International Nuclear Information System (INIS)
Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris
2011-01-01
Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....
General inverse problems for regular variation
DEFF Research Database (Denmark)
Damek, Ewa; Mikosch, Thomas Valentin; Rosinski, Jan
2014-01-01
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components ...
Optimization for nonlinear inverse problem
International Nuclear Information System (INIS)
Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.
2007-06-01
The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)
Regularized inversion of controlled source and earthquake data
International Nuclear Information System (INIS)
Ramachandran, Kumar
2012-01-01
Estimation of the seismic velocity structure of the Earth's crust and upper mantle from travel-time data has advanced greatly in recent years. Forward modelling trial-and-error methods have been superseded by tomographic methods which allow more objective analysis of large two-dimensional and three-dimensional refraction and/or reflection data sets. The fundamental purpose of travel-time tomography is to determine the velocity structure of a medium by analysing the time it takes for a wave generated at a source point within the medium to arrive at a distribution of receiver points. Tomographic inversion of first-arrival travel-time data is a nonlinear problem since both the velocity of the medium and ray paths in the medium are unknown. The solution for such a problem is typically obtained by repeated application of linearized inversion. Regularization of the nonlinear problem reduces the ill posedness inherent in the tomographic inversion due to the under-determined nature of the problem and the inconsistencies in the observed data. This paper discusses the theory of regularized inversion for joint inversion of controlled source and earthquake data, and results from synthetic data testing and application to real data. The results obtained from tomographic inversion of synthetic data and real data from the northern Cascadia subduction zone show that the velocity model and hypocentral parameters can be efficiently estimated using this approach. (paper)
Adaptive regularization of noisy linear inverse problems
DEFF Research Database (Denmark)
Hansen, Lars Kai; Madsen, Kristoffer Hougaard; Lehn-Schiøler, Tue
2006-01-01
In the Bayesian modeling framework there is a close relation between regularization and the prior distribution over parameters. For prior distributions in the exponential family, we show that the optimal hyper-parameter, i.e., the optimal strength of regularization, satisfies a simple relation: T......: The expectation of the regularization function, i.e., takes the same value in the posterior and prior distribution. We present three examples: two simulations, and application in fMRI neuroimaging....
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM
DEFF Research Database (Denmark)
Knudsen, Kim; Lassas, Matti; Mueller, Jennifer
2009-01-01
A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posed inverse conductivity problem is presented. The strategy utilizes truncation of the boundary integral...... the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel...
Geostatistical regularization operators for geophysical inverse problems on irregular meshes
Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA
2018-05-01
Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.
Incremental projection approach of regularization for inverse problems
Energy Technology Data Exchange (ETDEWEB)
Souopgui, Innocent, E-mail: innocent.souopgui@usm.edu [The University of Southern Mississippi, Department of Marine Science (United States); Ngodock, Hans E., E-mail: hans.ngodock@nrlssc.navy.mil [Naval Research Laboratory (United States); Vidard, Arthur, E-mail: arthur.vidard@imag.fr; Le Dimet, François-Xavier, E-mail: ledimet@imag.fr [Laboratoire Jean Kuntzmann (France)
2016-10-15
This paper presents an alternative approach to the regularized least squares solution of ill-posed inverse problems. Instead of solving a minimization problem with an objective function composed of a data term and a regularization term, the regularization information is used to define a projection onto a convex subspace of regularized candidate solutions. The objective function is modified to include the projection of each iterate in the place of the regularization. Numerical experiments based on the problem of motion estimation for geophysical fluid images, show the improvement of the proposed method compared with regularization methods. For the presented test case, the incremental projection method uses 7 times less computation time than the regularization method, to reach the same error target. Moreover, at convergence, the incremental projection is two order of magnitude more accurate than the regularization method.
Inverse Higgs effect in nonlinear realizations
International Nuclear Information System (INIS)
Ivanov, E.A.; Ogievetskij, V.I.
1975-01-01
In theories with nonlinearly realized symmetry it is possible in a number of cases to eliminate some initial Goldstone and gauge fields by means of putting appropriate Cartan forms equal to zero. This is called the inverse Higgs phenomenon. We give a general treatment of the inverse Higgs phenomenon for gauge and space-time symmetries and consider four instructive examples which are the elimination of unessential gauge fields in chiral symmetry and in non-linearly realized supersymmetry and also the elimination of unessential Goldstone fields in the spontaneously broken conformal and projective symmetries
Centered Differential Waveform Inversion with Minimum Support Regularization
Kazei, Vladimir
2017-05-26
Time-lapse full-waveform inversion has two major challenges. The first one is the reconstruction of a reference model (baseline model for most of approaches). The second is inversion for the time-lapse changes in the parameters. Common model approach is utilizing the information contained in all available data sets to build a better reference model for time lapse inversion. Differential (Double-difference) waveform inversion allows to reduce the artifacts introduced into estimates of time-lapse parameter changes by imperfect inversion for the baseline-reference model. We propose centered differential waveform inversion (CDWI) which combines these two approaches in order to benefit from both of their features. We apply minimum support regularization commonly used with electromagnetic methods of geophysical exploration. We test the CDWI method on synthetic dataset with random noise and show that, with Minimum support regularization, it provides better resolution of velocity changes than with total variation and Tikhonov regularizations in time-lapse full-waveform inversion.
Regularization method for solving the inverse scattering problem
International Nuclear Information System (INIS)
Denisov, A.M.; Krylov, A.S.
1985-01-01
The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table
A 2D nonlinear inversion of well-seismic data
International Nuclear Information System (INIS)
Métivier, Ludovic; Lailly, Patrick; Delprat-Jannaud, Florence; Halpern, Laurence
2011-01-01
Well-seismic data such as vertical seismic profiles are supposed to provide detailed information about the elastic properties of the subsurface at the vicinity of the well. Heterogeneity of sedimentary terrains can lead to far from negligible multiple scattering, one of the manifestations of the nonlinearity involved in the mapping between elastic parameters and seismic data. We present a 2D extension of an existing 1D nonlinear inversion technique in the context of acoustic wave propagation. In the case of a subsurface with gentle lateral variations, we propose a regularization technique which aims at ensuring the stability of the inversion in a context where the recorded seismic waves provide a very poor illumination of the subsurface. We deal with a huge size inverse problem. Special care has been taken for its numerical solution, regarding both the choice of the algorithms and the implementation on a cluster-based supercomputer. Our tests on synthetic data show the effectiveness of our regularization. They also show that our efforts in accounting for the nonlinearities are rewarded by an exceptional seismic resolution at distances of about 100 m from the well. They also show that the result is not very sensitive to errors in the estimation of the velocity distribution, as far as these errors remain realistic in the context of a medium with gentle lateral variations
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)
Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering
Ablowitz, Mark J.
1994-12-01
Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.
Full Waveform Inversion Using Nonlinearly Smoothed Wavefields
Li, Y.; Choi, Yun Seok; Alkhalifah, Tariq Ali; Li, Z.
2017-01-01
The lack of low frequency information in the acquired data makes full waveform inversion (FWI) conditionally converge to the accurate solution. An initial velocity model that results in data with events within a half cycle of their location in the observed data was required to converge. The multiplication of wavefields with slightly different frequencies generates artificial low frequency components. This can be effectively utilized by multiplying the wavefield with itself, which is nonlinear operation, followed by a smoothing operator to extract the artificially produced low frequency information. We construct the objective function using the nonlinearly smoothed wavefields with a global-correlation norm to properly handle the energy imbalance in the nonlinearly smoothed wavefield. Similar to the multi-scale strategy, we progressively reduce the smoothing width applied to the multiplied wavefield to welcome higher resolution. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to the conventional FWI except for the adjoint source. Examples on the Marmousi 2 model demonstrate the feasibility of the proposed FWI method to mitigate the cycle-skipping problem in the case of a lack of low frequency information.
Full Waveform Inversion Using Nonlinearly Smoothed Wavefields
Li, Y.
2017-05-26
The lack of low frequency information in the acquired data makes full waveform inversion (FWI) conditionally converge to the accurate solution. An initial velocity model that results in data with events within a half cycle of their location in the observed data was required to converge. The multiplication of wavefields with slightly different frequencies generates artificial low frequency components. This can be effectively utilized by multiplying the wavefield with itself, which is nonlinear operation, followed by a smoothing operator to extract the artificially produced low frequency information. We construct the objective function using the nonlinearly smoothed wavefields with a global-correlation norm to properly handle the energy imbalance in the nonlinearly smoothed wavefield. Similar to the multi-scale strategy, we progressively reduce the smoothing width applied to the multiplied wavefield to welcome higher resolution. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to the conventional FWI except for the adjoint source. Examples on the Marmousi 2 model demonstrate the feasibility of the proposed FWI method to mitigate the cycle-skipping problem in the case of a lack of low frequency information.
A new approach to nonlinear constrained Tikhonov regularization
Ito, Kazufumi
2011-09-16
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented. © 2011 IOP Publishing Ltd.
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong; Alkhalifah, Tariq Ali
2015-01-01
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect
Lavrentiev regularization method for nonlinear ill-posed problems
International Nuclear Information System (INIS)
Kinh, Nguyen Van
2002-10-01
In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x 0 of non ill-posed problems F(x)=y o , where instead of y 0 noisy data y δ is an element of X with absolut(y δ -y 0 ) ≤ δ are given and F:X→X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x α δ are obtained by solving the singularly perturbed nonlinear operator equation F(x)+α(x-x*)=y δ with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter α has been chosen properly. (author)
Nonlinear adaptive inverse control via the unified model neural network
Jeng, Jin-Tsong; Lee, Tsu-Tian
1999-03-01
In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.
Learning Inverse Rig Mappings by Nonlinear Regression.
Holden, Daniel; Saito, Jun; Komura, Taku
2017-03-01
We present a framework to design inverse rig-functions-functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.
Nonlinear Spatial Inversion Without Monte Carlo Sampling
Curtis, A.; Nawaz, A.
2017-12-01
High-dimensional, nonlinear inverse or inference problems usually have non-unique solutions. The distribution of solutions are described by probability distributions, and these are usually found using Monte Carlo (MC) sampling methods. These take pseudo-random samples of models in parameter space, calculate the probability of each sample given available data and other information, and thus map out high or low probability values of model parameters. However, such methods would converge to the solution only as the number of samples tends to infinity; in practice, MC is found to be slow to converge, convergence is not guaranteed to be achieved in finite time, and detection of convergence requires the use of subjective criteria. We propose a method for Bayesian inversion of categorical variables such as geological facies or rock types in spatial problems, which requires no sampling at all. The method uses a 2-D Hidden Markov Model over a grid of cells, where observations represent localized data constraining the model in each cell. The data in our example application are seismic properties such as P- and S-wave impedances or rock density; our model parameters are the hidden states and represent the geological rock types in each cell. The observations at each location are assumed to depend on the facies at that location only - an assumption referred to as `localized likelihoods'. However, the facies at a location cannot be determined solely by the observation at that location as it also depends on prior information concerning its correlation with the spatial distribution of facies elsewhere. Such prior information is included in the inversion in the form of a training image which represents a conceptual depiction of the distribution of local geologies that might be expected, but other forms of prior information can be used in the method as desired. The method provides direct (pseudo-analytic) estimates of posterior marginal probability distributions over each variable
Sieberling, S.; Chu, Q.P.; Mulder, J.A.
2010-01-01
This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of
Beamforming Through Regularized Inverse Problems in Ultrasound Medical Imaging.
Szasz, Teodora; Basarab, Adrian; Kouame, Denis
2016-12-01
Beamforming (BF) in ultrasound (US) imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum (DAS) is still extensively used nowadays in clinical applications, due to its real-time capabilities. The most common alternatives are minimum variance (MV) method and its variants, which overcome the drawbacks of DAS, at the cost of higher computational complexity that limits its utilization in real-time applications. In this paper, we propose to perform BF in US imaging through a regularized inverse problem based on a linear model relating the reflected echoes to the signal to be recovered. Our approach presents two major advantages: 1) its flexibility in the choice of statistical assumptions on the signal to be beamformed (Laplacian and Gaussian statistics are tested herein) and 2) its robustness to a reduced number of pulse emissions. The proposed framework is flexible and allows for choosing the right tradeoff between noise suppression and sharpness of the resulted image. We illustrate the performance of our approach on both simulated and experimental data, with in vivo examples of carotid and thyroid. Compared with DAS, MV, and two other recently published BF techniques, our method offers better spatial resolution, respectively contrast, when using Laplacian and Gaussian priors.
Spatially-Variant Tikhonov Regularization for Double-Difference Waveform Inversion
Energy Technology Data Exchange (ETDEWEB)
Lin, Youzuo [Los Alamos National Laboratory; Huang, Lianjie [Los Alamos National Laboratory; Zhang, Zhigang [Los Alamos National Laboratory
2011-01-01
Double-difference waveform inversion is a potential tool for quantitative monitoring for geologic carbon storage. It jointly inverts time-lapse seismic data for changes in reservoir geophysical properties. Due to the ill-posedness of waveform inversion, it is a great challenge to obtain reservoir changes accurately and efficiently, particularly when using time-lapse seismic reflection data. Regularization techniques can be utilized to address the issue of ill-posedness. The regularization parameter controls the smoothness of inversion results. A constant regularization parameter is normally used in waveform inversion, and an optimal regularization parameter has to be selected. The resulting inversion results are a trade off among regions with different smoothness or noise levels; therefore the images are either over regularized in some regions while under regularized in the others. In this paper, we employ a spatially-variant parameter in the Tikhonov regularization scheme used in double-difference waveform tomography to improve the inversion accuracy and robustness. We compare the results obtained using a spatially-variant parameter with those obtained using a constant regularization parameter and those produced without any regularization. We observe that, utilizing a spatially-variant regularization scheme, the target regions are well reconstructed while the noise is reduced in the other regions. We show that the spatially-variant regularization scheme provides the flexibility to regularize local regions based on the a priori information without increasing computational costs and the computer memory requirement.
Yong, Peng; Liao, Wenyuan; Huang, Jianping; Li, Zhenchuan
2018-04-01
Full waveform inversion is an effective tool for recovering the properties of the Earth from seismograms. However, it suffers from local minima caused mainly by the limited accuracy of the starting model and the lack of a low-frequency component in the seismic data. Because of the high velocity contrast between salt and sediment, the relation between the waveform and velocity perturbation is strongly nonlinear. Therefore, salt inversion can easily get trapped in the local minima. Since the velocity of salt is nearly constant, we can make the most of this characteristic with total variation regularization to mitigate the local minima. In this paper, we develop an adaptive primal dual hybrid gradient method to implement total variation regularization by projecting the solution onto a total variation norm constrained convex set, through which the total variation norm constraint is satisfied at every model iteration. The smooth background velocities are first inverted and the perturbations are gradually obtained by successively relaxing the total variation norm constraints. Numerical experiment of the projection of the BP model onto the intersection of the total variation norm and box constraints has demonstrated the accuracy and efficiency of our adaptive primal dual hybrid gradient method. A workflow is designed to recover complex salt structures in the BP 2004 model and the 2D SEG/EAGE salt model, starting from a linear gradient model without using low-frequency data below 3 Hz. The salt inversion processes demonstrate that wavefield reconstruction inversion with a total variation norm and box constraints is able to overcome local minima and inverts the complex salt velocity layer by layer.
Shi, Junwei; Zhang, Bin; Liu, Fei; Luo, Jianwen; Bai, Jing
2013-09-15
For the ill-posed fluorescent molecular tomography (FMT) inverse problem, the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise. However, the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory, especially for large-scale problems. An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption. The reconstruction results from phantom experiments demonstrate that the proposed algorithm can obtain high spatial resolution and high signal-to-noise ratio, as well as high localization accuracy for fluorescence targets.
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Hidden regularity for a strongly nonlinear wave equation
International Nuclear Information System (INIS)
Rivera, J.E.M.
