate and test the models. The discrete wavelet transform of NWT analyzes frequency of signal with respect to time at different scales. It decomposes time series into low (approximate and high (detail frequency components. The decomposition of approximate can be carried out up to desired multiple levels in order to provide more detail and approximate components which provides relatively smooth varying amplitude series. The neural network is trained with decorrelated approximate and detail wavelet coefficients. The outputs of networks during testing are reconstructed back using inverse DWT. The results were judged by drawing the wave plots, scatter plots and other error measures. The developed models show reasonable accuracy in prediction of significant wave heights from 6 to 24 hours. To compare the results traditional ANN models were also developed at the same location using the same data and for same time interval.
Test Review: Barkley Deficits in Executive Functioning Scale (BDEFS)
Allee-Smith, Paula J.; Winters, Rebecca R.; Drake, Amanda; Joslin, Amanda K.
2013-01-01
The Barkley Deficits in Executive Functioning Scale (BDEFS), authored by Russell A. Barkley and published by Guilford in 2011, is an individually administered assessment tool that may be used to evaluate adults ages 18 to 81. The purpose of this measure is to screen those who may be experiencing executive functioning (EF) deficits in…
Characterization and Simulation of Gunfire with Wavelets
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David O. Smallwood
1999-01-01
Full Text Available Gunfire is used as an example to show how the wavelet transform can be used to characterize and simulate nonstationary random events when an ensemble of events is available. The structural response to nearby firing of a high-firing rate gun has been characterized in several ways as a nonstationary random process. The current paper will explore a method to describe the nonstationary random process using a wavelet transform. The gunfire record is broken up into a sequence of transient waveforms each representing the response to the firing of a single round. A wavelet transform is performed on each of these records. The gunfire is simulated by generating realizations of records of a single-round firing by computing an inverse wavelet transform from Gaussian random coefficients with the same mean and standard deviation as those estimated from the previously analyzed gunfire record. The individual records are assembled into a realization of many rounds firing. A second-order correction of the probability density function is accomplished with a zero memory nonlinear function. The method is straightforward, easy to implement, and produces a simulated record much like the measured gunfire record.
Optimization and Assessment of Wavelet Packet Decompositions with Evolutionary Computation
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Schell Thomas
2003-01-01
Full Text Available In image compression, the wavelet transformation is a state-of-the-art component. Recently, wavelet packet decomposition has received quite an interest. A popular approach for wavelet packet decomposition is the near-best-basis algorithm using nonadditive cost functions. In contrast to additive cost functions, the wavelet packet decomposition of the near-best-basis algorithm is only suboptimal. We apply methods from the field of evolutionary computation (EC to test the quality of the near-best-basis results. We observe a phenomenon: the results of the near-best-basis algorithm are inferior in terms of cost-function optimization but are superior in terms of rate/distortion performance compared to EC methods.
Modified scaling function projective synchronization of chaotic systems
Institute of Scientific and Technical Information of China (English)
Xu Yu-Hua; Zhou Wu-Neng; Fang Jian-An
2011-01-01
This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point,a periodic orbit,or even a chaotic attractor in the phase space. Based on LaSa11e's invariance set principle,the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.
Construction of compactly supported biorthogonal wavelet based on Human Visual System
Hu, Haiping; Hou, Weidong; Liu, Hong; Mo, Yu L.
2000-11-01
As an important analysis tool, wavelet transform has made a great development in image compression coding, since Daubechies constructed a kind of compact support orthogonal wavelet and Mallat presented a fast pyramid algorithm for wavelet decomposition and reconstruction. In order to raise the compression ratio and improve the visual quality of reconstruction, it becomes very important to find a wavelet basis that fits the human visual system (HVS). Marr wavelet, as it is known, is a kind of wavelet, so it is not suitable for implementation of image compression coding. In this paper, a new method is provided to construct a kind of compactly supported biorthogonal wavelet based on human visual system, we employ the genetic algorithm to construct compactly supported biorthogonal wavelet that can approximate the modulation transform function for HVS. The novel constructed wavelet is applied to image compression coding in our experiments. The experimental results indicate that the visual quality of reconstruction with the new kind of wavelet is equivalent to other compactly biorthogonal wavelets in the condition of the same bit rate. It has good performance of reconstruction, especially used in texture image compression coding.
Image denoising using least squares wavelet support vector machines
Institute of Scientific and Technical Information of China (English)
Guoping Zeng; Ruizhen Zhao
2007-01-01
We propose a new method for image denoising combining wavelet transform and support vector machines (SVMs). A new image filter operator based on the least squares wavelet support vector machines (LSWSVMs) is presented. Noisy image can be denoised through this filter operator and wavelet thresholding technique. Experimental results show that the proposed method is better than the existing SVM regression with the Gaussian radial basis function (RBF) and polynomial RBF. Meanwhile, it can achieve better performance than other traditional methods such as the average filter and median filter.
Minimum-energy wavelet frame on the interval
Institute of Scientific and Technical Information of China (English)
GAO XiePing; CAO ChunHong
2008-01-01
The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper.They are as follows:1) give the definition of interval minimum-energy wavelet frame;2) give the necessary and sufficient conditions for the minimum-energy frames for L2[0,1];3) present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support γ;4) give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1].
Analyzing Planck-Like Data with Wavelets
Sanz, J. L.; Barreiro, R. B.; Cayón, L.; Martinez-González, E.; Ruiz, G. A.; Diaz, F. J.; Argüeso, F.; Toffolatti, L.
Basics on the continuous and discrete wavelet transform with two scales are outlined. We study maps representing anisotropies in the cosmic microwave background radiation (CMB) and the relation to the standard approach, based on the Cl's, is establised through the introduction of a wavelet spectrum. We apply this technique to small angular scale CMB map simulations of size 12.8 x 12.8 degrees and filtered with a 4'.5 Gaussian beam. This resolution resembles the experimental one expected for future high resolution experiments (e.g. the Planck mission). We consider temperature fluctuations derived from standard, open and flat-Lambda CDM models. We also introduce Gaussian noise (uniform and non-uniform) at different S/N levels and results are given regarding denoising.
Some Contributions to Wavelet Based Image Coding
2000-07-01
MSE or PSNR. However, it is noted that JZW does not implement the embedded property as in EZW and SPIHT and that the embedded property can be...achieved by passing the JND quantized wavelet coefficients to EZW or SPIHT. It is noted that the lowest frequency (the coarsest scale) band (LL band) is the...other higher frequency subbands can be efficiently encoded using our zero-tree encoding scheme which is derived from EZW and [improved version of EZW by
Addison, Paul S
2015-01-01
A novel method of identifying stable phase coupling behavior of two signals within the wavelet transform time-frequency plane is presented. The technique employs the cross-wavelet transform to provide a map of phase coupling followed by synchrosqueezing to collect the stable phase regime information. The resulting synchrosqueezed cross-wavelet transform method (Synchro-CrWT) is illustrated using a synthetic signal and then applied to the analysis of the relationship between biosignals used in the analysis of cerebral autoregulation function.
A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis
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Xingwu Zhang
2014-01-01
Full Text Available A stochastic finite element method based on B-spline wavelet on the interval (BSWI-SFEM is presented for static analysis of 1D and 2D structures in this paper. Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. By means of virtual work principle and BSWI, the wavelet finite elements of beam, plate, and plane rigid frame are obtained. Combining the Monte Carlo method and the constructed BSWI elements together, the BSWI-SFEM is formulated. The constructed BSWI-SFEM can deal with the problems of structural response uncertainty caused by the variability of the material properties, static load amplitudes, and so on. Taking the widely used Timoshenko beam, the Mindlin plate, and the plane rigid frame as examples, numerical results have demonstrated that the proposed method can give a higher accuracy and a better constringency than the conventional stochastic finite element methods.
Wavelet-based correlations of impedance cardiography signals and heart rate variability
Podtaev, Sergey; Dumler, Andrew; Stepanov, Rodion; Frick, Peter; Tziberkin, Kirill
2010-04-01
The wavelet-based correlation analysis is employed to study impedance cardiography signals (variation in the impedance of the thorax z(t) and time derivative of the thoracic impedance (- dz/dt)) and heart rate variability (HRV). A method of computer thoracic tetrapolar polyrheocardiography is used for hemodynamic registrations. The modulus of wavelet-correlation function shows the level of correlation, and the phase indicates the mean phase shift of oscillations at the given scale (frequency). Significant correlations essentially exceeding the values obtained for noise signals are defined within two spectral ranges, which correspond to respiratory activity (0.14-0.5 Hz), endothelial related metabolic activity and neuroendocrine rhythms (0.0095-0.02 Hz). Probably, the phase shift of oscillations in all frequency ranges is related to the peculiarities of parasympathetic and neuro-humoral regulation of a cardiovascular system.
Application of Wavelet Finite Element Method to Simulation of the Temperature Field of Copier Paper
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet-based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method,which provides a new method for improving the copier properties.
Sub-50 nm Scale to Micrometer Scale Soft Lithographic Patterning of Functional Materials
George, A.