1988-08-01
The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt
Centered Differential Waveform Inversion with Minimum Support Regularization
Kazei, Vladimir; Alkhalifah, Tariq Ali
2017-01-01
Time-lapse full-waveform inversion has two major challenges. The first one is the reconstruction of a reference model (baseline model for most of approaches). The second is inversion for the time-lapse changes in the parameters. Common model
Inverse operator theory method and its applications in nonlinear physics
International Nuclear Information System (INIS)
Fang Jinqing
1993-01-01
Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed
On multiple level-set regularization methods for inverse problems
International Nuclear Information System (INIS)
DeCezaro, A; Leitão, A; Tai, X-C
2009-01-01
We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional G α based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikhonov method. A multiple level-set algorithm is derived from the first-order optimality conditions for the Tikhonov functional G α , similarly as the iterated Tikhonov method. The proposed multiple level-set method is tested on an inverse potential problem. Numerical experiments show that the method is able to recover multiple objects as well as multiple contrast levels
A nonlinear approach of elastic reflection waveform inversion
Guo, Qiang
2016-09-06
Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.
A nonlinear approach of elastic reflection waveform inversion
Guo, Qiang; Alkhalifah, Tariq Ali
2016-01-01
Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.
Shi, Junwei; Liu, Fei; Zhang, Guanglei; Luo, Jianwen; Bai, Jing
2014-04-01
Owing to the high degree of scattering of light through tissues, the ill-posedness of fluorescence molecular tomography (FMT) inverse problem causes relatively low spatial resolution in the reconstruction results. Unlike L2 regularization, L1 regularization can preserve the details and reduce the noise effectively. Reconstruction is obtained through a restarted L1 regularization-based nonlinear conjugate gradient (re-L1-NCG) algorithm, which has been proven to be able to increase the computational speed with low memory consumption. The algorithm consists of inner and outer iterations. In the inner iteration, L1-NCG is used to obtain the L1-regularized results. In the outer iteration, the restarted strategy is used to increase the convergence speed of L1-NCG. To demonstrate the performance of re-L1-NCG in terms of spatial resolution, simulation and physical phantom studies with fluorescent targets located with different edge-to-edge distances were carried out. The reconstruction results show that the re-L1-NCG algorithm has the ability to resolve targets with an edge-to-edge distance of 0.1 cm at a depth of 1.5 cm, which is a significant improvement for FMT.
Integral equations of the first kind, inverse problems and regularization: a crash course
International Nuclear Information System (INIS)
Groetsch, C W
2007-01-01
This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the first kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided
Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.
2018-04-01
We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.
Heeding the waveform inversion nonlinearity by unwrapping the model and data
Alkhalifah, Tariq Ali; Choi, Yun Seok
2012-01-01
Unlike traveltime inversion, waveform inversion provides relatively higher-resolution inverted models. This feature, however, comes at the cost of introducing complex nonlinearity to the inversion operator complicating the convergence process. We
Uieda, Leonardo; Barbosa, Valéria C. F.
2017-01-01
Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyperparameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basin, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.
Fukuda, J.; Johnson, K. M.
2009-12-01
Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress
Elastic reflection based waveform inversion with a nonlinear approach
Guo, Qiang; Alkhalifah, Tariq Ali
2017-01-01
Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.
Elastic reflection based waveform inversion with a nonlinear approach
Guo, Qiang
2017-08-16
Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.
Success Stories in Control: Nonlinear Dynamic Inversion Control
Bosworth, John T.
2010-01-01
NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
Directory of Open Access Journals (Sweden)
S. L. Han
2012-01-01
Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.
Directory of Open Access Journals (Sweden)
Wei Gao
2016-01-01
Full Text Available According to the regularization method in the inverse problem of load identification, a new method for determining the optimal regularization parameter is proposed. Firstly, quotient function (QF is defined by utilizing the regularization parameter as a variable based on the least squares solution of the minimization problem. Secondly, the quotient function method (QFM is proposed to select the optimal regularization parameter based on the quadratic programming theory. For employing the QFM, the characteristics of the values of QF with respect to the different regularization parameters are taken into consideration. Finally, numerical and experimental examples are utilized to validate the performance of the QFM. Furthermore, the Generalized Cross-Validation (GCV method and the L-curve method are taken as the comparison methods. The results indicate that the proposed QFM is adaptive to different measuring points, noise levels, and types of dynamic load.
One-dimensional nonlinear inverse heat conduction technique
International Nuclear Information System (INIS)
Hills, R.G.; Hensel, E.C. Jr.
1986-01-01
The one-dimensional nonlinear problem of heat conduction is considered. A noniterative space-marching finite-difference algorithm is developed to estimate the surface temperature and heat flux from temperature measurements at subsurface locations. The trade-off between resolution and variance of the estimates of the surface conditions is discussed quantitatively. The inverse algorithm is stabilized through the use of digital filters applied recursively. The effect of the filters on the resolution and variance of the surface estimates is quantified. Results are presented which indicate that the technique is capable of handling noisy measurement data
Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.
Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji
2016-09-01
It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.
A new approach to nonlinear constrained Tikhonov regularization
Ito, Kazufumi; Jin, Bangti
2011-01-01
operator. The approach is exploited to derive convergence rate results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a
(2+1-dimensional regular black holes with nonlinear electrodynamics sources
Directory of Open Access Journals (Sweden)
Yun He
2017-11-01
Full Text Available On the basis of two requirements: the avoidance of the curvature singularity and the Maxwell theory as the weak field limit of the nonlinear electrodynamics, we find two restricted conditions on the metric function of (2+1-dimensional regular black hole in general relativity coupled with nonlinear electrodynamics sources. By the use of the two conditions, we obtain a general approach to construct (2+1-dimensional regular black holes. In this manner, we construct four (2+1-dimensional regular black holes as examples. We also study the thermodynamic properties of the regular black holes and verify the first law of black hole thermodynamics.
Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems
International Nuclear Information System (INIS)
Haber, E; Horesh, L; Tenorio, L
2010-01-01
Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.
Salt-body Inversion with Minimum Gradient Support and Sobolev Space Norm Regularizations
Kazei, Vladimir
2017-05-26
Full-waveform inversion (FWI) is a technique which solves the ill-posed seismic inversion problem of fitting our model data to the measured ones from the field. FWI is capable of providing high-resolution estimates of the model, and of handling wave propagation of arbitrary complexity (visco-elastic, anisotropic); yet, it often fails to retrieve high-contrast geological structures, such as salt. One of the reasons for the FWI failure is that the updates at earlier iterations are too smooth to capture the sharp edges of the salt boundary. We compare several regularization approaches, which promote sharpness of the edges. Minimum gradient support (MGS) regularization focuses the inversion on blocky models, even more than the total variation (TV) does. However, both approaches try to invert undesirable high wavenumbers in the model too early for a model of complex structure. Therefore, we apply the Sobolev space norm as a regularizing term in order to maintain a balance between sharp and smooth updates in FWI. We demonstrate the application of these regularizations on a Marmousi model, enriched by a chunk of salt. The model turns out to be too complex in some parts to retrieve its full velocity distribution, yet the salt shape and contrast are retrieved.
Full-waveform inversion using a nonlinearly smoothed wavefield
Li, Yuanyuan
2017-12-08
Conventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.
Regularized Laplace-Fourier-Domain Full Waveform Inversion Using a Weighted l 2 Objective Function
Jun, Hyunggu; Kwon, Jungmin; Shin, Changsoo; Zhou, Hongbo; Cogan, Mike
2017-03-01
Full waveform inversion (FWI) can be applied to obtain an accurate velocity model that contains important geophysical and geological information. FWI suffers from the local minimum problem when the starting model is not sufficiently close to the true model. Therefore, an accurate macroscale velocity model is essential for successful FWI, and Laplace-Fourier-domain FWI is appropriate for obtaining such a velocity model. However, conventional Laplace-Fourier-domain FWI remains an ill-posed and ill-conditioned problem, meaning that small errors in the data can result in large differences in the inverted model. This approach also suffers from certain limitations related to the logarithmic objective function. To overcome the limitations of conventional Laplace-Fourier-domain FWI, we introduce a weighted l 2 objective function, instead of the logarithmic objective function, as the data-domain objective function, and we also introduce two different model-domain regularizations: first-order Tikhonov regularization and prior model regularization. The weighting matrix for the data-domain objective function is constructed to suitably enhance the far-offset information. Tikhonov regularization smoothes the gradient, and prior model regularization allows reliable prior information to be taken into account. Two hyperparameters are obtained through trial and error and used to control the trade-off and achieve an appropriate balance between the data-domain and model-domain gradients. The application of the proposed regularizations facilitates finding a unique solution via FWI, and the weighted l 2 objective function ensures a more reasonable residual, thereby improving the stability of the gradient calculation. Numerical tests performed using the Marmousi synthetic dataset show that the use of the weighted l 2 objective function and the model-domain regularizations significantly improves the Laplace-Fourier-domain FWI. Because the Laplace-Fourier-domain FWI is improved, the
Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers
Czech Academy of Sciences Publication Activity Database
Adam, Lukáš; Branda, Martin
2016-01-01
Roč. 170, č. 2 (2016), s. 419-436 ISSN 0022-3239 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.289, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf
Nonlinear Dynamic Inversion Baseline Control Law: Architecture and Performance Predictions
Miller, Christopher J.
2011-01-01
A model reference dynamic inversion control law has been developed to provide a baseline control law for research into adaptive elements and other advanced flight control law components. This controller has been implemented and tested in a hardware-in-the-loop simulation; the simulation results show excellent handling qualities throughout the limited flight envelope. A simple angular momentum formulation was chosen because it can be included in the stability proofs for many basic adaptive theories, such as model reference adaptive control. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as basic as possible to simplify the addition of the adaptive elements. Those design choices are explained, along with their predicted impact on the handling qualities.
Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas
2018-06-01
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.
A general approach to regularizing inverse problems with regional data using Slepian wavelets
Michel, Volker; Simons, Frederik J.
2017-12-01
Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples.
Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten
2018-06-01
This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.
International Nuclear Information System (INIS)
Zhou, Jianmei; Shang, Qinglong; Wang, Hongnian; Wang, Jianxun; Yin, Changchun
2014-01-01
We present an algorithm for inverting controlled source audio-frequency magnetotelluric (CSAMT) data in horizontally layered transversely isotropic (TI) media. The popular inversion method parameterizes the media into a large number of layers which have fixed thickness and only reconstruct the conductivities (e.g. Occam's inversion), which does not enable the recovery of the sharp interfaces between layers. In this paper, we simultaneously reconstruct all the model parameters, including both the horizontal and vertical conductivities and layer depths. Applying the perturbation principle and the dyadic Green's function in TI media, we derive the analytic expression of Fréchet derivatives of CSAMT responses with respect to all the model parameters in the form of Sommerfeld integrals. A regularized iterative inversion method is established to simultaneously reconstruct all the model parameters. Numerical results show that the inverse algorithm, including the depths of the layer interfaces, can significantly improve the inverse results. It can not only reconstruct the sharp interfaces between layers, but also can obtain conductivities close to the true value. (paper)
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2017-09-01
Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.
Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering
Dorier, V.; Gevorgyan, M.; Ishkhanyan, A.; Leroy, C.; Jauslin, H. R.; Guérin, S.
2017-12-01
We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.
Explanation of the Inverse Doppler Effect Observed in Nonlinear Transmission Lines
International Nuclear Information System (INIS)
Kozyrev, Alexander B.; Weide, Daniel W. van der
2005-01-01
The theory of the inverse Doppler effect recently observed in magnetic nonlinear transmission lines is developed. We explain the crucial role of the backward spatial harmonic in the occurrence of an inverse Doppler effect and draw analogies of the magnetic nonlinear transmission line to the backward wave oscillator
Inverse problems with Poisson data: statistical regularization theory, applications and algorithms
International Nuclear Information System (INIS)
Hohage, Thorsten; Werner, Frank
2016-01-01
Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years. (topical review)
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, Roland [Univ. of California, Berkeley, CA (United States)
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_{p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
3D DC Resistivity Inversion with Topography Based on Regularized Conjugate Gradient Method
Directory of Open Access Journals (Sweden)
Jian-ke Qiang
2013-01-01
Full Text Available During the past decades, we observed a strong interest in 3D DC resistivity inversion and imaging with complex topography. In this paper, we implemented 3D DC resistivity inversion based on regularized conjugate gradient method with FEM. The Fréchet derivative is assembled with the electric potential in order to speed up the inversion process based on the reciprocity theorem. In this study, we also analyzed the sensitivity of the electric potential on the earth’s surface to the conductivity in each cell underground and introduced an optimized weighting function to produce new sensitivity matrix. The synthetic model study shows that this optimized weighting function is helpful to improve the resolution of deep anomaly. By incorporating topography into inversion, the artificial anomaly which is actually caused by topography can be eliminated. As a result, this algorithm potentially can be applied to process the DC resistivity data collected in mountain area. Our synthetic model study also shows that the convergence and computation speed are very stable and fast.
Directory of Open Access Journals (Sweden)
YanBin Liu
2017-01-01
Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.
Zhou, C.; Liu, L.; Lane, J.W.
2001-01-01
A nonlinear tomographic inversion method that uses first-arrival travel-time and amplitude-spectra information from cross-hole radar measurements was developed to simultaneously reconstruct electromagnetic velocity and attenuation distribution in earth materials. Inversion methods were developed to analyze single cross-hole tomography surveys and differential tomography surveys. Assuming the earth behaves as a linear system, the inversion methods do not require estimation of source radiation pattern, receiver coupling, or geometrical spreading. The data analysis and tomographic inversion algorithm were applied to synthetic test data and to cross-hole radar field data provided by the US Geological Survey (USGS). The cross-hole radar field data were acquired at the USGS fractured-rock field research site at Mirror Lake near Thornton, New Hampshire, before and after injection of a saline tracer, to monitor the transport of electrically conductive fluids in the image plane. Results from the synthetic data test demonstrate the algorithm computational efficiency and indicate that the method robustly can reconstruct electromagnetic (EM) wave velocity and attenuation distribution in earth materials. The field test results outline zones of velocity and attenuation anomalies consistent with the finding of previous investigators; however, the tomograms appear to be quite smooth. Further work is needed to effectively find the optimal smoothness criterion in applying the Tikhonov regularization in the nonlinear inversion algorithms for cross-hole radar tomography. ?? 2001 Elsevier Science B.V. All rights reserved.
An algorithmic framework for Mumford–Shah regularization of inverse problems in imaging
International Nuclear Information System (INIS)
Hohm, Kilian; Weinmann, Andreas; Storath, Martin
2015-01-01
The Mumford–Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this paper, we propose a new efficient algorithmic framework for Mumford–Shah regularization of inverse problems in imaging. It is based on a splitting into specific subproblems that can be solved exactly. We derive fast solvers for the subproblems which are key for an efficient overall algorithm. Our method neither requires a priori knowledge of the gray or color levels nor of the shape of the discontinuity set. We demonstrate the wide applicability of the method for different modalities. In particular, we consider the reconstruction from Radon data, inpainting, and deconvolution. Our method can be easily adapted to many further imaging setups. The relevant condition is that the proximal mapping of the data fidelity can be evaluated a within reasonable time. In other words, it can be used whenever classical Tikhonov regularization is possible. (paper)
Partial regularity of weak solutions to a PDE system with cubic nonlinearity
Liu, Jian-Guo; Xu, Xiangsheng
2018-04-01
In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.
Mesgouez, A.
2018-05-01
The determination of equivalent viscoelastic properties of heterogeneous objects remains challenging in various scientific fields such as (geo)mechanics, geophysics or biomechanics. The present investigation addresses the issue of the identification of effective constitutive properties of a binary object by using a nonlinear and full waveform inversion scheme. The inversion process, without any regularization technique or a priori information, aims at minimizing directly the discrepancy between the full waveform responses of a bi-material viscoelastic cylindrical object and its corresponding effective homogeneous object. It involves the retrieval of five constitutive equivalent parameters. Numerical simulations are performed in a laboratory-scale two-dimensional configuration: a transient acoustic plane wave impacts the object and the diffracted fluid pressure, solid stress or velocity component fields are determined using a semi-analytical approach. Results show that the retrieval of the density and of the real parts of both the compressional and the shear wave velocities have been carried out successfully regarding the number and location of sensors, the type of sensors, the size of the searching space, the frequency range of the incident plane pressure wave, and the change in the geometric or mechanical constitution of the bi-material object. The retrieval of the imaginary parts of the wave velocities can reveal in some cases the limitations of the proposed approach.
3D Inversion of Magnetic Data through Wavelet based Regularization Method
Directory of Open Access Journals (Sweden)
Maysam Abedi
2015-06-01
Full Text Available This study deals with the 3D recovering of magnetic susceptibility model by incorporating the sparsity-based constraints in the inversion algorithm. For this purpose, the area under prospect was divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Tikhonov cost functions with two sparsity functions were used to recover the smooth parts as well as the sharp boundaries of model parameters. A pre-selected basis namely wavelet can recover the region of smooth behaviour of susceptibility distribution while Haar or finite-difference (FD domains yield a solution with rough boundaries. Therefore, a regularizer function which can benefit from the advantages of both wavelets and Haar/FD operators in representation of the 3D magnetic susceptibility distributionwas chosen as a candidate for modeling magnetic anomalies. The optimum wavelet and parameter β which controls the weight of the two sparsifying operators were also considered. The algorithm assumed that there was no remanent magnetization and observed that magnetometry data represent only induced magnetization effect. The proposed approach is applied to a noise-corrupted synthetic data in order to demonstrate its suitability for 3D inversion of magnetic data. On obtaining satisfactory results, a case study pertaining to the ground based measurement of magnetic anomaly over a porphyry-Cu deposit located in Kerman providence of Iran. Now Chun deposit was presented to be 3D inverted. The low susceptibility in the constructed model coincides with the known location of copper ore mineralization.
Alkhalifah, Tariq Ali
2012-09-25
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
Alkhalifah, Tariq Ali; Choi, Yun Seok
2012-01-01
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1
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Henri Schurz
2010-09-01
Full Text Available Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.
Optimized nonlinear inversion of surface-wave dispersion data
International Nuclear Information System (INIS)
Raykova, Reneta B.
2014-01-01
A new code for inversion of surface wave dispersion data is developed to obtain Earth’s crustal and upper mantle velocity structure. The author developed Optimized Non–Linear Inversion ( ONLI ) software, based on Monte-Carlo search. The values of S–wave velocity VS and thickness h for a number of horizontal homogeneous layers are parameterized. Velocity of P–wave VP and density ρ of relevant layers are calculated by empirical or theoretical relations. ONLI explores parameters space in two modes, selective and full search, and the main innovation of software is evaluation of tested models. Theoretical dispersion curves are calculated if tested model satisfied specific conditions only, reducing considerably the computation time. A number of tests explored impact of parameterization and proved the ability of ONLI approach to deal successfully with non–uniqueness of inversion problem. Key words: Earth’s structure, surface–wave dispersion, non–linear inversion, software
Heeding the waveform inversion nonlinearity by unwrapping the model and data
Alkhalifah, Tariq Ali
2012-01-01
Unlike traveltime inversion, waveform inversion provides relatively higher-resolution inverted models. This feature, however, comes at the cost of introducing complex nonlinearity to the inversion operator complicating the convergence process. We use unwrapped-phase-based objective functions to reduce such nonlinearity in a domain in which the high-frequency component is given by the traveltime inversion. Such information is packaged in a frequency-dependent attribute (or traveltime) that can be easily manipulated at different frequencies. It unwraps the phase of the wavefield yielding far less nonlinearity in the objective function than those experienced with the conventional misfit objective function, and yet it still holds most of the critical waveform information in its frequency dependency. However, it suffers from nonlinearity introduced by the model (or reflectivity), as events interact with each other (something like cross talk). This stems from the sinusoidal nature of the band-limited reflectivity model. Unwrapping the phase for such a model can mitigate this nonlinearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced nonlinearity and, thus, make the inversion more convergent. Simple examples are used to highlight such features.
Full-waveform inversion using a nonlinearly smoothed wavefield
Li, Yuanyuan; Choi, Yun Seok; Alkhalifah, Tariq Ali; Li, Zhenchun; Zhang, Kai
2017-01-01
width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.
Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts
International Nuclear Information System (INIS)
Rakhmanov, M
2006-01-01
Coherent techniques for searches of gravitational-wave bursts effectively combine data from several detectors, taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most natural way to combine data, which can also be used without prior knowledge of the signal. Recent studies however have shown that straightforward application of the maximum likelihood method to gravitational waves with unknown waveforms can lead to inconsistencies and unphysical results such as discontinuity in the residual functional, or divergence of the variance of the estimated waveforms for some locations in the sky. So far the solutions to these problems have been based on rather different physical arguments. Following these investigations, we now find that all these inconsistencies stem from the rank deficiency of the underlying network response matrix. In this paper we show that the detection of gravitational-wave bursts with a network of interferometers belongs to the category of ill-posed problems. We then apply the method of Tikhonov regularization to resolve the rank deficiency and introduce a minimal regulator which yields a well-conditioned solution to the inverse problem for all locations on the sky
Directory of Open Access Journals (Sweden)
Sebastian Schaetz
2017-01-01
Full Text Available Purpose. To develop generic optimization strategies for image reconstruction using graphical processing units (GPUs in magnetic resonance imaging (MRI and to exemplarily report on our experience with a highly accelerated implementation of the nonlinear inversion (NLINV algorithm for dynamic MRI with high frame rates. Methods. The NLINV algorithm is optimized and ported to run on a multi-GPU single-node server. The algorithm is mapped to multiple GPUs by decomposing the data domain along the channel dimension. Furthermore, the algorithm is decomposed along the temporal domain by relaxing a temporal regularization constraint, allowing the algorithm to work on multiple frames in parallel. Finally, an autotuning method is presented that is capable of combining different decomposition variants to achieve optimal algorithm performance in different imaging scenarios. Results. The algorithm is successfully ported to a multi-GPU system and allows online image reconstruction with high frame rates. Real-time reconstruction with low latency and frame rates up to 30 frames per second is demonstrated. Conclusion. Novel parallel decomposition methods are presented which are applicable to many iterative algorithms for dynamic MRI. Using these methods to parallelize the NLINV algorithm on multiple GPUs, it is possible to achieve online image reconstruction with high frame rates.
Regularity of the solutions to a nonlinear boundary problem with indefinite weight
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Aomar Anane
2011-01-01
Full Text Available In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p−2}u in the bounded smooth domainOmega ⊂ R^N,with|∇u|^{p−2} partial_{nu} u = lambda V (x|u|^{p−2}u + h as a nonlinear boundary condition, where partial Omega is C^{2,beta}, with beta ∈]0, 1[, and V is a weight in L^s(partial Omega and h ∈ L^s(partial Omega for some s ≥ 1. We prove that all solutions are in L^{infty}(Omega cap L^{infty}(Omega, and using the D.Debenedetto’s theorem of regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega} for some alpha ∈ ]0, 1[.
A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics
DEFF Research Database (Denmark)
Engell-Nørregård, Morten; Erleben, Kenny
2009-01-01
Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...
International Nuclear Information System (INIS)
Alvarez-Estrada, R.F.
1979-01-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly
Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations
Nakamura, Gen; Vashisth, Manmohan
2017-01-01
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1993-01-01
The inverse operator method (IOM) for solutions of nonlinear dynamical systems (NDS) is briefly described and realized by the Mathematics-Mechanization (MM) in computers. For the first time IOM and MM are successfully applied to study the chaotic behaviors of Lorentz equation
Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays
International Nuclear Information System (INIS)
Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.
2005-04-01
We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)
Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao
2014-10-06
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.
International Nuclear Information System (INIS)
Najafi Mohammad; Arbabi Somayeh
2014-01-01
In this paper, we establish exact solutions for five complex nonlinear Schrödinger equations. The semi-inverse variational principle (SVP) is used to construct exact soliton solutions of five complex nonlinear Schrödinger equations. Many new families of exact soliton solutions of five complex nonlinear Schrödinger equations are successfully obtained. (general)
Measuring time series regularity using nonlinear similarity-based sample entropy
International Nuclear Information System (INIS)
Xie Hongbo; He Weixing; Liu Hui
2008-01-01
Sampe Entropy (SampEn), a measure quantifying regularity and complexity, is believed to be an effective analyzing method of diverse settings that include both deterministic chaotic and stochastic processes, particularly operative in the analysis of physiological signals that involve relatively small amount of data. However, the similarity definition of vectors is based on Heaviside function, of which the boundary is discontinuous and hard, may cause some problems in the validity and accuracy of SampEn. Sigmoid function is a smoothed and continuous version of Heaviside function. To overcome the problems SampEn encountered, a modified SampEn (mSampEn) based on nonlinear Sigmoid function was proposed. The performance of mSampEn was tested on the independent identically distributed (i.i.d.) uniform random numbers, the MIX stochastic model, the Rossler map, and the Hennon map. The results showed that mSampEn was superior to SampEn in several aspects, including giving entropy definition in case of small parameters, better relative consistency, robust to noise, and more independence on record length when characterizing time series generated from either deterministic or stochastic system with different regularities
International Nuclear Information System (INIS)
Yurtsever, E.; Brickmann, J.
1990-01-01
A two dimensional strongly nonharmonic vibrational system with nonlinear intermode coupling is studied both classically and quantum mechanically. The system was chosen such that there is a low lying transition (in energy) from a region where almost all trajectories move regularly to a region where chaotic dynamics strongly dominates. The corresponding quantum system is far away from the semiclassical limit. The eigenfunctions are calculated with high precision according to a linear variational scheme using conveniently chosen basis functions. It is the aim of this paper to check whether the prediction from semiclassical theory, namely that the measure of classically chaotic trajectories in phase space approaches the measure of irregular states in corresponding energy ranges, holds when the system is not close to the classical limit. It is also the aim to identify individual eigenfunctions with respect to regularity and to differentiate between local and normal vibrational states. It is found that there are quantitative and also qualitative differences between the quantum results and the semiclassical predictions. (orig./HK)
Analysis of regularized inversion of data corrupted by white Gaussian noise
International Nuclear Information System (INIS)
Kekkonen, Hanne; Lassas, Matti; Siltanen, Samuli
2014-01-01
Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement model for an unknown function u(x) is m(x) = Au(x) + δ ε (x), where δ > 0 is the noise magnitude. If ε was an L 2 -function, Tikhonov regularization gives an estimate T α (m) = u∈H r arg min { ||Au-m|| L 2 2 + α||u|| H r 2 } for u where α = α(δ) is the regularization parameter. Here penalization of the Sobolev norm ||u|| H r covers the cases of standard Tikhonov regularization (r = 0) and first derivative penalty (r = 1). Realizations of white Gaussian noise are almost never in L 2 , but do belong to H s with probability one if s < 0 is small enough. A modification of Tikhonov regularization theory is presented, covering the case of white Gaussian measurement noise. Furthermore, the convergence of regularized reconstructions to the correct solution as δ → 0 is proven in appropriate function spaces using microlocal analysis. The convergence of the related finite-dimensional problems to the infinite-dimensional problem is also analysed. (paper)
Avdyushev, Victor A.
2017-12-01
Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the
International Nuclear Information System (INIS)
Omura, Yoshiharu; Matsumoto, Hiroshi.
1989-01-01
Past theoretical and numerical studies of the nonlinear evolution of electromagnetic cyclotron waves are reviewed. Such waves are commonly observed in space plasmas such as Alfven waves in the solar wind or VLF whistler mode waves in the magnetosphere. The use of an electromagnetic full-particle code to study an electron cyclotron wave and of an electromagnetic hybrid code to study an ion cyclotron wave is demonstrated. Recent achievements in the simulations of nonlinear revolution of electromagnetic cyclotron waves are discussed. The inverse cascading processes of finite-amplitude whistler and Alfven waves is interpreted in terms of physical elementary processes. 65 refs
Campbell, Stefan F.; Kaneshige, John T.
2010-01-01
Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).
Bacon, Barton J.; Ostroff, Aaron J.
2000-01-01
This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.
Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A
2012-03-01
We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.
Rosenthal, Amir; Horowitz, Moshe; Kieckbusch, Sven; Brinkmeyer, Ernst
2007-10-01
We demonstrate experimentally, for the first time to our knowledge, a reconstruction of a highly reflecting fiber Bragg grating from its complex reflection spectrum by using a regularization algorithm. The regularization method is based on correcting the measured reflection spectrum at the Bragg zone frequencies and enables the reconstruction of the grating profile using the integral-layer-peeling algorithm. A grating with an approximately uniform profile and with a maximum reflectivity of 99.98% was accurately reconstructed by measuring only its complex reflection spectrum.
On the internal stability of non-linear dynamic inversion: application to flight control
Czech Academy of Sciences Publication Activity Database
Alam, M.; Čelikovský, Sergej
2017-01-01
Roč. 11, č. 12 (2017), s. 1849-1861 ISSN 1751-8644 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : flight control * non-linear dynamic inversion * stability Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 2.536, year: 2016 http://library.utia.cas.cz/separaty/2017/TR/celikovsky-0476150.pdf
Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method
Directory of Open Access Journals (Sweden)
Huan Ma
2015-01-01
Full Text Available Four kinds of array of induced polarization (IP methods (surface, borehole-surface, surface-borehole, and borehole-borehole are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI and graphics processing unit (GPU to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.
Yang, Hongxin; Su, Fulin
2018-01-01
We propose a moving target analysis algorithm using speeded-up robust features (SURF) and regular moment in inverse synthetic aperture radar (ISAR) image sequences. In our study, we first extract interest points from ISAR image sequences by SURF. Different from traditional feature point extraction methods, SURF-based feature points are invariant to scattering intensity, target rotation, and image size. Then, we employ a bilateral feature registering model to match these feature points. The feature registering scheme can not only search the isotropic feature points to link the image sequences but also reduce the error matching pairs. After that, the target centroid is detected by regular moment. Consequently, a cost function based on correlation coefficient is adopted to analyze the motion information. Experimental results based on simulated and real data validate the effectiveness and practicability of the proposed method.
International Nuclear Information System (INIS)
Vatankhah, Saeed; Ardestani, Vahid E; Renaut, Rosemary A
2014-01-01
The χ 2 principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data, when the stabilizing, or regularization, term is considered to be weighted by unknown inverse covariance information on the model parameters, the minimum of the Tikhonov functional becomes a random variable that follows a χ 2 -distribution with m+p−n degrees of freedom for the model matrix G of size m×n, m⩾n, and regularizer L of size p × n. Then, a Newton root-finding algorithm, employing the generalized singular value decomposition, or singular value decomposition when L = I, can be used to find the regularization parameter α. Here the result and algorithm are extended to the underdetermined case, m 2 algorithms when m 2 and unbiased predictive risk estimator of the regularization parameter are used for the first time in this context. For a simulated underdetermined data set with noise, these regularization parameter estimation methods, as well as the generalized cross validation method, are contrasted with the use of the L-curve and the Morozov discrepancy principle. Experiments demonstrate the efficiency and robustness of the χ 2 principle and unbiased predictive risk estimator, moreover showing that the L-curve and Morozov discrepancy principle are outperformed in general by the other three techniques. Furthermore, the minimum support stabilizer is of general use for the χ 2 principle when implemented without the desirable knowledge of the mean value of the model. (paper)
Frequency-domain full-waveform inversion with non-linear descent directions
Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.
2018-05-01
Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a
Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying
Directory of Open Access Journals (Sweden)
Inseok Yang
2014-01-01
Full Text Available The robust nonlinear dynamic inversion (RNDI control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI. NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC. SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.
Hamim, Salah Uddin Ahmed
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.
Inverse operator method for solutions of nonlinear dynamical equations and some typical applications
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1993-01-01
The inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coupled generalized Duffing equations are investigated by using the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields
Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H
2016-05-01
The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.