2011-01-01
This PhD thesis addresses two major issues: 1) Fabricating nanometer-scale patterns of functional materials, 2) Extending the applicability of soft lithographic processes to a wide range of functional materials on conventional silicon substrates and flexible plastic substrates. This thesis describes
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study
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Anestis Antoniadis
2001-06-01
Full Text Available Wavelet analysis has been found to be a powerful tool for the nonparametric estimation of spatially-variable objects. We discuss in detail wavelet methods in nonparametric regression, where the data are modelled as observations of a signal contaminated with additive Gaussian noise, and provide an extensive review of the vast literature of wavelet shrinkage and wavelet thresholding estimators developed to denoise such data. These estimators arise from a wide range of classical and empirical Bayes methods treating either individual or blocks of wavelet coefficients. We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced.
The Homoclinic Orbit Solution for Functional Equation
Institute of Scientific and Technical Information of China (English)
LIU Shi-Da; FU Zun-Tao; LIU Shi-Kuo; REN Kui
2002-01-01
In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform,and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equations too.And the solitary wave exists in generalized dynamical systems and functional systems.
The Homoclinic Orbit Solution for Functional Equation
Institute of Scientific and Technical Information of China (English)
LIUShi－Da; FUZun－Tao; 等
2002-01-01
In this paper,some examples,such as iterated functional systems,scaling equation of wavelet transform,and invariant measure system,are used to show that the homoclinic orbit solutions exist in the functional equations too.And the solitary wave exists in generalized dynamical systems and functional systems.
Random seismic noise attenuation using the Wavelet Transform
Aliouane, L.; Ouadfeul, S.; Boudella, A.; Eladj, S.
2012-04-01
In this paper we propose a technique of random noises attenuation from seismic data using the discrete and continuous wavelet transforms. Firstly the discrete wavelet transform (DWT) is applied to denoise seismic data. This last is based on the threshold method applied at the modulus of the DWT. After we calculate the continuous wavelet transform of the denoised seismic seismogram, the final denoised seismic seismogram is the continuous wavelet transform coefficients at the low scale. Application at a synthetic seismic seismogram shows the robustness of the proposed tool for random noises attenuation. We have applied this idea at a real seismic data of a vertical seismic profile realized in Algeria. Keywords: Seismic data, denoising, DWT, CWT, random noise.
Directory of Open Access Journals (Sweden)
Wang Wei
2016-08-01
Full Text Available This study aims to assess the vigilance task-related change in connectivity in healthy adults using wavelet phase coherence (WPCO analysis of near-infrared spectroscopy signals (NIRS. NIRS is a non-invasive neuroimaging technique for assessing brain activity. Continuous recordings of the NIRS signals were obtained from the prefrontal cortex (PFC and sensorimotor cortical areas of 20 young healthy adults (24.9±3.3 years during a 10-min resting state and a 20-min vigilance task state. The vigilance task was used to simulate driving mental load by judging three random numbers (i.e., whether odd numbers. The task was divided into two sessions: the first 10 minutes (Task t1 and the second 10 minutes (Task t2. The WPCO of six channel pairs were calculated in five frequency intervals: 0.6–2 Hz (I, 0.145–0.6 Hz (II, 0.052–0.145 Hz (III, 0.021–0.052 Hz (IV, and 0.0095–0.021 Hz (V. The significant WPCO formed global connectivity (GC maps in intervals I and II and functional connectivity (FC maps in intervals III to V. Results show that the GC levels in interval I and FC levels in interval III were significantly lower in the Task t2 than in the resting state (p < 0.05, particularly between the left PFC and bilateral sensorimotor regions. Also, the reaction time shows an increase in Task t2 compared with that in Task t1. However, no significant difference in WPCO was found between Task t1 and resting state. The results showed that the change in FC at the range of 0.6-2 Hz was not attributed to the vigilance task pe se, but the interaction effect of vigilance task and time factors. The findings suggest that the decreased attention level might be partly attributed to the reduced GC levels between the left prefrontal region and sensorimotor area. The present results provide a new insight into the vigilance task-related brain activity.
Weak transient fault feature extraction based on an optimized Morlet wavelet and kurtosis
Qin, Yi; Xing, Jianfeng; Mao, Yongfang
2016-08-01
Aimed at solving the key problem in weak transient detection, the present study proposes a new transient feature extraction approach using the optimized Morlet wavelet transform, kurtosis index and soft-thresholding. Firstly, a fast optimization algorithm based on the Shannon entropy is developed to obtain the optimized Morlet wavelet parameter. Compared to the existing Morlet wavelet parameter optimization algorithm, this algorithm has lower computation complexity. After performing the optimized Morlet wavelet transform on the analyzed signal, the kurtosis index is used to select the characteristic scales and obtain the corresponding wavelet coefficients. From the time-frequency distribution of the periodic impulsive signal, it is found that the transient signal can be reconstructed by the wavelet coefficients at several characteristic scales, rather than the wavelet coefficients at just one characteristic scale, so as to improve the accuracy of transient detection. Due to the noise influence on the characteristic wavelet coefficients, the adaptive soft-thresholding method is applied to denoise these coefficients. With the denoised wavelet coefficients, the transient signal can be reconstructed. The proposed method was applied to the analysis of two simulated signals, and the diagnosis of a rolling bearing fault and a gearbox fault. The superiority of the method over the fast kurtogram method was verified by the results of simulation analysis and real experiments. It is concluded that the proposed method is extremely suitable for extracting the periodic impulsive feature from strong background noise.
A CLASS OF MULTIWAVELETS AND PROJECTED FRAMES FROM TWO-DIRECTION WAVELETS
Institute of Scientific and Technical Information of China (English)
李尤发; 杨守志
2014-01-01
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting Rs, s>1. We give a sufficient condition for a two-direction refinable function belonging to L2(Rs). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L2(Rs) and their biorthogonal (orthogo-nal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L2(Rs) can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L2(Rs), we can get dual (tight) two-direction wavelet frames in L2(Rm), where m≤s. From the projected dual (tight) two-direction wavelet frames in L2(Rm), symmetric dual (tight) frames in L2(Rm) can be obtained easily. In the end, an example is given to illustrate theoretical results.
Element analysis: a wavelet-based method for analysing time-localized events in noisy time series
Lilly, Jonathan M.
2017-04-01
A method is derived for the quantitative analysis of signals that are composed of superpositions of isolated, time-localized `events'. Here, these events are taken to be well represented as rescaled and phase-rotated versions of generalized Morse wavelets, a broad family of continuous analytic functions. Analysing a signal composed of replicates of such a function using another Morse wavelet allows one to directly estimate the properties of events from the values of the wavelet transform at its own maxima. The distribution of events in general power-law noise is determined in order to establish significance based on an expected false detection rate. Finally, an expression for an event's `region of influence' within the wavelet transform permits the formation of a criterion for rejecting spurious maxima due to numerical artefacts or other unsuitable events. Signals can then be reconstructed based on a small number of isolated points on the time/scale plane. This method, termed element analysis, is applied to the identification of long-lived eddy structures in ocean currents as observed by along-track measurements of sea surface elevation from satellite altimetry.
Peak center and area estimation in gamma-ray energy spectra using a Mexican-hat wavelet
Qin, Zhang-jian; Chen, Chuan; Luo, Jun-song; Xie, Xing-hong; Ge, Liang-quan; Wu, Qi-fan
2017-06-01
Wavelet analysis is commonly used to detect and localize peaks within a signal, such as in Gamma-ray energy spectra. This paper presents a peak area estimation method based on a new wavelet analysis. Another Mexican Hat Wavelet Signal (MHWS) named after the new MHWS is obtained with the convolution of a Gaussian signal and a MHWS. During the transform, the overlapping background on the Gaussian signal caused by Compton scattering can be subtracted because the impulse response function MHWS is a second-order smooth function, and the amplitude of the maximum within the new MHWS is the net height corresponding to the Gaussian signal height, which can be used to estimate the Gaussian peak area. Moreover, the zero-crossing points within the new MHWS contain the information of the Gaussian variance whose valve should be obtained when the Gaussian peak area is estimated. Further, the new MHWS center is also the Gaussian peak center. With that distinguishing feature, the channel address of a characteristic peak center can be accurately obtained which is very useful in the stabilization of airborne Gamma energy spectra. In particular, a method for determining the correction coefficient k is given, where the peak area is calculated inaccurately because the value of the scale factor in wavelet transform is too small. The simulation and practical applications show the feasibility of the proposed peak center and area estimation method.
Multiscale functions, Scale dynamics and Applications to partial differential equations
Cresson, Jacky
2015-01-01
Modeling phenomena from experimental data, always begin with a \\emph{choice of hypothesis} on the observed dynamics such as \\emph{determinism}, \\emph{randomness}, \\emph{derivability} etc. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following : \\emph{"With a finite set of data concerning a phenomenon, can we recover its underlying nature ?} From this problem, we introduce in this paper the definition of \\emph{multi-scale functions}, \\emph{scale calculus} and \\emph{scale dynamics} based on the \\emph{time-scale calculus} (see \\cite{bohn}). These definitions will be illustrated on the \\emph{multi-scale Okamoto's functions}. The introduced formalism explains why there exists different continuous models associated to an equation with different \\emph{scale regimes} whereas the equation is \\emph{scale invariant}. A typical example of such an equation, is the \\emph{Euler-Lagrange equation} and particularly the \\emph{Newton's equation} ...