Directory of Open Access Journals (Sweden)
Merboldt Klaus-Dietmar
2010-07-01
Full Text Available Abstract Background Functional assessments of the heart by dynamic cardiovascular magnetic resonance (CMR commonly rely on (i electrocardiographic (ECG gating yielding pseudo real-time cine representations, (ii balanced gradient-echo sequences referred to as steady-state free precession (SSFP, and (iii breath holding or respiratory gating. Problems may therefore be due to the need for a robust ECG signal, the occurrence of arrhythmia and beat to beat variations, technical instabilities (e.g., SSFP "banding" artefacts, and limited patient compliance and comfort. Here we describe a new approach providing true real-time CMR with image acquisition times as short as 20 to 30 ms or rates of 30 to 50 frames per second. Methods The approach relies on a previously developed real-time MR method, which combines a strongly undersampled radial FLASH CMR sequence with image reconstruction by regularized nonlinear inversion. While iterative reconstructions are currently performed offline due to limited computer speed, online monitoring during scanning is accomplished using gridding reconstructions with a sliding window at the same frame rate but with lower image quality. Results Scans of healthy young subjects were performed at 3 T without ECG gating and during free breathing. The resulting images yield T1 contrast (depending on flip angle with an opposed-phase or in-phase condition for water and fat signals (depending on echo time. They completely avoid (i susceptibility-induced artefacts due to the very short echo times, (ii radiofrequency power limitations due to excitations with flip angles of 10° or less, and (iii the risk of peripheral nerve stimulation due to the use of normal gradient switching modes. For a section thickness of 8 mm, real-time images offer a spatial resolution and total acquisition time of 1.5 mm at 30 ms and 2.0 mm at 22 ms, respectively. Conclusions Though awaiting thorough clinical evaluation, this work describes a robust and
Zhang, Shuo; Uecker, Martin; Voit, Dirk; Merboldt, Klaus-Dietmar; Frahm, Jens
2010-07-08
Functional assessments of the heart by dynamic cardiovascular magnetic resonance (CMR) commonly rely on (i) electrocardiographic (ECG) gating yielding pseudo real-time cine representations, (ii) balanced gradient-echo sequences referred to as steady-state free precession (SSFP), and (iii) breath holding or respiratory gating. Problems may therefore be due to the need for a robust ECG signal, the occurrence of arrhythmia and beat to beat variations, technical instabilities (e.g., SSFP "banding" artefacts), and limited patient compliance and comfort. Here we describe a new approach providing true real-time CMR with image acquisition times as short as 20 to 30 ms or rates of 30 to 50 frames per second. The approach relies on a previously developed real-time MR method, which combines a strongly undersampled radial FLASH CMR sequence with image reconstruction by regularized nonlinear inversion. While iterative reconstructions are currently performed offline due to limited computer speed, online monitoring during scanning is accomplished using gridding reconstructions with a sliding window at the same frame rate but with lower image quality. Scans of healthy young subjects were performed at 3 T without ECG gating and during free breathing. The resulting images yield T1 contrast (depending on flip angle) with an opposed-phase or in-phase condition for water and fat signals (depending on echo time). They completely avoid (i) susceptibility-induced artefacts due to the very short echo times, (ii) radiofrequency power limitations due to excitations with flip angles of 10 degrees or less, and (iii) the risk of peripheral nerve stimulation due to the use of normal gradient switching modes. For a section thickness of 8 mm, real-time images offer a spatial resolution and total acquisition time of 1.5 mm at 30 ms and 2.0 mm at 22 ms, respectively. Though awaiting thorough clinical evaluation, this work describes a robust and flexible acquisition and reconstruction technique for
Formalev, V. F.; Kolesnik, S. A.
2017-11-01
The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.
Energy Distribution of a Regular Black Hole Solution in Einstein-Nonlinear Electrodynamics
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I. Radinschi
2015-01-01
Full Text Available A study about the energy momentum of a new four-dimensional spherically symmetric, static and charged, regular black hole solution developed in the context of general relativity coupled to nonlinear electrodynamics is presented. Asymptotically, this new black hole solution behaves as the Reissner-Nordström solution only for the particular value μ=4, where μ is a positive integer parameter appearing in the mass function of the solution. The calculations are performed by use of the Einstein, Landau-Lifshitz, Weinberg, and Møller energy momentum complexes. In all the aforementioned prescriptions, the expressions for the energy of the gravitating system considered depend on the mass M of the black hole, its charge q, a positive integer α, and the radial coordinate r. In all these pseudotensorial prescriptions, the momenta are found to vanish, while the Landau-Lifshitz and Weinberg prescriptions give the same result for the energy distribution. In addition, the limiting behavior of the energy for the cases r→∞, r→0, and q=0 is studied. The special case μ=4 and α=3 is also examined. We conclude that the Einstein and Møller energy momentum complexes can be considered as the most reliable tools for the study of the energy momentum localization of a gravitating system.
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1992-12-01
Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science
Regularization and Bayesian methods for inverse problems in signal and image processing
Giovannelli , Jean-François
2015-01-01
The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has si
Venugopal, M.; Roy, D.; Rajendran, K.; Guillas, S.; Dias, F.
2017-01-01
Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems. PMID:28989311
Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei
2016-07-01
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
Tikhonov regularization method for the numerical inversion of Mellin transforms using splines
International Nuclear Information System (INIS)
Iqbal, M.
2005-01-01
Mellin transform is an ill-posed problem. These problems arise in many branches of science and engineering. In the typical situation one is interested in recovering the original function, given a finite number of noisy measurements of data. In this paper, we shall convert Mellin transform to Laplace transform and then an integral equation of the first kind of convolution type. We solve the integral equation using Tikhonov regularization with splines as basis function. The method is applied to various test examples in the literature and results are shown in the table
Wu, Zedong; Alkhalifah, Tariq Ali
2017-01-01
Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current
International Nuclear Information System (INIS)
Frick, Klaus; Marnitz, Philipp; Munk, Axel
2012-01-01
This paper is concerned with a novel regularization technique for solving linear ill-posed operator equations in Hilbert spaces from data that are corrupted by white noise. We combine convex penalty functionals with extreme-value statistics of projections of the residuals on a given set of sub-spaces in the image space of the operator. We prove general consistency and convergence rate results in the framework of Bregman divergences which allows for a vast range of penalty functionals. Various examples that indicate the applicability of our approach will be discussed. We will illustrate in the context of signal and image processing that the presented method constitutes a locally adaptive reconstruction method. (paper)
International Nuclear Information System (INIS)
Wu, Ru-Shan; Wang, Benfeng; Hu, Chunhua
2015-01-01
We derived the renormalized nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator and its De Wolf approximation. The inverse propagator is based on a renormalization procedure to the forward and inverse transition matrix scattering series. The ITSP eliminates the divergence of the inverse Born series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at moderate perturbation (20% for the given model of Gaussian ball with a radius of 5 wavelength), while the ITSP has no divergence problem for any strong perturbations (up to 100% perturbation for test model). In addition, the ITSP is a non-iterative, marching algorithm with only one sweep, and therefore very efficient in comparison with the iterative inversion based on the inverse-Born scattering series. This convergence and efficiency improvement has potential applications to the iterative procedure of waveform inversion. (paper)
Wavelet-sparsity based regularization over time in the inverse problem of electrocardiography.
Cluitmans, Matthijs J M; Karel, Joël M H; Bonizzi, Pietro; Volders, Paul G A; Westra, Ronald L; Peeters, Ralf L M
2013-01-01
Noninvasive, detailed assessment of electrical cardiac activity at the level of the heart surface has the potential to revolutionize diagnostics and therapy of cardiac pathologies. Due to the requirement of noninvasiveness, body-surface potentials are measured and have to be projected back to the heart surface, yielding an ill-posed inverse problem. Ill-posedness ensures that there are non-unique solutions to this problem, resulting in a problem of choice. In the current paper, it is proposed to restrict this choice by requiring that the time series of reconstructed heart-surface potentials is sparse in the wavelet domain. A local search technique is introduced that pursues a sparse solution, using an orthogonal wavelet transform. Epicardial potentials reconstructed from this method are compared to those from existing methods, and validated with actual intracardiac recordings. The new technique improves the reconstructions in terms of smoothness and recovers physiologically meaningful details. Additionally, reconstruction of activation timing seems to be improved when pursuing sparsity of the reconstructed signals in the wavelet domain.
DEFF Research Database (Denmark)
Montoya-Martinez, Jair; Artes-Rodriguez, Antonio; Pontil, Massimiliano
2014-01-01
We consider the estimation of the Brain Electrical Sources (BES) matrix from noisy electroencephalographic (EEG) measurements, commonly named as the EEG inverse problem. We propose a new method to induce neurophysiological meaningful solutions, which takes into account the smoothness, structured...... sparsity, and low rank of the BES matrix. The method is based on the factorization of the BES matrix as a product of a sparse coding matrix and a dense latent source matrix. The structured sparse-low-rank structure is enforced by minimizing a regularized functional that includes the ℓ21-norm of the coding...... matrix and the squared Frobenius norm of the latent source matrix. We develop an alternating optimization algorithm to solve the resulting nonsmooth-nonconvex minimization problem. We analyze the convergence of the optimization procedure, and we compare, under different synthetic scenarios...
Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-04-01
We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature-dependent and strain-rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a pre-conditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.
Inverse Tasks In The Tsunami Problem: Nonlinear Regression With Inaccurate Input Data
Lavrentiev, M.; Shchemel, A.; Simonov, K.
A variant of modified training functional that allows considering inaccurate input data is suggested. A limiting case when a part of input data is completely undefined, and, therefore, a problem of reconstruction of hidden parameters should be solved, is also considered. Some numerical experiments are presented. It is assumed that a dependence of known output variables on known input ones should be found is the classic problem definition, which is widely used in the majority of neural nets algorithms. The quality of approximation is evaluated as a performance function. Often the error of the task is evaluated as squared distance between known input data and predicted data multiplied by weighed coefficients. These coefficients may be named "precision coefficients". When inputs are not known exactly, natural generalization of performance function is adding member that responsible for distance between known inputs and shifted inputs, which lessen model's error. It is desirable that the set of variable parameters is compact for training to be con- verging. In the above problem it is possible to choose variants of demands of a priori compactness, which allow meaningful interpretation in the smoothness of the model dependence. Two kinds of regularization was used, first limited squares of coefficients responsible for nonlinearity and second limited multiplication of the above coeffi- cients and linear coefficients. Asymptotic universality of neural net ability to approxi- mate various smooth functions with any accuracy by increase of the number of tunable parameters is often the base for selecting a type of neural net approximation. It is pos- sible to show that used neural net will approach to Fourier integral transform, which approximate abilities are known, with increasing of the number of tunable parameters. In the limiting case, when input data is set with zero precision, the problem of recon- struction of hidden parameters with observed output data appears. The
International Nuclear Information System (INIS)
Sen, S.; Roy Chowdhury, A.
1989-06-01
The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Peng, E-mail: peng@ices.utexas.edu [The Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, Stop C0200, Austin, TX 78712-1229 (United States); Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch [Seminar für Angewandte Mathematik, Eidgenössische Technische Hochschule, Römistrasse 101, CH-8092 Zürich (Switzerland)
2016-07-01
We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data
International Nuclear Information System (INIS)
Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino
2006-01-01
The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system
Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm
Sun, Cheng-Yu; Wang, Yan-Yan; Wu, Dun-Shi; Qin, Xiao-Jun
2017-12-01
At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm (SFLA), into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.
Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.
2018-01-01
To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.
Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation
International Nuclear Information System (INIS)
Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)
1982-01-01
The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces
International Nuclear Information System (INIS)
Jin, Qinian
2012-01-01
By making use of duality mappings, we formulate an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)
Fymat, A. L.
1976-01-01
The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.
Houborg, Rasmus
2015-01-19
Leaf area index (LAI) and leaf chlorophyll content (Chll) represent key biophysical and biochemical controls on water, energy and carbon exchange processes in the terrestrial biosphere. In combination, LAI and Chll provide critical information on vegetation density, vitality and photosynthetic potentials. However, simultaneous retrieval of LAI and Chll from space observations is extremely challenging. Regularization strategies are required to increase the robustness and accuracy of retrieved properties and enable more reliable separation of soil, leaf and canopy parameters. To address these challenges, the REGularized canopy reFLECtance model (REGFLEC) inversion system was refined to incorporate enhanced techniques for exploiting ancillary LAI and temporal information derived from multiple satellite scenes. In this current analysis, REGFLEC is applied to a time-series of Landsat data.A novel aspect of the REGFLEC approach is the fact that no site-specific data are required to calibrate the model, which may be run in a largely automated fashion using information extracted entirely from image-based and other widely available datasets. Validation results, based upon in-situ LAI and Chll observations collected over maize and soybean fields in central Nebraska for the period 2001-2005, demonstrate Chll retrieval with a relative root-mean-square-deviation (RMSD) on the order of 19% (RMSD=8.42μgcm-2). While Chll retrievals were clearly influenced by the version of the leaf optical properties model used (PROSPECT), the application of spatio-temporal regularization constraints was shown to be critical for estimating Chll with sufficient accuracy. REGFLEC also reproduced the dynamics of in-situ measured LAI well (r2 =0.85), but estimates were biased low, particularly over maize (LAI was underestimated by ~36 %). This disparity may be attributed to differences between effective and true LAI caused by significant foliage clumping not being properly accounted for in the canopy
Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping
2015-10-01
We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.
Samaras, Stefanos; Böckmann, Christine; Nicolae, Doina
2016-06-01
In this work we propose a two-step advancement of the Mie spherical-particle model accounting for particle non-sphericity. First, a naturally two-dimensional (2D) generalized model (GM) is made, which further triggers analogous 2D re-definitions of microphysical parameters. We consider a spheroidal-particle approach where the size distribution is additionally dependent on aspect ratio. Second, we incorporate the notion of a sphere-spheroid particle mixture (PM) weighted by a non-sphericity percentage. The efficiency of these two models is investigated running synthetic data retrievals with two different regularization methods to account for the inherent instability of the inversion procedure. Our preliminary studies show that a retrieval with the PM model improves the fitting errors and the microphysical parameter retrieval and it has at least the same efficiency as the GM. While the general trend of the initial size distributions is captured in our numerical experiments, the reconstructions are subject to artifacts. Finally, our approach is applied to a measurement case yielding acceptable results.
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
Chen, C.; Xia, J.; Liu, J.; Feng, G.
2006-01-01
Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant
Mizutani, Eiji; Demmel, James W
2003-01-01
This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).
Directory of Open Access Journals (Sweden)
Patrick Piprek
2018-02-01
Full Text Available This paper presents an approach to model a ski jumper as a multi-body system for an optimal control application. The modeling is based on the constrained Newton-Euler-Equations. Within this paper the complete multi-body modeling methodology as well as the musculoskeletal modeling is considered. For the musculoskeletal modeling and its incorporation in the optimization model, we choose a nonlinear dynamic inversion control approach. This approach uses the muscle models as nonlinear reference models and links them to the ski jumper movement by a control law. This strategy yields a linearized input-output behavior, which makes the optimal control problem easier to solve. The resulting model of the ski jumper can then be used for trajectory optimization whose results are compared to literature jumps. Ultimately, this enables the jumper to get a very detailed feedback of the flight. To achieve the maximal jump length, exact positioning of his body with respect to the air can be displayed.
Park, J. J.
2017-12-01
Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions Jeffrey Park, Yale University The interpretation of seismic receiver functions (RFs) in terms of isotropic and anisotropic layered structure can be complex. The relationship between structure and body-wave scattering is nonlinear. The anisotropy can involve more parameters than the observations can readily constrain. Finally, reflectivity-predicted layer reverberations are often not prominent in data, so that nonlinear waveform inversion can search in vain to match ghost signals. Multiple-taper correlation (MTC) receiver functions have uncertainties in the frequency domain that follow Gaussian statistics [Park and Levin, 2016a], so grid-searches for the best-fitting collections of interfaces can be performed rapidly to minimize weighted misfit variance. Tests for layer-reverberations can be performed in the frequency domain without reflectivity calculations, allowing flexible modelling of weak, but nonzero, reverberations. Park and Levin [2016b] linearized the hybridization of P and S body waves in an anisotropic layer to predict first-order Ps conversion amplitudes at crust and mantle interfaces. In an anisotropic layer, the P wave acquires small SV and SH components. To ensure continuity of displacement and traction at the top and bottom boundaries of the layer, shear waves are generated. Assuming hexagonal symmetry with an arbitrary symmetry axis, theory confirms the empirical stacking trick of phase-shifting transverse RFs by 90 degrees in back-azimuth [Shiomi and Park, 2008; Schulte-Pelkum and Mahan, 2014] to enhance 2-lobed and 4-lobed harmonic variation. Ps scattering is generated by sharp interfaces, so that RFs resemble the first derivative of the model. MTC RFs in the frequency domain can be manipulated to obtain a first-order reconstruction of the layered anisotropy, under the above modeling constraints and neglecting reverberations. Examples from long
Hybrid Model Representation of a TLP Including Flexible Topsides in Non-Linear Regular Waves
DEFF Research Database (Denmark)
Wehmeyer, Christof; Ferri, Francesco; Andersen, Morten Thøtt
2014-01-01
technologies able to solve this challenge is the floating wind turbine foundation. For the ultimate limit state, where higher order wave loads have a significant influence, a design tool that couples non-linear excitations with structural dynamics is required. To properly describe the behavior...