Wavelet-Based Quantum Field Theory
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Mikhail V. Altaisky
2007-11-01
Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
Linear Scaling Density Functional Calculations with Gaussian Orbitals
Scuseria, Gustavo E.
1999-01-01
Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.
Institute of Scientific and Technical Information of China (English)
ZHANG Xinming; HE Yongyong; HAO Rujiang; CHU Fulei
2007-01-01
Morlet wavelet is suitable to extract the impulse components of mechanical fault signals.And thus its continuous wavelet transform (CWT) has been successfully used in the field of fault diagnosis. The principle of scale selection in CWT is discussed. Based on genetic algorithm, an optimization strategy for the waveform parameters of the mother wavelet is proposed with wavelet entropy as the optimization target. Based on the optimized waveform parameters, the wavelet scalogram is used to analyze the simulated acoustic emission (AE) signal and real AE signal of rolling bearing.The results indicate that the proposed method is useful and efficient to improve the quality of CWT.
Garzilli, A; Kim, T -S; Leach, S; Viel, M
2012-01-01
We investigate the thermal history of the intergalactic medium (IGM) in the redshift interval z=1.7--3.2 by studying the small-scale fluctuations in the Lyman alpha forest transmitted flux. We apply a wavelet filtering technique to eighteen high resolution quasar spectra obtained with the Ultraviolet and Visual Echelle Spectrograph (UVES), and compare these data to synthetic spectra drawn from a suite of hydrodynamical simulations in which the IGM thermal state and cosmological parameters are varied. From the wavelet analysis we obtain estimates of the IGM thermal state that are in good agreement with other recent, independent wavelet-based measurements. We also perform a reanalysis of the same data set using the Lyman alpha forest flux probability distribution function (PDF), which has previously been used to measure the IGM temperature-density relation. This provides an important consistency test for measurements of the IGM thermal state, as it enables a direct comparison of the constraints obtained using t...
Bitenc, M.; Kieffer, D. S.; Khoshelham, K.
2016-06-01
Terrestrial Laser Scanning (TLS) is a well-known remote sensing tool that enables precise 3D acquisition of surface morphology from distances of a few meters to a few kilometres. The morphological representations obtained are important in engineering geology and rock mechanics, where surface morphology details are of particular interest in rock stability problems and engineering construction. The actual size of the discernible surface detail depends on the instrument range error (noise effect) and effective data resolution (smoothing effect). Range error can be (partly) removed by applying a denoising method. Based on the positive results from previous studies, two denoising methods, namely 2D wavelet transform (WT) and non-local mean (NLM), are tested here, with the goal of obtaining roughness estimations that are suitable in the context of rock engineering practice. Both methods are applied in two variants: conventional Discrete WT (DWT) and Stationary WT (SWT), classic NLM (NLM) and probabilistic NLM (PNLM). The noise effect and denoising performance are studied in relation to the TLS effective data resolution. Analyses are performed on the reference data acquired by a highly precise Advanced TOpometric Sensor (ATOS) on a 20x30 cm rock joint sample. Roughness ratio is computed by comparing the noisy and denoised surfaces to the original ATOS surface. The roughness ratio indicates the success of all denoising methods. Besides, it shows that SWT oversmoothes the surface and the performance of the DWT, NLM and PNLM vary with the noise level and data resolution. The noise effect becomes less prominent when data resolution decreases.
Wavelet operational matrix method for solving the Riccati differential equation
Li, Yuanlu; Sun, Ning; Zheng, Bochao; Wang, Qi; Zhang, Yingchao
2014-03-01
A Haar wavelet operational matrix method (HWOMM) was derived to solve the Riccati differential equations. As a result, the computation of the nonlinear term was simplified by using the Block pulse function to expand the Haar wavelet one. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. The capability and the simplicity of the proposed method was demonstrated by some examples and comparison with other methods.
Directory of Open Access Journals (Sweden)
B.Karuna kumar
2009-09-01
Full Text Available Fingerprints are today the most widely used biometric features for personal identification. With the increasing usage of biometric systems the question arises naturally how to store and handle the acquired sensor data. Our algorithm for the digitized images is based on adaptive uniform scalar quantization of discrete wavelet transform sub band decomposition. This technique referred to as the wavelet scalar quantization method. The algorithm produces archival quality images at compression ratios of around 15 to 1 and will allow the current database of paper finger print cards to be replaced by digital imagery. A compliance testing program is also being implemented to ensure high standards of image quality and interchangeability of data between different implementations.
Huang, Wei; Oh, Sung-Kwun; Pedrycz, Witold
2017-08-11
This paper presents a hybrid fuzzy wavelet neural network (HFWNN) realized with the aid of polynomial neural networks (PNNs) and fuzzy inference-based wavelet neurons (FIWNs). Two types of FIWNs including fuzzy set inference-based wavelet neurons (FSIWNs) and fuzzy relation inference-based wavelet neurons (FRIWNs) are proposed. In particular, a FIWN without any fuzzy set component (viz., a premise part of fuzzy rule) becomes a wavelet neuron (WN). To alleviate the limitations of the conventional wavelet neural networks or fuzzy wavelet neural networks whose parameters are determined based on a purely random basis, the parameters of wavelet functions standing in FIWNs or WNs are initialized by using the C-Means clustering method. The overall architecture of the HFWNN is similar to the one of the typical PNNs. The main strategies in the design of HFWNN are developed as follows. First, the first layer of the network consists of FIWNs (e.g., FSIWN or FRIWN) that are used to reflect the uncertainty of data, while the second and higher layers consist of WNs, which exhibit a high level of flexibility and realize a linear combination of wavelet functions. Second, the parameters used in the design of the HFWNN are adjusted through genetic optimization. To evaluate the performance of the proposed HFWNN, several publicly available data are considered. Furthermore a thorough comparative analysis is covered.
2007-11-02
Daubechies-DeVore (Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman...DeVore (Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman, Cargese – p.49...Cohen-Daubechies-Gulleryuz-Orchard) This encoder is optimal on all Besov classes compactly embedded into L2 EZW , Said-Pearlman, Cargese – p.49/49 Wavelet
Steerable Wavelet Machines (SWM): Learning Moving Frames for Texture Classification.
Depeursinge, Adrien; Puspoki, Zsuzsanna; Ward, John Paul; Unser, Michael
2017-04-01
We present texture operators encoding class-specific local organizations of image directions (LOIDs) in a rotation-invariant fashion. The LOIDs are key for visual understanding, and are at the origin of the success of the popular approaches, such as local binary patterns (LBPs) and the scale-invariant feature transform (SIFT). Whereas, LBPs and SIFT yield hand-crafted image representations, we propose to learn data-specific representations of the LOIDs in a rotation-invariant fashion. The image operators are based on steerable circular harmonic wavelets (CHWs), offering a rich and yet compact initial representation for characterizing natural textures. The joint location and orientation required to encode the LOIDs is preserved by using moving frames (MFs) texture representations built from locally-steered image gradients that are invariant to rigid motions. In a second step, we use support vector machines to learn a multi-class shaping matrix for the initial CHW representation, yielding data-driven MFs called steerable wavelet machines (SWMs). The SWM forward function is composed of linear operations (i.e., convolution and weighted combinations) interleaved with non-linear steermax operations. We experimentally demonstrate the effectiveness of the proposed operators for classifying natural textures. Our scheme outperforms recent approaches on several test suites of the Outex and the CUReT databases.
Wavelet transform domain communication systems
Orr, Richard S.; Pike, Cameron; Lyall, Michael J.
1995-04-01
In this paper we introduce a new class of communications systems called wavelet transform domain (WTD) systems. WTD systems are transmultiplexer (TMUX) structures in which information to be communicated over a channel is encoded, via an inverse discrete wavelet transform (IDWT), as the wavelet coefficients of the transmitted signal, and extracted at the receiver by a discrete wavelet transform (DWT). WTD constructs can be used for covert, or low probability of intercept/detection (LPI/D) communications, baseband bandwidth efficient communications, or code-division multiple access (CDMA). This paper concentrates on the spread spectrum applications.
Application of Wavelet Packet Energy Spectrum to Extract the Feature of the Pulse Signal
Institute of Scientific and Technical Information of China (English)
Dian-guo CAO; Yu-qiang WU; Xue-wen SHI; Peng WANG
2010-01-01
The wavelet packet is presented as a new kind of multi-scale analysis technique followed by Wavelet analysis. The fundamental and realization arithmetic of the wavelet packet analysis method are described in this paper. A new application approach of the wavelet packed method to extract the feature of the pulse signal from energy distributing angle is expatiated. It is convenient for the microchip to process and judge by using the wavelet packet analysis method to make the pulse signals quantized and analyzed. Kinds of experiments are simulated in the lab, and the experiments prove that it is a convenient and accurate method to extract the feature of the pulse signal based on wavelet packed-energy spectrum analysis.