Smeur, E.J.J.; Remes, B.D.W.; de Wagter, C.; Chu, Q.; J.-M. Moschetta G. Hattenberger, H. de Plinval
2017-01-01
Maintaining stable flight during high turbulence intensities is challenging for fixed-wing micro air vehicles (MAV). Two methods are proposed
to improve the disturbance rejection performance of the MAV: incremental nonlinear dynamic inversion (INDI) control and phaseadvanced pitch probes. INDI
Houborg, Rasmus
2015-10-14
Accurate retrieval of canopy biophysical and leaf biochemical constituents from space observations is critical to diagnosing the functioning and condition of vegetation canopies across spatio-temporal scales. Retrieved vegetation characteristics may serve as important inputs to precision farming applications and as constraints in spatially and temporally distributed model simulations of water and carbon exchange processes. However significant challenges remain in the translation of composite remote sensing signals into useful biochemical, physiological or structural quantities and treatment of confounding factors in spectrum-trait relations. Bands in the red-edge spectrum have particular potential for improving the robustness of retrieved vegetation properties. The development of observationally based vegetation retrieval capacities, effectively constrained by the enhanced information content afforded by bands in the red-edge, is a needed investment towards optimizing the benefit of current and future satellite sensor systems. In this study, a REGularized canopy reFLECtance model (REGFLEC) for joint leaf chlorophyll (Chll) and leaf area index (LAI) retrieval is extended to sensor systems with a band in the red-edge region for the first time. Application to time-series of 5 m resolution multi-spectral RapidEye data is demonstrated over an irrigated agricultural region in central Saudi Arabia, showcasing the value of satellite-derived crop information at this fine scale for precision management. Validation against in-situ measurements in fields of alfalfa, Rhodes grass, carrot and maize indicate improved accuracy of retrieved vegetation properties when exploiting red-edge information in the model inversion process. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
Levinson, Howard W; Markel, Vadim A
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
Nonlinear waves in earth crust faults: application to regular and slow earthquakes
Gershenzon, Naum; Bambakidis, Gust
2015-04-01
The genesis, development and cessation of regular earthquakes continue to be major problems of modern geophysics. How are earthquakes initiated? What factors determine the rapture velocity, slip velocity, rise time and geometry of rupture? How do accumulated stresses relax after the main shock? These and other questions still need to be answered. In addition, slow slip events have attracted much attention as an additional source for monitoring fault dynamics. Recently discovered phenomena such as deep non-volcanic tremor (NVT), low frequency earthquakes (LFE), very low frequency earthquakes (VLF), and episodic tremor and slip (ETS) have enhanced and complemented our knowledge of fault dynamic. At the same time, these phenomena give rise to new questions about their genesis, properties and relation to regular earthquakes. We have developed a model of macroscopic dry friction which efficiently describes laboratory frictional experiments [1], basic properties of regular earthquakes including post-seismic stress relaxation [3], the occurrence of ambient and triggered NVT [4], and ETS events [5, 6]. Here we will discuss the basics of the model and its geophysical applications. References [1] Gershenzon N.I. & G. Bambakidis (2013) Tribology International, 61, 11-18, http://dx.doi.org/10.1016/j.triboint.2012.11.025 [2] Gershenzon, N.I., G. Bambakidis and T. Skinner (2014) Lubricants 2014, 2, 1-x manuscripts; doi:10.3390/lubricants20x000x; arXiv:1411.1030v2 [3] Gershenzon N.I., Bykov V. G. and Bambakidis G., (2009) Physical Review E 79, 056601 [4] Gershenzon, N. I, G. Bambakidis, (2014a), Bull. Seismol. Soc. Am., 104, 4, doi: 10.1785/0120130234 [5] Gershenzon, N. I.,G. Bambakidis, E. Hauser, A. Ghosh, and K. C. Creager (2011), Geophys. Res. Lett., 38, L01309, doi:10.1029/2010GL045225. [6] Gershenzon, N.I. and G. Bambakidis (2014) Bull. Seismol. Soc. Am., (in press); arXiv:1411.1020
Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations
Athanassoulis, Agissilaos
2018-03-01
We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1 + 1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.
Williams, Charles A.; Richardson, Randall M.
1988-01-01
A nonlinear weighted least-squares analysis was performed for a synthetic elastic layer over a viscoelastic half-space model of strike-slip faulting. Also, an inversion of strain rate data was attempted for the locked portions of the San Andreas fault in California. Based on an eigenvector analysis of synthetic data, it is found that the only parameter which can be resolved is the average shear modulus of the elastic layer and viscoelastic half-space. The other parameters were obtained by performing a suite of inversions for the fault. The inversions on data from the northern San Andreas resulted in predicted parameter ranges similar to those produced by inversions on data from the whole fault.
Surface waves tomography and non-linear inversion in the southeast Carpathians
International Nuclear Information System (INIS)
Raykova, R.B.; Panza, G.F.
2005-11-01
A set of shear-wave velocity models of the lithosphere-asthenosphere system in the southeast Carpathians is determined by the non-linear inversion of surface wave group velocity data, obtained from a tomographic analysis. The local dispersion curves are assembled for the period range 7 s - 150 s, combining regional group velocity measurements and published global Rayleigh wave dispersion data. The lithosphere-asthenosphere velocity structure is reliably reconstructed to depths of about 250 km. The thickness of the lithosphere in the region varies from about 120 km to 250 km and the depth of the asthenosphere between 150 km and 250 km. Mantle seismicity concentrates where the high velocity lid is detected just below the Moho. The obtained results are in agreement with recent seismic refraction, receiver function, and travel time P-wave tomography investigations in the region. The similarity among the results obtained from different kinds of structural investigations (including the present work) highlights some new features of the lithosphere-asthenosphere system in southeast Carpathians, as the relatively thin crust under Transylvania basin and Vrancea zone. (author)
Burger, Karin; Koehler, Thomas; Chabior, Michael; Allner, Sebastian; Marschner, Mathias; Fehringer, Andreas; Willner, Marian; Pfeiffer, Franz; Noël, Peter
2014-12-29
Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.
Nonlinear rolling of a biased ship in a regular beam wave under external and parametric excitations
Energy Technology Data Exchange (ETDEWEB)
El-Bassiouny, A.F. [Mathematics Dept., Benha Univ., Benha (Egypt)
2007-10-15
We consider a nonlinear oscillator simultaneously excited by external and parametric functions. The oscillator has a bias parameter that breaks the symmetry of the motion. The example that we use to illustrate the problem is the rolling oscillation of a biased ship in longitudinal waves, but many mechanical systems display similar features. The analysis took into consideration linear, quadratic, cubic, quintic, and seven terms in the polynomial expansion of the relative roll angle. The damping moment consists of the linear term associated with radiation and viscous damping and a cubic term due to frictional resistance and eddies behind bilge keels and hard bilge corners. Two methods (the averaging and the multiple time scales) are used to investigate the first-order approximate analytical solution. The modulation equations of the amplitudes and phases are obtained. These equations are used to obtain the stationary state. The stability of the proposed solution is determined applying Liapunov's first method. Effects of different parameters on the system behaviour are investigated numerically. Results are presented graphically and discussed. The results obtained by two methods are in excellent agreement. (orig.)
DEFF Research Database (Denmark)
Hubmer, Simon; Sherina, Ekaterina; Neubauer, Andreas
2018-01-01
. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam´e parameters from displacement data simulating......We consider a problem of quantitative static elastography, the estimation of the Lam´e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically...... a static elastography experiment are presented....
Smith, G. A.; Meyer, G.
1981-01-01
A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.
International Nuclear Information System (INIS)
Jin Qinian
2008-01-01
In this paper we consider the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed inverse problems. Under merely the Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense
Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing
Chu, W. P.
1985-01-01
The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.
DEFF Research Database (Denmark)
Hodicky, Kamil; Hulin, Thomas; Schmidt, Jacob Wittrup
2014-01-01
The fracture behaviour of three fiber reinforced and regular HPC (high performance concretes) is presented in this paper. Two mixes are based on optimization of HPC whereas the third mix was a commercial mix developed by CONTEC ApS (Denmark). The wedge splitting test setup with 48 cubical specimens...
Swanson, C.; Jandovitz, P.; Cohen, S. A.
2018-02-01
We measured Electron Energy Distribution Functions (EEDFs) from below 200 eV to over 8 keV and spanning five orders-of-magnitude in intensity, produced in a low-power, RF-heated, tandem mirror discharge in the PFRC-II apparatus. The EEDF was obtained from the x-ray energy distribution function (XEDF) using a novel Poisson-regularized spectrum inversion algorithm applied to pulse-height spectra that included both Bremsstrahlung and line emissions. The XEDF was measured using a specially calibrated Amptek Silicon Drift Detector (SDD) pulse-height system with 125 eV FWHM at 5.9 keV. The algorithm is found to out-perform current leading x-ray inversion algorithms when the error due to counting statistics is high.
Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang
2017-09-01
Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.
Yankovskii, A. P.
2018-01-01
On the basis of constitutive equations of the Rabotnov nonlinear hereditary theory of creep, the problem on the rheonomic flexural behavior of layered plates with a regular structure is formu-lated. Equations allowing one to describe, with different degrees of accuracy, the stress-strain state of such plates with account of their weakened resistance to transverse shear were ob-tained. From them, the relations of the nonclassical Reissner- and Reddytype theories can be found. For axially loaded annular plates clamped at one edge and loaded quasistatically on the other edge, a simplified version of the refined theory, whose complexity is comparable to that of the Reissner and Reddy theories, is developed. The flexural strains of such metal-composite annular plates in shortterm and long-term loadings at different levels of heat action are calcu-lated. It is shown that, for plates with a relative thickness of order of 1/10, neither the classical theory, nor the traditional nonclassical Reissner and Reddy theories guarantee reliable results for deflections even with the rough 10% accuracy. The accuracy of these theories decreases at elevated temperatures and with time under long-term loadings of structures. On the basic of relations of the refined theory, it is revealed that, in bending of layered metal-composite heat-sensitive plates under elevated temperatures, marked edge effects arise in the neighborhood of the supported edge, which characterize the shear of these structures in the transverse direction
International Nuclear Information System (INIS)
Rijssel, Jos van; Kuipers, Bonny W.M.; Erné, Ben H.
2014-01-01
A numerical inversion method known from the analysis of light scattering by colloidal dispersions is now applied to magnetization curves of ferrofluids. The distribution of magnetic particle sizes or dipole moments is determined without assuming that the distribution is unimodal or of a particular shape. The inversion method enforces positive number densities via a non-negative least squares procedure. It is tested successfully on experimental and simulated data for ferrofluid samples with known multimodal size distributions. The created computer program MINORIM is made available on the web. - Highlights: • A method from light scattering is applied to analyze ferrofluid magnetization curves. • A magnetic size distribution is obtained without prior assumption of its shape. • The method is tested successfully on ferrofluids with a known size distribution. • The practical limits of the method are explored with simulated data including noise. • This method is implemented in the program MINORIM, freely available online
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1
International Nuclear Information System (INIS)
Krivitsky, V.S.; Vladimirov, S.V.
1991-01-01
An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)
Coordinate-invariant regularization
International Nuclear Information System (INIS)
Halpern, M.B.
1987-01-01
A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc
Wu, Zedong
2017-07-04
Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current RWI implementations usually neglect the multi-scattered energy, which will cause some artifacts in the image and the update of the background. To improve existing RWI implementations in taking multi-scattered energy into consideration, we split the velocity model into background and perturbation components, integrate them directly in the wave equation, and formulate a new optimization problem for both components. In this case, the perturbed model is no longer a single-scattering model, but includes all scattering. Through introducing a new cheap implementation of scattering angle enrichment, the separation of the background and perturbation components can be implemented efficiently. We optimize both components simultaneously to produce updates to the velocity model that is nonlinear with respect to both the background and the perturbation. The newly introduced perturbation model can absorb the non-smooth update of the background in a more consistent way. We apply the proposed approach on the Marmousi model with data that contain frequencies starting from 5 Hz to show that this method can converge to an accurate velocity starting from a linearly increasing initial velocity. Also, our proposed method works well when applied to a field data set.
Linearized versus non-linear inverse methods for seismic localization of underground sources
DEFF Research Database (Denmark)
Oh, Geok Lian; Jacobsen, Finn
2013-01-01
The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem, a...
Vaibhav, V.K.
2017-01-01
This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the
Directory of Open Access Journals (Sweden)
Birgül Kınalıbalaban
2013-08-01
Full Text Available In this study, the province of Gaziantep, Şehitkamil district, there are thought to be chrome-metallic mine in the village of Sofalıca the localization of gravity and economical method was to investigate whether it has a reserve. Approximately 189 hectares of land gravity measurements over the measurement point in the study area was 220. By differentiating regional and residual Bouguer gravity map of the generated residual maps were obtained on areas likely to be created on the source. The inversion method of pre-NTG was required for the selection model is the appropriate start. On the structure of polygon slices as a result of application received in the form of the inversion in the range of 125 meters and 450 meters long, 25 meters to 70 meters in thickness in the range of existence of geometric structures have been identified.
Inverse Free Iterative Methods for Nonlinear Ill-Posed Operator Equations
Directory of Open Access Journals (Sweden)
Ioannis K. Argyros
2014-01-01
ill-posed operator equation F(x=y. The proposed method is a modified form of Tikhonov gradient (TIGRA method considered by Ramlau (2003. The regularization parameter is chosen according to the balancing principle considered by Pereverzev and Schock (2005. The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper.
Ramirez, Daniel Perez; Whiteman, David N.; Veselovskii, Igor; Kolgotin, Alexei; Korenskiy, Michael; Alados-Arboledas, Lucas
2013-01-01
In this work we study the effects of systematic and random errors on the inversion of multiwavelength (MW) lidar data using the well-known regularization technique to obtain vertically resolved aerosol microphysical properties. The software implementation used here was developed at the Physics Instrumentation Center (PIC) in Troitsk (Russia) in conjunction with the NASA/Goddard Space Flight Center. Its applicability to Raman lidar systems based on backscattering measurements at three wavelengths (355, 532 and 1064 nm) and extinction measurements at two wavelengths (355 and 532 nm) has been demonstrated widely. The systematic error sensitivity is quantified by first determining the retrieved parameters for a given set of optical input data consistent with three different sets of aerosol physical parameters. Then each optical input is perturbed by varying amounts and the inversion is repeated. Using bimodal aerosol size distributions, we find a generally linear dependence of the retrieved errors in the microphysical properties on the induced systematic errors in the optical data. For the retrievals of effective radius, number/surface/volume concentrations and fine-mode radius and volume, we find that these results are not significantly affected by the range of the constraints used in inversions. But significant sensitivity was found to the allowed range of the imaginary part of the particle refractive index. Our results also indicate that there exists an additive property for the deviations induced by the biases present in the individual optical data. This property permits the results here to be used to predict deviations in retrieved parameters when multiple input optical data are biased simultaneously as well as to study the influence of random errors on the retrievals. The above results are applied to questions regarding lidar design, in particular for the spaceborne multiwavelength lidar under consideration for the upcoming ACE mission.
Meresescu, Alina G.; Kowalski, Matthieu; Schmidt, Frédéric; Landais, François
2018-06-01
The Water Residence Time distribution is the equivalent of the impulse response of a linear system allowing the propagation of water through a medium, e.g. the propagation of rain water from the top of the mountain towards the aquifers. We consider the output aquifer levels as the convolution between the input rain levels and the Water Residence Time, starting with an initial aquifer base level. The estimation of Water Residence Time is important for a better understanding of hydro-bio-geochemical processes and mixing properties of wetlands used as filters in ecological applications, as well as protecting fresh water sources for wells from pollutants. Common methods of estimating the Water Residence Time focus on cross-correlation, parameter fitting and non-parametric deconvolution methods. Here we propose a 1D full-deconvolution, regularized, non-parametric inverse problem algorithm that enforces smoothness and uses constraints of causality and positivity to estimate the Water Residence Time curve. Compared to Bayesian non-parametric deconvolution approaches, it has a fast runtime per test case; compared to the popular and fast cross-correlation method, it produces a more precise Water Residence Time curve even in the case of noisy measurements. The algorithm needs only one regularization parameter to balance between smoothness of the Water Residence Time and accuracy of the reconstruction. We propose an approach on how to automatically find a suitable value of the regularization parameter from the input data only. Tests on real data illustrate the potential of this method to analyze hydrological datasets.
Directory of Open Access Journals (Sweden)
Murray L. Ireland
2015-06-01
Full Text Available Multirotor is the umbrella term for the family of unmanned aircraft, which include the quadrotor, hexarotor and other vertical take-off and landing (VTOL aircraft that employ multiple main rotors for lift and control. Development and testing of novel multirotor designs has been aided by the proliferation of 3D printing and inexpensive flight controllers and components. Different multirotor configurations exhibit specific strengths, while presenting unique challenges with regards to design and control. This article highlights the primary differences between three multirotor platforms: a quadrotor; a fully-actuated hexarotor; and an octorotor. Each platform is modelled and then controlled using non-linear dynamic inversion. The differences in dynamics, control and performance are then discussed.
International Nuclear Information System (INIS)
Gardner, R.P.; Guo, P.; Sood, A.; Mayo, C.W.; Dobbs, C.L.
1998-01-01
A review of our work on the application of the PGNAA method as applied to five industrial applications is given. Some introductory material is first given on the importance and use of Monte Carlo simulation in this area, some comments on the place of PGNAA in elemental analysis, and a brief description of the Monte Carlo - Library Least-Squares (MCLLS) approach to the nonlinear inverse PGNAA analysis problem. Then the applications of PGNAA are discussed for: (1) on-line bulk coal analysis, (2) nuclear oil well logging, (3) vitrified waste, (4) the analysis of sodium and aluminium in 'green liquor' in the presence of chlorine, and (5) the conveyor belt sorting of aluminum alloy samples. It is concluded that PGNAA is a rapidly emerging important new technology and measurement approach. (author)
The inverse problem of determining several coefficients in a nonlinear Lotka–Volterra system
International Nuclear Information System (INIS)
Roques, Lionel; Cristofol, Michel
2012-01-01
In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of a system of two parabolic equations, which corresponds to a Lotka–Volterra competition model. Our result gives a sufficient condition for the uniqueness of the determination of four coefficients of the system. This sufficient condition only involves pointwise measurements of the solution (u, v) of the system and of the spatial derivative ∂u/∂x or ∂v/∂x of one component at a single point x 0 , during a time interval (0, ε). Our results are illustrated by numerical computations. (paper)
International Nuclear Information System (INIS)
Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.
2012-01-01
In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.
Geodynamic inversion to constrain the non-linear rheology of the lithosphere
Baumann, T. S.; Kaus, Boris J. P.
2015-08-01
One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology
An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling
Li, Weixuan; Lin, Guang; Zhang, Dongxiao
2014-02-01
The probabilistic collocation-based Kalman filter (PCKF) is a recently developed approach for solving inverse problems. It resembles the ensemble Kalman filter (EnKF) in every aspect-except that it represents and propagates model uncertainty by polynomial chaos expansion (PCE) instead of an ensemble of model realizations. Previous studies have shown PCKF is a more efficient alternative to EnKF for many data assimilation problems. However, the accuracy and efficiency of PCKF depends on an appropriate truncation of the PCE series. Having more polynomial chaos basis functions in the expansion helps to capture uncertainty more accurately but increases computational cost. Selection of basis functions is particularly important for high-dimensional stochastic problems because the number of polynomial chaos basis functions required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases. In classic PCKF algorithms, the PCE basis functions are pre-set based on users' experience. Also, for sequential data assimilation problems, the basis functions kept in PCE expression remain unchanged in different Kalman filter loops, which could limit the accuracy and computational efficiency of classic PCKF algorithms. To address this issue, we present a new algorithm that adaptively selects PCE basis functions for different problems and automatically adjusts the number of basis functions in different Kalman filter loops. The algorithm is based on adaptive functional ANOVA (analysis of variance) decomposition, which approximates a high-dimensional function with the summation of a set of low-dimensional functions. Thus, instead of expanding the original model into PCE, we implement the PCE expansion on these low-dimensional functions, which is much less costly. We also propose a new adaptive criterion for ANOVA that is more suited for solving inverse problems. The new algorithm was tested with different examples and demonstrated
Shuguang Liua; Pamela Anderson; Guoyi Zhoud; Boone Kauffman; Flint Hughes; David Schimel; Vicente Watson; Joseph. Tosi
2008-01-01
Objectively assessing the performance of a model and deriving model parameter values from observations are critical and challenging in landscape to regional modeling. In this paper, we applied a nonlinear inversion technique to calibrate the ecosystem model CENTURY against carbon (C) and nitrogen (N) stock measurements collected from 39 mature tropical forest sites in...
Mitigating nonlinearity in full waveform inversion using scaled-Sobolev pre-conditioning
Zuberi, M. AH; Pratt, R. G.
2018-04-01
The Born approximation successfully linearizes seismic full waveform inversion if the background velocity is sufficiently accurate. When the background velocity is not known it can be estimated by using model scale separation methods. A frequently used technique is to separate the spatial scales of the model according to the scattering angles present in the data, by using either first- or second-order terms in the Born series. For example, the well-known `banana-donut' and the `rabbit ear' shaped kernels are, respectively, the first- and second-order Born terms in which at least one of the scattering events is associated with a large angle. Whichever term of the Born series is used, all such methods suffer from errors in the starting velocity model because all terms in the Born series assume that the background Green's function is known. An alternative approach to Born-based scale separation is to work in the model domain, for example, by Gaussian smoothing of the update vectors, or some other approach for separation by model wavenumbers. However such model domain methods are usually based on a strict separation in which only the low-wavenumber updates are retained. This implies that the scattered information in the data is not taken into account. This can lead to the inversion being trapped in a false (local) minimum when sharp features are updated incorrectly. In this study we propose a scaled-Sobolev pre-conditioning (SSP) of the updates to achieve a constrained scale separation in the model domain. The SSP is obtained by introducing a scaled Sobolev inner product (SSIP) into the measure of the gradient of the objective function with respect to the model parameters. This modified measure seeks reductions in the L2 norm of the spatial derivatives of the gradient without changing the objective function. The SSP does not rely on the Born prediction of scale based on scattering angles, and requires negligible extra computational cost per iteration. Synthetic
Nonlinear evolution-type equations and their exact solutions using inverse variational methods
International Nuclear Information System (INIS)
Kara, A H; Khalique, C M
2005-01-01
We present the role of invariants in obtaining exact solutions of differential equations. Firstly, conserved vectors of a partial differential equation (p.d.e.) allow us to obtain reduced forms of the p.d.e. for which some of the Lie point symmetries (in vector field form) are easily concluded and, therefore, provide a mechanism for further reduction. Secondly, invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. In this latter case, the reductions carry all the usual advantages regarding Noether symmetries and double reductions. The examples we consider are nonlinear evolution-type equations such as the Korteweg-deVries equation, but a detailed analysis is made on the Fisher equation (which describes reaction-diffusion waves in biology, inter alia). Other diffusion-type equations lend themselves well to the method we describe (e.g., the Fitzhugh Nagumo equation, which is briefly discussed). Some aspects of Painleve properties are also suggested
Sparsity regularization for parameter identification problems
International Nuclear Information System (INIS)
Jin, Bangti; Maass, Peter
2012-01-01
The investigation of regularization schemes with sparsity promoting penalty terms has been one of the dominant topics in the field of inverse problems over the last years, and Tikhonov functionals with ℓ p -penalty terms for 1 ⩽ p ⩽ 2 have been studied extensively. The first investigations focused on regularization properties of the minimizers of such functionals with linear operators and on iteration schemes for approximating the minimizers. These results were quickly transferred to nonlinear operator equations, including nonsmooth operators and more general function space settings. The latest results on regularization properties additionally assume a sparse representation of the true solution as well as generalized source conditions, which yield some surprising and optimal convergence rates. The regularization theory with ℓ p sparsity constraints is relatively complete in this setting; see the first part of this review. In contrast, the development of efficient numerical schemes for approximating minimizers of Tikhonov functionals with sparsity constraints for nonlinear operators is still ongoing. The basic iterated soft shrinkage approach has been extended in several directions and semi-smooth Newton methods are becoming applicable in this field. In particular, the extension to more general non-convex, non-differentiable functionals by variational principles leads to a variety of generalized iteration schemes. We focus on such iteration schemes in the second part of this review. A major part of this survey is devoted to applying sparsity constrained regularization techniques to parameter identification problems for partial differential equations, which we regard as the prototypical setting for nonlinear inverse problems. Parameter identification problems exhibit different levels of complexity and we aim at characterizing a hierarchy of such problems. The operator defining these inverse problems is the parameter-to-state mapping. We first summarize some
Parekh, Ankit
Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal
Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie; Benna, Mehdi; Kofman, Wlodek; Herique, Alain
We investigate the inverse problem of imaging the internal structure of comet 67P/ Churyumov-Gerasimenko from radiotomography CONSERT data by using a coupled regularized inversion of the Helmholtz equations. A first set of Helmholtz equations, written w.r.t a basis of 3D Hankel functions describes the wave propagation outside the comet at large distances, a second set of Helmholtz equations, written w.r.t. a basis of 3D Zernike functions describes the wave propagation throughout the comet with avariable permittivity. Both sets are connected by continuity equations over a sphere that surrounds the comet. This approach, derived from GPS water vapor tomography of the atmosphere,will permit a full 3D inversion of the internal structure of the comet, contrary to traditional approaches that use a discretization of space at a fraction of the radiowave wavelength.
International Nuclear Information System (INIS)
Sakhnovich, Alexander
2008-01-01
A Borg–Marchenko-type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve the inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by a new and simple sufficient condition on the potential, which implies this asymptotic condition. The evolution of the Weyl function is discussed and the solution of an initial-boundary-value problem for the N-wave equation follows. Explicit solutions of an inverse problem are obtained. The system with a shifted argument is treated
Energy Technology Data Exchange (ETDEWEB)
Liu Guanghui [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Guo Kangxian, E-mail: axguo@sohu.com [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Wang Chao [Institute of Public Administration, Guangzhou University, Guangzhou 510006 (China)
2012-06-15
The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.
International Nuclear Information System (INIS)
Liu Guanghui; Guo Kangxian; Wang Chao
2012-01-01
The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.
Chudnovsky, D V
1978-09-01
For systems of nonlinear equations having the form [L(n) - ( partial differential/ partial differentialt), L(m) - ( partial differential/ partial differentialy)] = 0 the class of meromorphic solutions obtained from the linear equations [Formula: see text] is presented.
Belmiloudi, A.; Mahé, F.
2014-01-01
International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...
Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.
2018-04-01
The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.
DEFF Research Database (Denmark)
Rubæk, Tonny; Meaney, P. M.; Meincke, Peter
2007-01-01
is presented which is based on the conjugate gradient least squares (CGLS) algorithm. The iterative CGLS algorithm is capable of solving the update problem by operating on just the Jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations. The new...
Seismic waveform inversion best practices: regional, global and exploration test cases
Modrak, Ryan; Tromp, Jeroen
2016-09-01
Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.
Energy Technology Data Exchange (ETDEWEB)
Saide, Pablo (CGRER, Center for Global and Regional Environmental Research, Univ. of Iowa, Iowa City, IA (United States)), e-mail: pablo-saide@uiowa.edu; Bocquet, Marc (Universite Paris-Est, CEREA Joint Laboratory Ecole des Ponts ParisTech and EDF RandD, Champs-sur-Marne (France); INRIA, Paris Rocquencourt Research Center (France)); Osses, Axel (Departamento de Ingeniera Matematica, Universidad de Chile, Santiago (Chile); Centro de Modelamiento Matematico, UMI 2807/Universidad de Chile-CNRS, Santiago (Chile)); Gallardo, Laura (Centro de Modelamiento Matematico, UMI 2807/Universidad de Chile-CNRS, Santiago (Chile); Departamento de Geofisica, Universidad de Chile, Santiago (Chile))
2011-07-15
When constraining surface emissions of air pollutants using inverse modelling one often encounters spurious corrections to the inventory at places where emissions and observations are colocated, referred to here as the colocalization problem. Several approaches have been used to deal with this problem: coarsening the spatial resolution of emissions; adding spatial correlations to the covariance matrices; adding constraints on the spatial derivatives into the functional being minimized; and multiplying the emission error covariance matrix by weighting factors. Intercomparison of methods for a carbon monoxide inversion over a city shows that even though all methods diminish the colocalization problem and produce similar general patterns, detailed information can greatly change according to the method used ranging from smooth, isotropic and short range modifications to not so smooth, non-isotropic and long range modifications. Poisson (non-Gaussian) and Gaussian assumptions both show these patterns, but for the Poisson case the emissions are naturally restricted to be positive and changes are given by means of multiplicative correction factors, producing results closer to the true nature of emission errors. Finally, we propose and test a new two-step, two-scale, fully Bayesian approach that deals with the colocalization problem and can be implemented for any prior density distribution
Nativi, S; Mazzetti, P
2004-01-01
In a previous work, an operative procedure to estimate precipitable and liquid water in non-raining conditions over sea was developed and assessed. The procedure is based on a fast non-linear physical inversion scheme and a forward model; it is valid for most of satellite microwave radiometers and it also estimates water effective profiles. This paper presents two improvements of the procedure: first, a refinement to provide modularity of the software components and portability across different computation system architectures; second, the adoption of the CERN MINUIT minimisation package, which addresses the problem of global minimisation but is computationally more demanding. Together with the increased computational performance that allowed to impose stricter requirements on the quality of fit, these refinements improved fitting precision and reliability, and allowed to relax the requirements on the initial guesses for the model parameters. The re-analysis of the same data-set considered in the previous pap...
Ma, Denglong; Tan, Wei; Zhang, Zaoxiao; Hu, Jun
2017-03-05
In order to identify the parameters of hazardous gas emission source in atmosphere with less previous information and reliable probability estimation, a hybrid algorithm coupling Tikhonov regularization with particle swarm optimization (PSO) was proposed. When the source location is known, the source strength can be estimated successfully by common Tikhonov regularization method, but it is invalid when the information about both source strength and location is absent. Therefore, a hybrid method combining linear Tikhonov regularization and PSO algorithm was designed. With this method, the nonlinear inverse dispersion model was transformed to a linear form under some assumptions, and the source parameters including source strength and location were identified simultaneously by linear Tikhonov-PSO regularization method. The regularization parameters were selected by L-curve method. The estimation results with different regularization matrixes showed that the confidence interval with high-order regularization matrix is narrower than that with zero-order regularization matrix. But the estimation results of different source parameters are close to each other with different regularization matrixes. A nonlinear Tikhonov-PSO hybrid regularization was also designed with primary nonlinear dispersion model to estimate the source parameters. The comparison results of simulation and experiment case showed that the linear Tikhonov-PSO method with transformed linear inverse model has higher computation efficiency than nonlinear Tikhonov-PSO method. The confidence intervals from linear Tikhonov-PSO are more reasonable than that from nonlinear method. The estimation results from linear Tikhonov-PSO method are similar to that from single PSO algorithm, and a reasonable confidence interval with some probability levels can be additionally given by Tikhonov-PSO method. Therefore, the presented linear Tikhonov-PSO regularization method is a good potential method for hazardous emission
Geometric continuum regularization of quantum field theory
International Nuclear Information System (INIS)
Halpern, M.B.