Wavelet analysis for ground penetrating radar applications: a case study
Javadi, Mehdi; Ghasemzadeh, Hasan
2017-10-01
Noises may significantly disturb ground penetrating radar (GPR) signals, therefore, filtering undesired information using wavelet analysis would be challenging, despite the fact that several methods have been presented. Noises are gathered by probe, particularly from deep locations, and they may conceal reflections, suffering from small altitudes, because of signal attenuation. Multiple engineering fields need data analysis to distinguish valued material, based on information obtained by underground observations. Using wavelets as one of the useful methods for analyzing data is considered in this paper. However, optimal wavelet analysis would be challenging in the realm of exploring GPR signals. There is no doubt that accounting for wavelet function, decomposition level, threshold estimation method and threshold transformation, in the matter of de-noising and investigating signals, is of great importance; they must be chosen with judgment as they influence the results enormously if they are not carefully designated. Multiple wavelet functions are applied to perform de-noising and reconstruction on synthetic noisy signals generated by the finite-difference time-domain (FDTD) method to account for the most appropriate function for the purpose. In addition, various possible decomposition levels, threshold estimation methods and threshold transformations in the de-noising procedure are tested. The optimal wavelet analysis is also evaluated by examining real data acquired from several antenna frequencies which are common in engineering practice.
Analysis of a Gyroscope's Rotor Nonlinear Supported Magnetic Field Based on the B-Spline Wavelet-FEM
Institute of Scientific and Technical Information of China (English)
LIU Jian-feng; YUAN Gan-nan; HUANG Xu; YU Li
2005-01-01
A supported framework of a gyroscope′s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedron. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.
Institute of Scientific and Technical Information of China (English)
余海军; 白龙; 翁甲强; 罗晓曙; 方锦清
2008-01-01
基于束晕-混沌的非线性控制策略,对周期性聚焦磁场中初始分布满足K-V分布的粒子束进行模拟研究,提出了控制其束晕-混沌的实Morlet小波函数控制器,并给出具体的实施方案.数值模拟研究表明,在适当的参数条件下,运用这种方法不仅可以消除束晕及其再生现象,达到对束晕-混沌的有效控制,而且可以控制束流到均匀分布.%The Kapchinsky-Vladimirsky (K-V) beam through an axisymmetric periodic-focusing magnetic field is studied using the particle-core model. The beam halo-chaos is found, and a real Morlet wavelet function controller is proposed based on the mechanism of halo formation and the strategy of controlling halo-chaos. The method is applied to the multi-particle simulation to control the halo. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively by using the real Morlet wavelet function control method. At the same time, the radial particle density is uniform at the center of the beam as long as the control method and appropriate parameter are chosen.
IRREGULAR WAVELET FRAMES AND GABOR FRAMES
Institute of Scientific and Technical Information of China (English)
Ole Christensen; Sergio Favier; Felipe Zó
2001-01-01
Given g ∈ L2 (R), we consider irregular wavelet systems of theform {λ g(λj x-kb) }j z. kz, where λj ＞0 and b＞0. Sufficient conditions for the wavelet system to constitute a frame for L2(R) are given. For a class of functions g ∈ L 2 (R) we prove that certain growth conditions on {λj} will lead to frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system {exib(j,x)g(x-λh)}jzn,kz to be a frame.CLC Number：O17 Document ID：AAuthor Resume：Ole Christensen;E-mail: Ole. Christensen@mat. dtu. dk Sergio Favier and Felipe Zó ;e-mails : sfavier@unsl. edu. ar fzo@unsl. edu. ar References：[1]Casaza,P.G. and Christensen,O.,Weyl-Heisenberg Frames for Subspaces of L2(R),Proc.Amer. Math. Soc. ,129(2001),145-154.[2]Casazza,P.G. and Christensen,O. ,Classifying Certain Irregular Gabor Frames,preprint[2]001.[3]Christensen,O. and Lindner,A. ,Lower Bounds for Finite Wavelet and Gabor Systems,Appr. Theory and Appl.,17(2001),17-31.[4]Chui,C.K. and Shi,X. ,Inequalities of Litdewood-Paley Type for Frames and Wavelets,SIAM J. Math. Anal. ,24:1(1993),263-277.[5]Daubechies,I. ,Ten Lectures on Wavelets,SIAM,Philadelphia,1992.[6]Favier,S. and Zalik,R. ,On the Stability of Frames and Riesz Bases,Appl. Comp. Ham.Anal. ,2(1995),160-173.[7]Feichtinger,H.G. and Strohmer,T. ,(Eds.),Gabor Analysis and Algorithms : Theory and Applications,Birkhauser,1998.[8]Heil,C.E. and Walnut,D.F. ,Continuous and Discrete Wavelet Transforms,SIAM Review,31:4(1989),628-666.[9]Sun,W. and Zhou,X. ,Irregular Wavelet Frames,Science in China (Series A),43:2(2000),122-127.Manuscript Received：2001年7月10日Manuscript Revised：2001年7月23日Published：2001年9月1日
Information filtering via a scaling-based function.
Qiu, Tian; Zhang, Zi-Ke; Chen, Guang
2013-01-01
Finding a universal description of the algorithm optimization is one of the key challenges in personalized recommendation. In this article, for the first time, we introduce a scaling-based algorithm (SCL) independent of recommendation list length based on a hybrid algorithm of heat conduction and mass diffusion, by finding out the scaling function for the tunable parameter and object average degree. The optimal value of the tunable parameter can be abstracted from the scaling function, which is heterogeneous for the individual object. Experimental results obtained from three real datasets, Netflix, MovieLens and RYM, show that the SCL is highly accurate in recommendation. More importantly, compared with a number of excellent algorithms, including the mass diffusion method, the original hybrid method, and even an improved version of the hybrid method, the SCL algorithm remarkably promotes the personalized recommendation in three other aspects: solving the accuracy-diversity dilemma, presenting a high novelty, and solving the key challenge of cold start problem.
Functional Independent Scaling Relation for ORR/OER Catalysts
DEFF Research Database (Denmark)
Christensen, Rune; Hansen, Heine Anton; Dickens, Colin F.
2016-01-01
A widely used adsorption energy scaling relation between OH* and OOH* intermediates in the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), has previously been determined using density functional theory and shown to dictate a minimum thermodynamic overpotential for both reacti...
Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales
Institute of Scientific and Technical Information of China (English)
ZHANG JI; LIU ZHEN-XIN
2011-01-01
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△ ＝ A(t)x on time scales.Moreover, for the nonlinear perturbed equation x△ ＝ A(t)x + f(t,x) we give the instability of the zero solution when f is sufficiently small.
Large-scale data analysis using the Wigner function
Earnshaw, R. A.; Lei, C.; Li, J.; Mugassabi, S.; Vourdas, A.
2012-04-01
Large-scale data are analysed using the Wigner function. It is shown that the 'frequency variable' provides important information, which is lost with other techniques. The method is applied to 'sentiment analysis' in data from social networks and also to financial data.
Local Analysis, Cardinality, and Split Trick of Quasi-biorthogonal Frame Wavelets
Institute of Scientific and Technical Information of China (English)
Zhi Hua ZHANG
2011-01-01
The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthogonal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions.In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruction formulas of the corresponding subspaces. Next we show that the lower bound of its cardinalities depends on a pair of dual frame multiresolution analyses deriving it. Finally, we present a split trick and show that any quasi-biorthogonal frame wavelet can be split into a new quasi-biorthogonal frame wavelet with an arbitrarily large cardinality. For generality,we work in the setting of matrix dilations.
NOVEL FIBER GRATING SENSOR DEMODULATION TECHNIQUE BASED ON OPTICAL WAVELET FILTERING
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The optical wavelet filter is designed. It can filter and choose frequency swiftly. It can realize demodulation of distributed fiber Bragg grating(FBG) measurement system. Its scanning resolution and scanning period depend on wavelet function. Wavelet function is controlled by computer. Compared to conventional scan filter, optical wavelet filtering has some advantages such as simple structure, high scan frequency, high resolution and good linearity. At last, the error of optical wavelet filter scanning procedure is analyzed. Scanning step length refers to the shifting of optical wavelet window's central frequency. It affects system precision directly. If scanning step length is different, the measured signal is different. The methods of reducing step length guarantee scanning periodic time are presented.
Wavelet neural network and its application in fault diagnosis of rolling bearing
Wang, Guo-Feng; Wang, Tai-Yong
2005-12-01
In order to realize diagnosis of rolling bearing of rotating machines, the wavelet neural network was proposed. This kind of artificial neural network takes wavelet function as neuron of hidden layer so as to realize nonlinear mapping between fault and symptoms. A algorithm based on minimum mean square error was given to obtain the weight value of network, dilation and translation parameter of wavelet function. To testify the correctness of wavelet neural network, it was adopted in diagnosing the fault type and location of rolling bearing. The final result shows that it can recognize the fault of outer race, inner race and roller accurately.
Features of long-term health monitored strains of a bridge with wavelet analysis
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper analyses the five years' monitored strains collected from a long-term health monitoring system installed on a bridge with wavelet transform.In the analysis,the monitored strains are pre-processed,features of the monitored data are summarized briefly.The influences of the base functions on the results of wavelet analysis are studied simultaneously.The results show that the db wavelet is a good mother wavelet function in the analysis,and the order N should be larger than 20,but less than 46 in deco...
A DISCUSSION ABOUT SCALE INVARIANTS FOR TENSOR FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Huang Yongnian; Luo Xiongping; Emily S.C.Ching
2000-01-01
It is found that in some cases the complete and irreducible scale invariants given by Ref.[1]are not independent.There are some implicit functional relations among them.The scale invariants for two different cases are calculated.The first case is an arbitrary second order tensor.The second case includes a symmetric tensor,an antisymmetric tensor and a vector.By using the eigentensor notation it is proved that in the first case there are only six independent scale invariants rather than seven as reported in Ref.[1]and in the second case there are only nine independent scale invariants which are leas than that obtained in Ref.[1].
Directory of Open Access Journals (Sweden)
Carsten Proppe
2012-01-01
Full Text Available Multiresolution analysis for problems involving random parameter fields is considered. The random field is discretized by a Karhunen-Loève expansion. The eigenfunctions involved in this representation are computed by a wavelet expansion. The wavelet expansion allows to control the spatial resolution of the problem. Fine and coarse scales are defined, and the fine scales are taken into account by projection operators. The influence of the truncation level for the wavelet expansion on the computed reliability is documented.
Structure and function of large-scale brain systems.
Koziol, Leonard F; Barker, Lauren A; Joyce, Arthur W; Hrin, Skip
2014-01-01
This article introduces the functional neuroanatomy of large-scale brain systems. Both the structure and functions of these brain networks are presented. All human behavior is the result of interactions within and between these brain systems. This system of brain function completely changes our understanding of how cognition and behavior are organized within the brain, replacing the traditional lesion model. Understanding behavior within the context of brain network interactions has profound implications for modifying abstract constructs such as attention, learning, and memory. These constructs also must be understood within the framework of a paradigm shift, which emphasizes ongoing interactions within a dynamically changing environment.
Applications of large-scale density functional theory in biology
Cole, Daniel J.; Hine, Nicholas D. M.
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.
Quadratic vs cubic spline-wavelets for image representations and compression
Marais, P.C.; Blake, E.H.; Kuijk, A.A.M.
1997-01-01
The Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary transform data. The use of semi-orthogonal quadratic spline wavelets allows one
Quadratic vs cubic spline-wavelets for image representation and compression
Marais, P.C.; Blake, E.H.; Kuijk, A.A.M.
1994-01-01
The Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary ransform data. The use of semi-orthogonal quadratic spline wavelets allows one t
Continuous wavelet transform of wind and wind-induced pressures on a building in suburban terrain
Geurts, C.P.W.; Hajj, M.R.; Tieleman, H.W.
1998-01-01
The wavelet transform is a promising tool for the analysis of incident wind and wind loading on structures. The continuous wavelet transform is applied to full-scale velocity and pressure measurements, taken at the main building of Eindhoven University of Technology. Initial results indicate that th
Evaluating the Initialization Methods of Wavelet Networks for Hyperspectral Image Classification
Hsu, Pai-Hui
2016-06-01
The idea of using artificial neural network has been proven useful for hyperspectral image classification. However, the high dimensionality of hyperspectral images usually leads to the failure of constructing an effective neural network classifier. To improve the performance of neural network classifier, wavelet-based feature extraction algorithms can be applied to extract useful features for hyperspectral image classification. However, the extracted features with fixed position and dilation parameters of the wavelets provide insufficient characteristics of spectrum. In this study, wavelet networks which integrates the advantages of wavelet-based feature extraction and neural networks classification is proposed for hyperspectral image classification. Wavelet networks is a kind of feed-forward neural networks using wavelets as activation function. Both the position and the dilation parameters of the wavelets are optimized as well as the weights of the network during the training phase. The value of wavelet networks lies in their capabilities of optimizing network weights and extracting essential features simultaneously for hyperspectral images classification. In this study, the influence of the learning rate and momentum term during the network training phase is presented, and several initialization modes of wavelet networks were used to test the performance of wavelet networks.
Shoaib, Muhammad; Shamseldin, Asaad Y.; Melville, Bruce W.; Khan, Mudasser Muneer
2016-04-01
In order to predict runoff accurately from a rainfall event, the multilayer perceptron type of neural network models are commonly used in hydrology. Furthermore, the wavelet coupled multilayer perceptron neural network (MLPNN) models has also been found superior relative to the simple neural network models which are not coupled with wavelet. However, the MLPNN models are considered as static and memory less networks and lack the ability to examine the temporal dimension of data. Recurrent neural network models, on the other hand, have the ability to learn from the preceding conditions of the system and hence considered as dynamic models. This study for the first time explores the potential of wavelet coupled time lagged recurrent neural network (TLRNN) models for runoff prediction using rainfall data. The Discrete Wavelet Transformation (DWT) is employed in this study to decompose the input rainfall data using six of the most commonly used wavelet functions. The performance of the simple and the wavelet coupled static MLPNN models is compared with their counterpart dynamic TLRNN models. The study found that the dynamic wavelet coupled TLRNN models can be considered as alternative to the static wavelet MLPNN models. The study also investigated the effect of memory depth on the performance of static and dynamic neural network models. The memory depth refers to how much past information (lagged data) is required as it is not known a priori. The db8 wavelet function is found to yield the best results with the static MLPNN models and with the TLRNN models having small memory depths. The performance of the wavelet coupled TLRNN models with large memory depths is found insensitive to the selection of the wavelet function as all wavelet functions have similar performance.
POINTWISE CONVERGENCE OF THE WAVELET SOLUTION TO THE PARABOLIC EQUATION WITH VARIABLE COEFFICIENTS
Institute of Scientific and Technical Information of China (English)
Jinru Wang; Hua Zhang
2008-01-01
We consider the parabolic equation with variable coefficients k(x)uxx = ui, O,x ≤ 1, t ≥ 0, where 0 < a ≤ k(x) < +∞, the solution on the boundary x = O is a given function g and ux(O,t) = O. We use wavelet Galerkin method with Meyer multi-resolution analy-sis to obtain a wavelet approximating solution, and also get an estimate between the exact solution and the wavelet approximating solution of the problem.
Wavelet-based denoising using local Laplace prior
Rabbani, Hossein; Vafadust, Mansur; Selesnick, Ivan
2007-09-01
Although wavelet-based image denoising is a powerful tool for image processing applications, relatively few publications have addressed so far wavelet-based video denoising. The main reason is that the standard 3-D data transforms do not provide useful representations with good energy compaction property, for most video data. For example, the multi-dimensional standard separable discrete wavelet transform (M-D DWT) mixes orientations and motions in its subbands, and produces the checkerboard artifacts. So, instead of M-D DWT, usually oriented transforms suchas multi-dimensional complex wavelet transform (M-D DCWT) are proposed for video processing. In this paper we use a Laplace distribution with local variance to model the statistical properties of noise-free wavelet coefficients. This distribution is able to simultaneously model the heavy-tailed and intrascale dependency properties of wavelets. Using this model, simple shrinkage functions are obtained employing maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimators. These shrinkage functions are proposed for video denoising in DCWT domain. The simulation results shows that this simple denoising method has impressive performance visually and quantitatively.
基于多尺度二维小波变换的静脉图像融合%Vein Image Fusion Based on Two-dimensional Wavelet Multi-scale Transform
Institute of Scientific and Technical Information of China (English)
欧锋; 黄丹飞
2015-01-01
Venous blood vessels visible image detail is rich but vascular hazy outline;Venous blood vessels infrared image contour obviously but lack of details;Aiming at the shortcomings of the single vein image, this paper proposes a vein image fusion method based on multi-scale wavelet transform,the fusion image retain the source image for more infor-mation,richer details,clearer outline,better visual effect,provide very good auxiliary effect for clinical venipuncture.%静脉可见光图像血管细节较丰富，但血管轮廓模糊；静脉红外图像血管轮廓明显，但细节欠缺。针对单一静脉图像存在的不足，提出了一种基于多尺度二维小波变换的静脉图像融合方法，通过实验证实融合后的静脉图像保留了源图像更多的信息，静脉血管细节丰富、轮廓清晰、视觉效果良好，为临床静脉穿刺提供辅助作用，具有很好的临床应用价值。
Getz, Neil H.
1993-11-01
The discrete wavelet transform (DWT) is adapted to functions on the discrete circle to create a discrete periodic wavelet transform (DPWT) for bounded periodic sequences. This extension also offers a solution to the problem of non-invertibility that arises in the application of the DWT to finite length sequences and provides the proper theoretical setting for the completion of some previous incomplete solutions to the invertibility problem. It is proven that the same filter coefficients used with the DWT to create orthonormal wavelets on compact support in l(infinity ) (Z) may be incorporated through the DPWT to create an orthonormal basis of discrete periodic wavelets. By exploiting transform symmetry and periodicity we arrive at easily implementable and fast synthesis and analysis algorithms.
Wavelet representation of the nuclear dynamics
Energy Technology Data Exchange (ETDEWEB)
Jouault, B.; Sebille, F.; Mota, V. de la
1997-12-31
The study of transport phenomena in nuclear matter is addressed in a new approach named DYWAN, based on the projection methods of statistical physics and on the mathematical theory of wavelets. Strongly compressed representations of the nuclear systems are obtained with an accurate description of the wave functions and of their antisymmetrization. The results of the approach are illustrated for the ground state description as well as for the dissipative dynamics of nuclei at intermediate energies. (K.A.). 52 refs.