1989-01-01
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs
Miller, Christopher J.
2011-01-01
A model reference nonlinear dynamic inversion control law has been developed to provide a baseline controller for research into simple adaptive elements for advanced flight control laws. This controller has been implemented and tested in a hardware-in-the-loop simulation and in flight. The flight results agree well with the simulation predictions and show good handling qualities throughout the tested flight envelope with some noteworthy deficiencies highlighted both by handling qualities metrics and pilot comments. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as simple as possible to easily allow the addition of the adaptive elements. The flight-test results and how they compare to the simulation predictions are discussed, along with a discussion about how each element affected pilot opinions. Additionally, aspects of the design that performed better than expected are presented, as well as some simple improvements that will be suggested for follow-on work.
International Nuclear Information System (INIS)
Snider, D.M.
1981-02-01
INVERT 1.0 is a digital computer program written in FORTRAN IV which calculates the surface heat flux of a one-dimensional solid using an interior-measured temperature and a physical description of the solid. By using two interior-measured temperatures, INVERT 1.0 can provide a solution for the heat flux at two surfaces, the heat flux at a boundary and the time dependent power, or the heat flux at a boundary and the time varying thermal conductivity of a material composing the solid. The analytical solution to inversion problem is described for the one-dimensional cylinder, sphere, or rectangular slab. The program structure, input instructions, and sample problems demonstrating the accuracy of the solution technique are included
Sharp spatially constrained inversion
DEFF Research Database (Denmark)
Vignoli, Giulio G.; Fiandaca, Gianluca G.; Christiansen, Anders Vest C A.V.C.
2013-01-01
We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted...... by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes...... inversions are compared against classical smooth results and available boreholes. With the focusing approach, the obtained blocky results agree with the underlying geology and allow for easier interpretation by the end-user....
Spegazzini, Nicolas; Siesler, Heinz W; Ozaki, Yukihiro
2012-08-02
The doublet of the ν(C=O) carbonyl band in isomeric urethane systems has been extensively discussed in qualitative terms on the basis of FT-IR spectroscopy of the macromolecular structures. Recently, a reaction extent model was proposed as an inverse kinetic problem for the synthesis of diphenylurethane for which hydrogen-bonded and non-hydrogen-bonded C=O functionalities were identified. In this article, the heteronuclear C=O···H-N hydrogen bonding in the isomeric structure of diphenylurethane synthesized from phenylisocyanate and phenol was investigated via FT-IR spectroscopy, using a methodology of regularization for the inverse reaction extent model through an eigenvalue problem. The kinetic and thermodynamic parameters of this system were derived directly from the spectroscopic data. The activation and thermodynamic parameters of the isomeric structures of diphenylurethane linked through a hydrogen bonding equilibrium were studied. The study determined the enthalpy (ΔH = 15.25 kJ/mol), entropy (TΔS = 14.61 kJ/mol), and free energy (ΔG = 0.6 kJ/mol) of heteronuclear C=O···H-N hydrogen bonding by FT-IR spectroscopy through direct calculation from the differences in the kinetic parameters (δΔ(‡)H, -TδΔ(‡)S, and δΔ(‡)G) at equilibrium in the chemical reaction system. The parameters obtained in this study may contribute toward a better understanding of the properties of, and interactions in, supramolecular systems, such as the switching behavior of hydrogen bonding.
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
Phase reconstruction by a multilevel iteratively regularized Gauss–Newton method
International Nuclear Information System (INIS)
Langemann, Dirk; Tasche, Manfred
2008-01-01
In this paper we consider the numerical solution of a phase retrieval problem for a compactly supported, linear spline f : R → C with the Fourier transform f-circumflex, where values of |f| and |f-circumflex| at finitely many equispaced nodes are given. The unknown phases of complex spline coefficients fulfil a well-structured system of nonlinear equations. Thus the phase reconstruction leads to a nonlinear inverse problem, which is solved by a multilevel strategy and iterative Tikhonov regularization. The multilevel strategy concentrates the main effort of the solution of the phase retrieval problem in the coarse, less expensive levels and provides convenient initial guesses at the next finer level. On each level, the corresponding nonlinear system is solved by an iteratively regularized Gauss–Newton method. The multilevel strategy is motivated by convergence results of IRGN. This method is applicable to a wide range of examples as shown in several numerical tests for noiseless and noisy data
Morozov-type discrepancy principle for nonlinear ill-posed problems ...
Indian Academy of Sciences (India)
[3] Engl H W, Kunisch K and Neubauer A, Convergence rates for Tikhonov regularization of nonliner problems, Inverse Problems 5 (1989) 523–540. [4] Hanke M, Neubauer A and Scherzer O, A convergence analysis of Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995) 21–37. [5] Hofmann B and ...
DEFF Research Database (Denmark)
Hansen, Lars Kai; Rasmussen, Carl Edward; Svarer, C.
1994-01-01
Regularization, e.g., in the form of weight decay, is important for training and optimization of neural network architectures. In this work the authors provide a tool based on asymptotic sampling theory, for iterative estimation of weight decay parameters. The basic idea is to do a gradient desce...
Support minimized inversion of acoustic and elastic wave scattering
International Nuclear Information System (INIS)
Safaeinili, A.
1994-01-01
This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion
An analysis of electrical impedance tomography with applications to Tikhonov regularization
Jin, Bangti
2012-01-16
This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in L p-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov regularization, for both linearized and nonlinear models. Some important properties, e.g., existence, stability, consistency and convergence rates, are established. This provides some theoretical justifications of their practical usage. © EDP Sciences, SMAI, 2012.
An analysis of electrical impedance tomography with applications to Tikhonov regularization
Jin, Bangti; Maass, Peter
2012-01-01
This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in L p-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov regularization, for both linearized and nonlinear models. Some important properties, e.g., existence, stability, consistency and convergence rates, are established. This provides some theoretical justifications of their practical usage. © EDP Sciences, SMAI, 2012.
Alternating minimisation for glottal inverse filtering
International Nuclear Information System (INIS)
Bleyer, Ismael Rodrigo; Lybeck, Lasse; Auvinen, Harri; Siltanen, Samuli; Airaksinen, Manu; Alku, Paavo
2017-01-01
A new method is proposed for solving the glottal inverse filtering (GIF) problem. The goal of GIF is to separate an acoustical speech signal into two parts: the glottal airflow excitation and the vocal tract filter. To recover such information one has to deal with a blind deconvolution problem. This ill-posed inverse problem is solved under a deterministic setting, considering unknowns on both sides of the underlying operator equation. A stable reconstruction is obtained using a double regularization strategy, alternating between fixing either the glottal source signal or the vocal tract filter. This enables not only splitting the nonlinear and nonconvex problem into two linear and convex problems, but also allows the use of the best parameters and constraints to recover each variable at a time. This new technique, called alternating minimization glottal inverse filtering (AM-GIF), is compared with two other approaches: Markov chain Monte Carlo glottal inverse filtering (MCMC-GIF), and iterative adaptive inverse filtering (IAIF), using synthetic speech signals. The recent MCMC-GIF has good reconstruction quality but high computational cost. The state-of-the-art IAIF method is computationally fast but its accuracy deteriorates, particularly for speech signals of high fundamental frequency ( F 0). The results show the competitive performance of the new method: With high F 0, the reconstruction quality is better than that of IAIF and close to MCMC-GIF while reducing the computational complexity by two orders of magnitude. (paper)
Bayesian inversion of refraction seismic traveltime data
Ryberg, T.; Haberland, Ch
2018-03-01
We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test
Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging
Desmal, Abdulla
2016-03-01
Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using
Relevance vector machine technique for the inverse scattering problem
International Nuclear Information System (INIS)
Wang Fang-Fang; Zhang Ye-Rong
2012-01-01
A novel method based on the relevance vector machine (RVM) for the inverse scattering problem is presented in this paper. The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered. The nonlinearity is embodied in the relation between the scattered field and the target property, which can be obtained through the RVM training process. Besides, rather than utilizing regularization, the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output. Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy, convergence, robustness, generalization, and improved performance in terms of sparse property in comparison with the support vector machine (SVM) based approach. (general)
Calculation of the inverse data space via sparse inversion
Saragiotis, Christos
2011-01-01
The inverse data space provides a natural separation of primaries and surface-related multiples, as the surface multiples map onto the area around the origin while the primaries map elsewhere. However, the calculation of the inverse data is far from trivial as theory requires infinite time and offset recording. Furthermore regularization issues arise during inversion. We perform the inversion by minimizing the least-squares norm of the misfit function by constraining the $ell_1$ norm of the solution, being the inverse data space. In this way a sparse inversion approach is obtained. We show results on field data with an application to surface multiple removal.
Nonlinear generalization of special relativity
International Nuclear Information System (INIS)
Winterberg, F.
1985-01-01
In Poincares axiomatic formulation special relativity is a derived consequence of a true Lorentz contraction, for a rod in absolute motion through a substratum. Furthermore, Lorentz had shown that the rod contraction can be understood by an inverse square law interaction and therefore special relativity derived from more fundamental principles. The derivation by Lorentz shows that the root of the divergence problems is the singular inverse square law. By replacing the inverse square law with a regular one through the introduction of a finite length, the author has succeeded in deriving a nonlinear generalization of special relativity which eliminates all infinities. Besides the relative velocities, these nonlinear transformation equations also contain absolute velocities against a substratum, but in the limit of small energies they go over into the linear Lorentz transformations. Depending on the smallness of the fundamental length, departures from special relativity can be observed only at very high energies. The theorem that the velocity of light is the same in all reference systems still holds and likewise the conservation laws for energy and momentum
Information operator approach and iterative regularization methods for atmospheric remote sensing
International Nuclear Information System (INIS)
Doicu, A.; Hilgers, S.; Bargen, A. von; Rozanov, A.; Eichmann, K.-U.; Savigny, C. von; Burrows, J.P.
2007-01-01
In this study, we present the main features of the information operator approach for solving linear inverse problems arising in atmospheric remote sensing. This method is superior to the stochastic version of the Tikhonov regularization (or the optimal estimation method) due to its capability to filter out the noise-dominated components of the solution generated by an inappropriate choice of the regularization parameter. We extend this approach to iterative methods for nonlinear ill-posed problems and derive the truncated versions of the Gauss-Newton and Levenberg-Marquardt methods. Although the paper mostly focuses on discussing the mathematical details of the inverse method, retrieval results have been provided, which exemplify the performances of the methods. These results correspond to the NO 2 retrieval from SCIAMACHY limb scatter measurements and have been obtained by using the retrieval processors developed at the German Aerospace Center Oberpfaffenhofen and Institute of Environmental Physics of the University of Bremen
Regularization modeling for large-eddy simulation
Geurts, Bernardus J.; Holm, D.D.
2003-01-01
A new modeling approach for large-eddy simulation (LES) is obtained by combining a "regularization principle" with an explicit filter and its inversion. This regularization approach allows a systematic derivation of the implied subgrid model, which resolves the closure problem. The central role of
Nonlinear regularization with applications in geophysics
DEFF Research Database (Denmark)
Berglund, Eva Ann-Charlotte
2002-01-01
-posed problems. We find that a for a special class of discrete linear ill-posed problems, we can calculate approximations to the singular values as well as approximations to the Fourier coefficients directly from the CGLS iterations. This finding makes it possible to design a new stopping rule for the CGLS...... iterations, base upon the fact that the ratio between the Fourier coefficients and the singular values decays as long as we can extract information about the solution from the right-hand side....
Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara
2012-10-01
Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety
Regularization methods in Banach spaces
Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S
2012-01-01
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B
Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule
Jin, Qinian; Wang, Wei
2018-03-01
The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.
UNFOLDED REGULAR AND SEMI-REGULAR POLYHEDRA
Directory of Open Access Journals (Sweden)
IONIŢĂ Elena
2015-06-01
Full Text Available This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra are convex polyhedra whose faces are regular and equal polygons, with the same number of sides, and whose polyhedral angles are also regular and equal. Semi-regular polyhedra are convex polyhedra with regular polygon faces, several types and equal solid angles of the same type. A net of a polyhedron is a collection of edges in the plane which are the unfolded edges of the solid. Modeling and unfolding Platonic and Arhimediene polyhedra will be using 3dsMAX program. This paper is intended as an example of descriptive geometry applications.
Phaseless tomographic inverse scattering in Banach spaces
International Nuclear Information System (INIS)
Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.; Tavanti, E.
2016-01-01
In conventional microwave imaging, a hidden dielectric object under test is illuminated by microwave incident waves and the field it scatters is measured in magnitude and phase in order to retrieve the dielectric properties by solving the related non-homogenous Helmholtz equation or its Lippmann-Schwinger integral formulation. Since the measurement of the phase of electromagnetic waves can be still considered expensive in real applications, in this paper only the magnitude of the scattering wave fields is measured in order to allow a reduction of the cost of the measurement apparatus. In this respect, we firstly analyse the properties of the phaseless scattering nonlinear forward modelling operator in its integral form and we provide an analytical expression for computing its Fréchet derivative. Then, we propose an inexact Newton method to solve the associated nonlinear inverse problems, where any linearized step is solved by a L p Banach space iterative regularization method which acts on the dual space L p* . Indeed, it is well known that regularization in special Banach spaces, such us L p with 1 < p < 2, allows to promote sparsity and to reduce Gibbs phenomena and over-smoothness. Preliminary results concerning numerically computed field data are shown. (paper)
International Nuclear Information System (INIS)
Duque, C.M.; Mora-Ramos, M.E.; Duque, C.A.
2013-01-01
The calculation of the second and third harmonic generation coefficients is carried out within the framework of the effective mass approximation in two-dimensional GaAs quantum discs under the combined effect of an external magnetic field and parabolic and inverse square confining potentials. Due to the electric dipole selection rules, the system is shown to have second harmonic generation coefficient identically zero for all the values of incident frequency. The generation of third optical harmonics is significantly dependent on the values of the different input parameters, with the presence of resonant peak blueshifts associated with the magnitudes of the parabolic confinement and the applied magnetic field. -- Highlights: ► One-electron conduction states in a two-dimensional quantum dot. ► Magnetic field and an inverse square repulsive potential. ► Generation of second harmonics is always null. ► Magnetic field induces a blueshift of the resonant peaks. ► The inverse square potential induces a reduction of the peak intensities
Energy Technology Data Exchange (ETDEWEB)
Duque, C.M. [Instituto de Física, Universidad de Antioquia, AA 1226 Medellín (Colombia); Mora-Ramos, M.E. [Instituto de Física, Universidad de Antioquia, AA 1226 Medellín (Colombia); Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave, Universidad 1001, CP 62209 Cuernavaca, Morelos (Mexico); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Instituto de Física, Universidad de Antioquia, AA 1226 Medellín (Colombia)
2013-06-15
The calculation of the second and third harmonic generation coefficients is carried out within the framework of the effective mass approximation in two-dimensional GaAs quantum discs under the combined effect of an external magnetic field and parabolic and inverse square confining potentials. Due to the electric dipole selection rules, the system is shown to have second harmonic generation coefficient identically zero for all the values of incident frequency. The generation of third optical harmonics is significantly dependent on the values of the different input parameters, with the presence of resonant peak blueshifts associated with the magnitudes of the parabolic confinement and the applied magnetic field. -- Highlights: ► One-electron conduction states in a two-dimensional quantum dot. ► Magnetic field and an inverse square repulsive potential. ► Generation of second harmonics is always null. ► Magnetic field induces a blueshift of the resonant peaks. ► The inverse square potential induces a reduction of the peak intensities.
Inverse Diffusion Curves Using Shape Optimization.
Zhao, Shuang; Durand, Fredo; Zheng, Changxi
2018-07-01
The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.
Condition Number Regularized Covariance Estimation.
Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala
2013-06-01
Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the "large p small n " setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required.
Condition Number Regularized Covariance Estimation*
Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala
2012-01-01
Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the “large p small n” setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required. PMID:23730197
Regularization of Instantaneous Frequency Attribute Computations
Yedlin, M. J.; Margrave, G. F.; Van Vorst, D. G.; Ben Horin, Y.