Wavelet frames and their duals
DEFF Research Database (Denmark)
Lemvig, Jakob
2008-01-01
structure. The dilation of the wavelet building blocks in higher dimension is done via a square matrix which is usually taken to be integer valued. In this thesis we step away from the "usual" integer, expansive dilation and consider more general, expansive dilations. In most applications of wavelet frames...
Research on Mechanical Fault Diagnosis Scheme Based on Improved Wavelet Total Variation Denoising
Directory of Open Access Journals (Sweden)
Wentao He
2016-01-01
Full Text Available Wavelet analysis is a powerful tool for signal processing and mechanical equipment fault diagnosis due to the advantages of multiresolution analysis and excellent local characteristics in time-frequency domain. Wavelet total variation (WATV was recently developed based on the traditional wavelet analysis method, which combines the advantages of wavelet-domain sparsity and total variation (TV regularization. In order to guarantee the sparsity and the convexity of the total objective function, nonconvex penalty function is chosen as a new wavelet penalty function in WATV. The actual noise reduction effect of WATV method largely depends on the estimation of the noise signal variance. In this paper, an improved wavelet total variation (IWATV denoising method was introduced. The local variance analysis on wavelet coefficients obtained from the wavelet decomposition of noisy signals is employed to estimate the noise variance so as to provide a scientific evaluation index. Through the analysis of the numerical simulation signal and real-word failure data, the results demonstrated that the IWATV method has obvious advantages over the traditional wavelet threshold denoising and total variation denoising method in the mechanical fault diagnose.
Investigation of Shannon and PolyWog Wavelet Neural Networks In Monthly River Flow Modeling
Abghari, H.; van de Giesen, N.; Noury, M.
2009-04-01
Intelligence models consist of distributed parallel processors that learn to reproduce the relationship between input and output signals and present the best topology of patterns simulation. Due to nonlinearity of hydrological events the learning process has restrictions . In this study, using a combination of Wavelet theory and a Multi Layer Perceptron Network, two Wavelet Neural Network models for monthly flow of Nazloochaei River basin in Iran were developed. Instead of using common sigmoid activation functions in the MLP network a wavelet function was used, The hybrid wavelet neural network (WNNs) employing a nonlinear wavelet basis was developed as an alternative approach to nonlinear fitting. Result of MLP base model show the 86% in training and 79% in model testing. Results of the MLP base model show a goodness of fit of 86% in training and 79% in model testing. Results shows that the Polywog neural network with the best topology has a 94% accuracy in the training phase and 89% in testing of model. The Shannon neural network with the best topology produces 79% accuracy in training phase and 61% in testing of model. Comparison of WNN and MLP shows that Polywog wavelet could have better accuracy in time series modeling. Classic sigmoid activation functions in the MLP network show better results than the Shannon wavelet. Keywords: Shannon and PolyWog Wavelet, Wavelet Neural Networks, Nazloochaei River Basin, River Flow Modeling.
Development of large-scale functional brain networks in children.
Directory of Open Access Journals (Sweden)
Kaustubh Supekar
2009-07-01
Full Text Available The ontogeny of large-scale functional organization of the human brain is not well understood. Here we use network analysis of intrinsic functional connectivity to characterize the organization of brain networks in 23 children (ages 7-9 y and 22 young-adults (ages 19-22 y. Comparison of network properties, including path-length, clustering-coefficient, hierarchy, and regional connectivity, revealed that although children and young-adults' brains have similar "small-world" organization at the global level, they differ significantly in hierarchical organization and interregional connectivity. We found that subcortical areas were more strongly connected with primary sensory, association, and paralimbic areas in children, whereas young-adults showed stronger cortico-cortical connectivity between paralimbic, limbic, and association areas. Further, combined analysis of functional connectivity with wiring distance measures derived from white-matter fiber tracking revealed that the development of large-scale brain networks is characterized by weakening of short-range functional connectivity and strengthening of long-range functional connectivity. Importantly, our findings show that the dynamic process of over-connectivity followed by pruning, which rewires connectivity at the neuronal level, also operates at the systems level, helping to reconfigure and rebalance subcortical and paralimbic connectivity in the developing brain. Our study demonstrates the usefulness of network analysis of brain connectivity to elucidate key principles underlying functional brain maturation, paving the way for novel studies of disrupted brain connectivity in neurodevelopmental disorders such as autism.
Time scale hierarchies in the functional organization of complex behaviors.
Directory of Open Access Journals (Sweden)
Dionysios Perdikis
2011-09-01
Full Text Available Traditional approaches to cognitive modelling generally portray cognitive events in terms of 'discrete' states (point attractor dynamics rather than in terms of processes, thereby neglecting the time structure of cognition. In contrast, more recent approaches explicitly address this temporal dimension, but typically provide no entry points into cognitive categorization of events and experiences. With the aim to incorporate both these aspects, we propose a framework for functional architectures. Our approach is grounded in the notion that arbitrary complex (human behaviour is decomposable into functional modes (elementary units, which we conceptualize as low-dimensional dynamical objects (structured flows on manifolds. The ensemble of modes at an agent's disposal constitutes his/her functional repertoire. The modes may be subjected to additional dynamics (termed operational signals, in particular, instantaneous inputs, and a mechanism that sequentially selects a mode so that it temporarily dominates the functional dynamics. The inputs and selection mechanisms act on faster and slower time scales then that inherent to the modes, respectively. The dynamics across the three time scales are coupled via feedback, rendering the entire architecture autonomous. We illustrate the functional architecture in the context of serial behaviour, namely cursive handwriting. Subsequently, we investigate the possibility of recovering the contributions of functional modes and operational signals from the output, which appears to be possible only when examining the output phase flow (i.e., not from trajectories in phase space or time.
Wavelet-analysis for Laser Images of Blood Plasma
Directory of Open Access Journals (Sweden)
ANGELSKY, A.-P.
2011-05-01
Full Text Available The possibilities of the local wavelet-analysis of polarization-inhomogeneous laser image of human blood plasma were considered. The set of statistics, correlation and fractal parameters of the distributions of wavelet-coefficients that are characterize different scales of the polarization maps of polycrystalline networks of amino acids of blood plasma were defined. The criteria for the differentiation of the transformation of birefringence optical-anisotropic structures of blood plasma at different scales of their geometric dimensions were determined.
Adaptive boxcar/wavelet transform
Sezer, Osman G.; Altunbasak, Yucel
2009-01-01
This paper presents a new adaptive Boxcar/Wavelet transform for image compression. Boxcar/Wavelet decomposition emphasizes the idea of average-interpolation representation which uses dyadic averages and their interpolation to explain a special case of biorthogonal wavelet transforms (BWT). This perspective for image compression together with lifting scheme offers the ability to train an optimum 2-D filter set for nonlinear prediction (interpolation) that will adapt to the context around the low-pass wavelet coefficients for reducing energy in the high-pass bands. Moreover, the filters obtained after training is observed to posses directional information with some textural clues that can provide better prediction performance. This work addresses a firrst step towards obtaining this new set of training-based fillters in the context of Boxcar/Wavelet transform. Initial experimental results show better subjective quality performance compared to popular 9/7-tap and 5/3-tap BWTs with comparable results in objective quality.
Scaling relations and multicritical phenomena from functional renormalization.
Boettcher, Igor
2015-06-01
We investigate multicritical phenomena in O(N)+O(M) models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications for the analysis of multicritical phenomena with truncated flow equations. These findings are an important step towards studies of competing orders and multicritical quantum phase transitions within the framework of functional renormalization.
A Study on Integrated Wavelet Neural Networks in Fault Diagnosis Based on Information Fusion
Institute of Scientific and Technical Information of China (English)
ANG Xue-ye
2007-01-01
The tight wavelet neural network was constituted by taking the nonlinear Morlet wavelet radices as the excitation function. The idiographic algorithm was presented. It combined the advantages of wavelet analysis and neural networks. The integrated wavelet neural network fault diagnosis system was set up based on both the information fusion technology and actual fault diagnosis, which took the sub-wavelet neural network as primary diagnosis from different sides, then came to the conclusions through decision-making fusion. The realizable policy of the diagnosis system and established principle of the sub-wavelet neural networks were given . It can be deduced from the examples that it takes full advantage of diversified characteristic information, and improves the diagnosis rate.
An efficient wavelet finite element method in fault prognosis of incipient crack
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The method of constructing any scale wavelet finite element (WFE) based on the one-dimensional or two-dimensional Daubechies scaling functions was presented, and the corresponding WFE adaptive lifting algorithm was given. In order to obtain the nested increasing approximate subspaces of multiscale finite element, the Daubechies scaling functions with the properties of multi-resolution analysis were employed as the finite element interpolating functions. Thus, the WFE could adaptively mesh the singularity domain caused by local cracks, which resulted in better approximate solutions than the traditional finite element methods. The calculations of natural frequencies of cracked beam were used to check the accuracy of given methods. In addition, the results of cracked cantilever beam and engineering application were satisfied. So, the current methods can provide effective tools in the numerical modeling of the fault prognosis of incipient crack.
Hill, Paul; Achim, Alin; Al-Mualla, Mohammed Ebrahim; Bull, David
2016-04-11
Accurate estimation of the contrast sensitivity of the human visual system is crucial for perceptually based image processing in applications such as compression, fusion and denoising. Conventional Contrast Sensitivity Functions (CSFs) have been obtained using fixed sized Gabor functions. However, the basis functions of multiresolution decompositions such as wavelets often resemble Gabor functions but are of variable size and shape. Therefore to use conventional contrast sensitivity functions in such cases is not appropriate. We have therefore conducted a set of psychophysical tests in order to obtain the contrast sensitivity function for a range of multiresolution transforms: the Discrete Wavelet Transform (DWT), the Steerable Pyramid, the Dual-Tree Complex Wavelet Transform (DT-CWT) and the Curvelet Transform. These measures were obtained using contrast variation of each transforms' basis functions in a 2AFC experiment combined with an adapted version of the QUEST psychometric function method. The results enable future image processing applications that exploit these transforms such as signal fusion, super-resolution processing, denoising and motion estimation, to be perceptually optimised in a principled fashion. The results are compared to an existing vision model (HDR-VDP2) and are used to show quantitative improvements within a denoising application compared to using conventional CSF values.
Density Functional Theory and Materials Modeling at Atomistic Length Scales
Directory of Open Access Journals (Sweden)
Swapan K. Ghosh
2002-04-01
Full Text Available Abstract: We discuss the basic concepts of density functional theory (DFT as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy density functional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.
Estimating ventilation time scales using overturning stream functions
Thompson, Bijoy; Nycander, Jonas; Nilsson, Johan; Jakobsson, Martin; Döös, Kristofer
2014-06-01
A simple method for estimating ventilation time scales from overturning stream functions is proposed. The stream function may be computed using either geometric coordinates or a generalized vertical coordinate, such as potential density (salinity in our study). The method is tested with a three-dimensional circulation model describing an idealized semi-enclosed ocean basin ventilated through a narrow strait over a sill, and the result is compared to age estimates obtained from a passive numerical age tracer. The best result is obtained when using the stream function in salinity coordinates. In this case, the reservoir-averaged advection time obtained from the overturning stream function in salinity coordinates agrees rather well with the mean age of the age tracer, and the corresponding maximum ages agree very well.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Wavelet transform is used to analyze the scaling rule convection flow from two aspects. By utilizing the method of extended self similarity (ESS), one can find the obtained scaling exponent agrees well with the one obtained from the temperature data in a experiment of wind tunnel. And then we propose a newly defined formula based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data. The obtained results demonstrate that we can correctly extract ξ(q) by using the method which is named as wavelet transform maximum modulus (WTMM).``
Ng, Desmond; Wong, Fu Tian; Withayachumnankul, Withawat; Findlay, David; Ferguson, Bradley; Abbott, Derek
2007-12-01
In this work we investigate new feature extraction algorithms on the T-ray response of normal human bone cells and human osteosarcoma cells. One of the most promising feature extraction methods is the Discrete Wavelet Transform (DWT). However, the classification accuracy is dependant on the specific wavelet base chosen. Adaptive wavelets circumvent this problem by gradually adapting to the signal to retain optimum discriminatory information, while removing redundant information. Using adaptive wavelets, classification accuracy, using a quadratic Bayesian classifier, of 96.88% is obtained based on 25 features. In addition, the potential of using rational wavelets rather than the standard dyadic wavelets in classification is explored. The advantage it has over dyadic wavelets is that it allows a better adaptation of the scale factor according to the signal. An accuracy of 91.15% is obtained through rational wavelets with 12 coefficients using a Support Vector Machine (SVM) as the classifier. These results highlight adaptive and rational wavelets as an efficient feature extraction method and the enormous potential of T-rays in cancer detection.
Synchrosqueezed wavelet transform for damping identification
Mihalec, Marko; Slavič, Janko; Boltežar, Miha
2016-12-01
Synchrosqueezing is a procedure for improving the frequency localization of a continuous wavelet transform. This research focuses on using a synchrosqueezed wavelet transform (SWT) to determine the damping ratios of a vibrating system using a free-response signal. While synchrosqueezing is advantageous due to its localisation in the frequency, damping identification with the original SWT is not sufficiently accurate. Here, the synchrosqueezing was researched in detail, and it was found that an error in the frequency occurs as a result of the numerical calculation of the preliminary frequencies. If this error were to be compensated, a better damping identification would be expected. To minimize the frequency-shift error, three different strategies are investigated: the scale-dependent coefficient method, the shifted-coefficient method and the autocorrelated-frequency method. Furthermore, to improve the SWT, two synchrosqueezing criteria are introduced: the average SWT and the proportional SWT. Finally, the proposed modifications are tested against close modes and the noise in the signals. It was numerically and experimentally confirmed that the SWT with the proportional criterion offers better frequency localization and performs better than the continuous wavelet transform when tested against noisy signals.
Efficient hemodynamic event detection utilizing relational databases and wavelet analysis
Saeed, M.; Mark, R. G.
2001-01-01
Development of a temporal query framework for time-oriented medical databases has hitherto been a challenging problem. We describe a novel method for the detection of hemodynamic events in multiparameter trends utilizing wavelet coefficients in a MySQL relational database. Storage of the wavelet coefficients allowed for a compact representation of the trends, and provided robust descriptors for the dynamics of the parameter time series. A data model was developed to allow for simplified queries along several dimensions and time scales. Of particular importance, the data model and wavelet framework allowed for queries to be processed with minimal table-join operations. A web-based search engine was developed to allow for user-defined queries. Typical queries required between 0.01 and 0.02 seconds, with at least two orders of magnitude improvement in speed over conventional queries. This powerful and innovative structure will facilitate research on large-scale time-oriented medical databases.
Dual tree fractional quaternion wavelet transform for disparity estimation.
Kumar, Sanoj; Kumar, Sanjeev; Sukavanam, Nagarajan; Raman, Balasubramanian
2014-03-01
This paper proposes a novel phase based approach for computing disparity as the optical flow from the given pair of consecutive images. A new dual tree fractional quaternion wavelet transform (FrQWT) is proposed by defining the 2D Fourier spectrum upto a single quadrant. In the proposed FrQWT, each quaternion wavelet consists of a real part (a real DWT wavelet) and three imaginary parts that are organized according to the quaternion algebra. First two FrQWT phases encode the shifts of image features in the absolute horizontal and vertical coordinate system, while the third phase has the texture information. The FrQWT allowed a multi-scale framework for calculating and adjusting local disparities and executing phase unwrapping from coarse to fine scales with linear computational efficiency.
An Introduction to Wavelet Theory and Analysis
Energy Technology Data Exchange (ETDEWEB)
Miner, N.E.
1998-10-01
This report reviews the history, theory and mathematics of wavelet analysis. Examination of the Fourier Transform and Short-time Fourier Transform methods provides tiormation about the evolution of the wavelet analysis technique. This overview is intended to provide readers with a basic understanding of wavelet analysis, define common wavelet terminology and describe wavelet amdysis algorithms. The most common algorithms for performing efficient, discrete wavelet transforms for signal analysis and inverse discrete wavelet transforms for signal reconstruction are presented. This report is intended to be approachable by non- mathematicians, although a basic understanding of engineering mathematics is necessary.
A wavelet approach for active-passive vibration control of laminated plates
Institute of Scientific and Technical Information of China (English)
Ji-Zeng Wang; Xiao-Min Wang; You-He Zhou
2012-01-01
As an extension of the wavelet approach to vibration control of piezoelectric beam-type plates developed earlier by the authors,this paper proposes a hybrid activepassive control strategy for suppressing vibrations of laminated rectangular plates bonded with distributed piezoelectric sensors and actuators via thin viscoelastic bonding layers.Owing to the low-pass filtering property of scaling function transform in orthogonal wavelet theory,this waveletbased control method has the ability to automatically filter out noise-like signal in the feedback control loop,hence reducing the risk of residual coupling effects which are usually the source of spillover instability.Moreover,the existence of thin viscoelastic bonding layers can further improve robustness and reliability of the system through dissipating the energy of any other possible noise induced partially by numerical errors during the control process.A simulation procedure based on an advanced wavelet-Galerkin technique is suggested to realize the hybrid active-passive control process.Numerical results demonstrate the efficiency of the proposed approach.
Wavelet and statistical analysis for melanoma classification
Nimunkar, Amit; Dhawan, Atam P.; Relue, Patricia A.; Patwardhan, Sachin V.
2002-05-01
The present work focuses on spatial/frequency analysis of epiluminesence images of dysplastic nevus and melanoma. A three-level wavelet decomposition was performed on skin-lesion images to obtain coefficients in the wavelet domain. A total of 34 features were obtained by computing ratios of the mean, variance, energy and entropy of the wavelet coefficients along with the mean and standard deviation of image intensity. An unpaired t-test for a normal distribution based features and the Wilcoxon rank-sum test for non-normal distribution based features were performed for selecting statistically correlated features. For our data set, the statistical analysis of features reduced the feature set from 34 to 5 features. For classification, the discriminant functions were computed in the feature space using the Mahanalobis distance. ROC curves were generated and evaluated for false positive fraction from 0.1 to 0.4. Most of the discrimination functions provided a true positive rate for melanoma of 93% with a false positive rate up to 21%.
Wavelet Transform Signal Processing Applied to Ultrasonics.
1995-05-01
THE WAVELET TRANSFORM IS APPLIED TO THE ANALYSIS OF ULTRASONIC WAVES FOR IMPROVED SIGNAL DETECTION AND ANALYSIS OF THE SIGNALS. In instances where...the mother wavelet is well defined, the wavelet transform has relative insensitivity to noise and does not need windowing. Peak detection of...ultrasonic pulses using the wavelet transform is described and results show good detection even when large white noise was added. The use of the wavelet
Wavelet-Based Methodology for Evolutionary Spectra Estimation of Nonstationary Typhoon Processes
Directory of Open Access Journals (Sweden)
Guang-Dong Zhou
2015-01-01
Full Text Available Closed-form expressions are proposed to estimate the evolutionary power spectral density (EPSD of nonstationary typhoon processes by employing the wavelet transform. Relying on the definition of the EPSD and the concept of the wavelet transform, wavelet coefficients of a nonstationary typhoon process at a certain time instant are interpreted as the Fourier transform of a new nonstationary oscillatory process, whose modulating function is equal to the modulating function of the nonstationary typhoon process multiplied by the wavelet function in time domain. Then, the EPSD of nonstationary typhoon processes is deduced in a closed form and is formulated as a weighted sum of the squared moduli of time-dependent wavelet functions. The weighted coefficients are frequency-dependent functions defined by the wavelet coefficients of the nonstationary typhoon process and the overlapping area of two shifted wavelets. Compared with the EPSD, defined by a sum of the squared moduli of the wavelets in frequency domain in literature, this paper provides an EPSD estimation method in time domain. The theoretical results are verified by uniformly modulated nonstationary typhoon processes and non-uniformly modulated nonstationary typhoon processes.
Information filtering via a scaling-based function.
Directory of Open Access Journals (Sweden)
Tian Qiu
Full Text Available Finding a universal description of the algorithm optimization is one of the key challenges in personalized recommendation. In this article, for the first time, we introduce a scaling-based algorithm (SCL independent of recommendation list length based on a hybrid algorithm of heat conduction and mass diffusion, by finding out the scaling function for the tunable parameter and object average degree. The optimal value of the tunable parameter can be abstracted from the scaling function, which is heterogeneous for the individual object. Experimental results obtained from three real datasets, Netflix, MovieLens and RYM, show that the SCL is highly accurate in recommendation. More importantly, compared with a number of excellent algorithms, including the mass diffusion method, the original hybrid method, and even an improved version of the hybrid method, the SCL algorithm remarkably promotes the personalized recommendation in three other aspects: solving the accuracy-diversity dilemma, presenting a high novelty, and solving the key challenge of cold start problem.
Institute of Scientific and Technical Information of China (English)
ZHANG Hua-rong; QU Guo-qing; REN Ting
2012-01-01
There are various influencing factors that affect the deformation observation,and deformation signals show different characteristics under different scales.Wavelet analysis possesses multi-scale property,and the information entropy has great representational capability to the complexity of information.By hamming window to the wavelet coefficients and windowed wavelet energy obtained by multi-resolution analysis (MRA),it can be achieved to measure the wavelet time entropy (WTE) and wavelet energy entropy (WEE).The paper established deformation signals,selected the parameters,and compared the singularity detection ability and anti-noise ability of two kinds of wavelet entropy and applied them to the singularity detection at the GPS continuously operating reference stations.It is shown that the WTE performs well in weak singularity information detection in finite frequency components signals and the WEE is more suitable for detecting the singularity in the signals with complex,strong background noise.
Tailoring wavelets for chaos control.
Wei, G W; Zhan, Meng; Lai, C-H
2002-12-31
Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature.
Cavalier, Paul; Baghai-Wadji, Alireza; Poprawski, Yohann; Inggs, Michael
2016-11-01
Wavelet methods have been used in potential fields study to estimate source properties such as depth or structural index, through the analysis of Wavelet Transform Modulus Maxima Lines (WTMML) intersections and slopes at high scales. Little has been done on the study of maximum points of the wavelet diagram, that we call here Maximum Wavelet Coefficient Scales (MWCS). Previous works have shown interesting correlations between MWCS and source depths, depending on the wavelet used in regards to the source nature and the data derivative order. In this paper, we introduce an empirical law involving spectral parameters that have not been studied so far, which allows analytical calculation of the MWCS, knowing the source characteristics and using certain wavelets. In return, the study of MWCS allows recovering source characteristics from the use of a single wavelet, without prior knowledge on the source. We demonstrate through synthetic models that the new capability of predicting the source type and depth according to the wavelet coefficient behaviour allows new ways of potential fields' sources characterization and identification. We show an application of the formula on a real case example in the Uinta Mountains (Utah, USA).
Pigmented skin lesion detection using random forest and wavelet-based texture
Hu, Ping; Yang, Tie-jun
2016-10-01
The incidence of cutaneous malignant melanoma, a disease of worldwide distribution and is the deadliest form of skin cancer, has been rapidly increasing over the last few decades. Because advanced cutaneous melanoma is still incurable, early detection is an important step toward a reduction in mortality. Dermoscopy photographs are commonly used in melanoma diagnosis and can capture detailed features of a lesion. A great variability exists in the visual appearance of pigmented skin lesions. Therefore, in order to minimize the diagnostic errors that result from the difficulty and subjectivity of visual interpretation, an automatic detection approach is required. The objectives of this paper were to propose a hybrid method using random forest and Gabor wavelet transformation to accurately differentiate which part belong to lesion area and the other is not in a dermoscopy photographs and analyze segmentation accuracy. A random forest classifier consisting of a set of decision trees was used for classification. Gabor wavelets transformation are the mathematical model of visual cortical cells of mammalian brain and an image can be decomposed into multiple scales and multiple orientations by using it. The Gabor function has been recognized as a very useful tool in texture analysis, due to its optimal localization properties in both spatial and frequency domain. Texture features based on Gabor wavelets transformation are found by the Gabor filtered image. Experiment results indicate the following: (1) the proposed algorithm based on random forest outperformed the-state-of-the-art in pigmented skin lesions detection (2) and the inclusion of Gabor wavelet transformation based texture features improved segmentation accuracy significantly.
Directory of Open Access Journals (Sweden)
Shinya Ito
Full Text Available Understanding the detailed circuitry of functioning neuronal networks is one of the major goals of neuroscience. Recent improvements in neuronal recording techniques have made it possible to record the spiking activity from hundreds of neurons simultaneously with sub-millisecond temporal resolution. Here we used a 512-channel multielectrode array system to record the activity from hundreds of neurons in organotypic cultures of cortico-hippocampal brain slices from mice. To probe the network structure, we employed a wavelet transform of the cross-correlogram to categorize the functional connectivity in different frequency ranges. With this method we directly compare, for the first time, in any preparation, the neuronal network structures of cortex and hippocampus, on the scale of hundreds of neurons, with sub-millisecond time resolution. Among the three frequency ranges that we investigated, the lower two frequency ranges (gamma (30-80 Hz and beta (12-30 Hz range showed similar network structure between cortex and hippocampus, but there were many significant differences between these structures in the high frequency range (100-1000 Hz. The high frequency networks in cortex showed short tailed degree-distributions, shorter decay length of connectivity density, smaller clustering coefficients, and positive assortativity. Our results suggest that our method can characterize frequency dependent differences of network architecture from different brain regions. Crucially, because these differences between brain regions require millisecond temporal scales to be observed and characterized, these results underscore the importance of high temporal resolution recordings for the understanding of functional networks in neuronal systems.
Do wavelet filters provide more accurate estimates of reverberation times at low frequencies
DEFF Research Database (Denmark)
Sobreira Seoane, Manuel A.; Pérez Cabo, David; Agerkvist, Finn T.
2016-01-01
the continuous wavelet transform (CTW) has been implemented using a Morlet mother function. Although in general, the wavelet filter bank performs better than the usual filters, the influence of decaying modes outside the filter bandwidth on the measurements has been detected, leading to a biased estimation...
Molecular-Scale Electronics: From Concept to Function.
Xiang, Dong; Wang, Xiaolong; Jia, Chuancheng; Lee, Takhee; Guo, Xuefeng
2016-04-13
Creating functional electrical circuits using individual or ensemble molecules, often termed as "molecular-scale electronics", not only meets the increasing technical demands of the miniaturization of traditional Si-based electronic devices, but also provides an ideal window of exploring the intrinsic properties of materials at the molecular level. This Review covers the major advances with the most general applicability and emphasizes new insights into the development of efficient platform methodologies for building reliable molecular electronic devices with desired functionalities through the combination of programmed bottom-up self-assembly and sophisticated top-down device fabrication. First, we summarize a number of different approaches of forming molecular-scale junctions and discuss various experimental techniques for examining these nanoscale circuits in details. We then give a full introduction of characterization techniques and theoretical simulations for molecular electronics. Third, we highlight the major contributions and new concepts of integrating molecular functionalities into electrical circuits. Finally, we provide a critical discussion of limitations and main challenges that still exist for the development of molecular electronics. These analyses should be valuable for deeply understanding charge transport through molecular junctions, the device fabrication process, and the roadmap for future practical molecular electronics.