2014-12-01
We compare two different methods of computation of a temporally local frequency:1) A stabilized instantaneous frequency using the theory of the analytic signal.2) A temporally variant centroid (or dominant) frequency estimated from a time-frequency decomposition.The first method derives from Taner et al (1979) as modified by Fomel (2007) and utilizes the derivative of the instantaneous phase of the analytic signal. The second method computes the power centroid (Cohen, 1995) of the time-frequency spectrum, obtained using either the Gabor or Stockwell Transform. Common to both methods is the necessity of division by a diagonal matrix, which requires appropriate regularization.We modify Fomel's (2007) method by explicitly penalizing the roughness of the estimate. Following Farquharson and Oldenburg (2004), we employ both the L curve and GCV methods to obtain the smoothest model that fits the data in the L2 norm.Using synthetic data, quarry blast, earthquakes and the DPRK tests, our results suggest that the optimal method depends on the data. One of the main applications for this work is the discrimination between blast events and earthquakesFomel, Sergey. " Local seismic attributes." , Geophysics, 72.3 (2007): A29-A33.Cohen, Leon. " Time frequency analysis theory and applications." USA: Prentice Hall, (1995).Farquharson, Colin G., and Douglas W. Oldenburg. "A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems." Geophysical Journal International 156.3 (2004): 411-425.Taner, M. Turhan, Fulton Koehler, and R. E. Sheriff. " Complex seismic trace analysis." Geophysics, 44.6 (1979): 1041-1063.
International Nuclear Information System (INIS)
Namatame, Hirofumi; Taniguchi, Masaki
1994-01-01
Photoelectron spectroscopy is regarded as the most powerful means since it can measure almost perfectly the occupied electron state. On the other hand, inverse photoelectron spectroscopy is the technique for measuring unoccupied electron state by using the inverse process of photoelectron spectroscopy, and in principle, the similar experiment to photoelectron spectroscopy becomes feasible. The development of the experimental technology for inverse photoelectron spectroscopy has been carried out energetically by many research groups so far. At present, the heightening of resolution of inverse photoelectron spectroscopy, the development of inverse photoelectron spectroscope in which light energy is variable and so on are carried out. But the inverse photoelectron spectroscope for vacuum ultraviolet region is not on the market. In this report, the principle of inverse photoelectron spectroscopy and the present state of the spectroscope are described, and the direction of the development hereafter is groped. As the experimental equipment, electron guns, light detectors and so on are explained. As the examples of the experiment, the inverse photoelectron spectroscopy of semimagnetic semiconductors and resonance inverse photoelectron spectroscopy are reported. (K.I.)
Waveform inversion for acoustic VTI media in frequency domain
Wu, Zedong; Alkhalifah, Tariq Ali
2016-01-01
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the background model using a single scattered wavefield from an inverted perturbation. However, current
Directory of Open Access Journals (Sweden)
Shkvarko Yuriy
2006-01-01
Full Text Available We address a new approach to solve the ill-posed nonlinear inverse problem of high-resolution numerical reconstruction of the spatial spectrum pattern (SSP of the backscattered wavefield sources distributed over the remotely sensed scene. An array or synthesized array radar (SAR that employs digital data signal processing is considered. By exploiting the idea of combining the statistical minimum risk estimation paradigm with numerical descriptive regularization techniques, we address a new fused statistical descriptive regularization (SDR strategy for enhanced radar imaging. Pursuing such an approach, we establish a family of the SDR-related SSP estimators, that encompass a manifold of existing beamforming techniques ranging from traditional matched filter to robust and adaptive spatial filtering, and minimum variance methods.
Nonlinear transport of dynamic system phase space
International Nuclear Information System (INIS)
Xie Xi; Xia Jiawen
1993-01-01
The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example
Energy functions for regularization algorithms
Delingette, H.; Hebert, M.; Ikeuchi, K.
1991-01-01
Regularization techniques are widely used for inverse problem solving in computer vision such as surface reconstruction, edge detection, or optical flow estimation. Energy functions used for regularization algorithms measure how smooth a curve or surface is, and to render acceptable solutions these energies must verify certain properties such as invariance with Euclidean transformations or invariance with parameterization. The notion of smoothness energy is extended here to the notion of a differential stabilizer, and it is shown that to void the systematic underestimation of undercurvature for planar curve fitting, it is necessary that circles be the curves of maximum smoothness. A set of stabilizers is proposed that meet this condition as well as invariance with rotation and parameterization.
Ingram, WT
2012-01-01
Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influen
Uniqueness and numerical methods in inverse obstacle scattering
International Nuclear Information System (INIS)
Kress, Rainer
2007-01-01
The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages
Wave-equation reflection traveltime inversion
Zhang, Sanzong; Schuster, Gerard T.; Luo, Yi
2011-01-01
The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear
3D CSEM inversion based on goal-oriented adaptive finite element method
Zhang, Y.; Key, K.
2016-12-01
We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with
Accretion onto some well-known regular black holes
International Nuclear Information System (INIS)
Jawad, Abdul; Shahzad, M.U.
2016-01-01
In this work, we discuss the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, nonlinear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. We obtain the critical radius, critical speed, and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density, and the rate of change of the mass for each of the regular black holes. (orig.)
Accretion onto some well-known regular black holes
Energy Technology Data Exchange (ETDEWEB)
Jawad, Abdul; Shahzad, M.U. [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan)
2016-03-15
In this work, we discuss the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, nonlinear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. We obtain the critical radius, critical speed, and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density, and the rate of change of the mass for each of the regular black holes. (orig.)
Accretion onto some well-known regular black holes
Jawad, Abdul; Shahzad, M. Umair
2016-03-01
In this work, we discuss the accretion onto static spherically symmetric regular black holes for specific choices of the equation of state parameter. The underlying regular black holes are charged regular black holes using the Fermi-Dirac distribution, logistic distribution, nonlinear electrodynamics, respectively, and Kehagias-Sftesos asymptotically flat regular black holes. We obtain the critical radius, critical speed, and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density, and the rate of change of the mass for each of the regular black holes.
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
Nijholt, Antinus
1980-01-01
Culik II and Cogen introduced the class of LR-regular grammars, an extension of the LR(k) grammars. In this paper we consider an analogous extension of the LL(k) grammars called the LL-regular grammars. The relation of this class of grammars to other classes of grammars will be shown. Any LL-regular
Approximation of Bayesian Inverse Problems for PDEs
Cotter, S. L.; Dashti, M.; Stuart, A. M.
2010-01-01
Inverse problems are often ill posed, with solutions that depend sensitively on data.n any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as t...
Three-dimensional inversion of multisource array electromagnetic data
Tartaras, Efthimios
Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM
Inversion algorithms for large-scale geophysical electromagnetic measurements
International Nuclear Information System (INIS)
Abubakar, A; Habashy, T M; Li, M; Liu, J
2009-01-01
Low-frequency surface electromagnetic prospecting methods have been gaining a lot of interest because of their capabilities to directly detect hydrocarbon reservoirs and to compliment seismic measurements for geophysical exploration applications. There are two types of surface electromagnetic surveys. The first is an active measurement where we use an electric dipole source towed by a ship over an array of seafloor receivers. This measurement is called the controlled-source electromagnetic (CSEM) method. The second is the Magnetotelluric (MT) method driven by natural sources. This passive measurement also uses an array of seafloor receivers. Both surface electromagnetic methods measure electric and magnetic field vectors. In order to extract maximal information from these CSEM and MT data we employ a nonlinear inversion approach in their interpretation. We present two types of inversion approaches. The first approach is the so-called pixel-based inversion (PBI) algorithm. In this approach the investigation domain is subdivided into pixels, and by using an optimization process the conductivity distribution inside the domain is reconstructed. The optimization process uses the Gauss–Newton minimization scheme augmented with various forms of regularization. To automate the algorithm, the regularization term is incorporated using a multiplicative cost function. This PBI approach has demonstrated its ability to retrieve reasonably good conductivity images. However, the reconstructed boundaries and conductivity values of the imaged anomalies are usually not quantitatively resolved. Nevertheless, the PBI approach can provide useful information on the location, the shape and the conductivity of the hydrocarbon reservoir. The second method is the so-called model-based inversion (MBI) algorithm, which uses a priori information on the geometry to reduce the number of unknown parameters and to improve the quality of the reconstructed conductivity image. This MBI approach can
Regular Expression Pocket Reference
Stubblebine, Tony
2007-01-01
This handy little book offers programmers a complete overview of the syntax and semantics of regular expressions that are at the heart of every text-processing application. Ideal as a quick reference, Regular Expression Pocket Reference covers the regular expression APIs for Perl 5.8, Ruby (including some upcoming 1.9 features), Java, PHP, .NET and C#, Python, vi, JavaScript, and the PCRE regular expression libraries. This concise and easy-to-use reference puts a very powerful tool for manipulating text and data right at your fingertips. Composed of a mixture of symbols and text, regular exp
The forced nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Kaup, D.J.; Hansen, P.J.
1985-01-01
The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)
International Nuclear Information System (INIS)
Kılıç, Emre; Eibert, Thomas F.
2015-01-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
Inverse Problems for Nonlinear Delay Systems
2011-03-15
population dynamics. We consider the delay between birth and adulthood for neonate pea aphids and present a mathematical model that treats this delay as...which there is currently no known cure. For HIV, the core of the virus is composed of single-stranded viral RNA and protein components. As depicted in...at a CD4 receptor site and the viral core is injected into the cell. Once inside, the protein components enable transcription and integration of the
Non-perturbational surface-wave inversion: A Dix-type relation for surface waves
Haney, Matt; Tsai, Victor C.
2015-01-01
We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shear-wave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a near-surface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion.
Statistical perspectives on inverse problems
DEFF Research Database (Denmark)
Andersen, Kim Emil
of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...
Regularization by External Variables
DEFF Research Database (Denmark)
Bossolini, Elena; Edwards, R.; Glendinning, P. A.
2016-01-01
Regularization was a big topic at the 2016 CRM Intensive Research Program on Advances in Nonsmooth Dynamics. There are many open questions concerning well known kinds of regularization (e.g., by smoothing or hysteresis). Here, we propose a framework for an alternative and important kind of regula......Regularization was a big topic at the 2016 CRM Intensive Research Program on Advances in Nonsmooth Dynamics. There are many open questions concerning well known kinds of regularization (e.g., by smoothing or hysteresis). Here, we propose a framework for an alternative and important kind...
Goyvaerts, Jan
2009-01-01
This cookbook provides more than 100 recipes to help you crunch data and manipulate text with regular expressions. Every programmer can find uses for regular expressions, but their power doesn't come worry-free. Even seasoned users often suffer from poor performance, false positives, false negatives, or perplexing bugs. Regular Expressions Cookbook offers step-by-step instructions for some of the most common tasks involving this tool, with recipes for C#, Java, JavaScript, Perl, PHP, Python, Ruby, and VB.NET. With this book, you will: Understand the basics of regular expressions through a
Directory of Open Access Journals (Sweden)
Joel Sereno
2010-01-01
Full Text Available Inverse kinematics is the process of converting a Cartesian point in space into a set of joint angles to more efficiently move the end effector of a robot to a desired orientation. This project investigates the inverse kinematics of a robotic hand with fingers under various scenarios. Assuming the parameters of a provided robot, a general equation for the end effector point was calculated and used to plot the region of space that it can reach. Further, the benefits obtained from the addition of a prismatic joint versus an extra variable angle joint were considered. The results confirmed that having more movable parts, such as prismatic points and changing angles, increases the effective reach of a robotic hand.
International Nuclear Information System (INIS)
Desesquelles, P.
1997-01-01
Computer Monte Carlo simulations occupy an increasingly important place between theory and experiment. This paper introduces a global protocol for the comparison of model simulations with experimental results. The correlated distributions of the model parameters are determined using an original recursive inversion procedure. Multivariate analysis techniques are used in order to optimally synthesize the experimental information with a minimum number of variables. This protocol is relevant in all fields if physics dealing with event generators and multi-parametric experiments. (authors)
Convex blind image deconvolution with inverse filtering
Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong
2018-03-01
Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.
Regularities of Multifractal Measures
Indian Academy of Sciences (India)
First, we prove the decomposition theorem for the regularities of multifractal Hausdorff measure and packing measure in R R d . This decomposition theorem enables us to split a set into regular and irregular parts, so that we can analyze each separately, and recombine them without affecting density properties. Next, we ...
Stochastic analytic regularization
International Nuclear Information System (INIS)
Alfaro, J.
1984-07-01
Stochastic regularization is reexamined, pointing out a restriction on its use due to a new type of divergence which is not present in the unregulated theory. Furthermore, we introduce a new form of stochastic regularization which permits the use of a minimal subtraction scheme to define the renormalized Green functions. (author)
On quasiclassical approximation in the inverse scattering method
International Nuclear Information System (INIS)
Geogdzhaev, V.V.
1985-01-01
Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem
Coupling regularizes individual units in noisy populations
International Nuclear Information System (INIS)
Ly Cheng; Ermentrout, G. Bard
2010-01-01
The regularity of a noisy system can modulate in various ways. It is well known that coupling in a population can lower the variability of the entire network; the collective activity is more regular. Here, we show that diffusive (reciprocal) coupling of two simple Ornstein-Uhlenbeck (O-U) processes can regularize the individual, even when it is coupled to a noisier process. In cellular networks, the regularity of individual cells is important when a select few play a significant role. The regularizing effect of coupling surprisingly applies also to general nonlinear noisy oscillators. However, unlike with the O-U process, coupling-induced regularity is robust to different kinds of coupling. With two coupled noisy oscillators, we derive an asymptotic formula assuming weak noise and coupling for the variance of the period (i.e., spike times) that accurately captures this effect. Moreover, we find that reciprocal coupling can regularize the individual period of higher dimensional oscillators such as the Morris-Lecar and Brusselator models, even when coupled to noisier oscillators. Coupling can have a counterintuitive and beneficial effect on noisy systems. These results have implications for the role of connectivity with noisy oscillators and the modulation of variability of individual oscillators.
Obtaining sparse distributions in 2D inverse problems
Reci, A; Sederman, Andrew John; Gladden, Lynn Faith
2017-01-01
The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L1 regularization to a class of inverse problems; relaxat...
RES: Regularized Stochastic BFGS Algorithm
Mokhtari, Aryan; Ribeiro, Alejandro
2014-12-01
RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.
Directory of Open Access Journals (Sweden)
Jing Wang
2013-01-01
Full Text Available The image reconstruction for electrical impedance tomography (EIT mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.
Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography
Xu, Feng; Deshpande, Manohar
2012-01-01
Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.
Stability study of pre-stack seismic inversion based on the full Zoeppritz equation
Liang, Lifeng; Zhang, Hongbing; Guo, Qiang; Saeed, Wasif; Shang, Zuoping; Huang, Guojiao
2017-10-01
Pre-stack seismic inversion is highly important and complicated. Its result is non-unique, and the process is unstable because pre-stack seismic inversion is an ill-posed problem that simultaneously obtains the results of multiple parameters. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularization (EPR) can help mitigate the problem. To achieve this combination, we developed an inversion method by constructing a new objective function, which includes the EPR and the Markov random field. The method directly gains reflectivity R PP by the full Zoeppritz equation instead of its approximations and effectively controls the stability of simultaneous inversion by two additional assumptions: the sectional constant V S/V P and the generalized Gardner equation. Thus, the simultaneous inversion of multiple parameters is directed toward to V P, ΔL S (the fitting deviation of V S) and density, and the generalized Gardner equation is regarded as a constraint from which the fitting relationship is derived. We applied the fast simulated annealing algorithm to solve the nonlinear optimization problem. The test results on 2D synthetic data indicated that the stability of simultaneous inversion for V P, ΔL S and density is better than these for V P, V S, and density. The inverted result of density gradually worsens as the deviation ΔL D (the fitting deviation of the density) increases. Moreover, the inverted results were acceptable when using the fitting relationships with error, although they showed varying degrees of influence. We constructed time-varying and space-varying fitting relationships using the logging data in pre-stack inversion of the field seismic data. This improved the inverted results of the simultaneous inversion for complex geological models. Finally, the inverted results of the field data distinctly revealed more detailed information about the layers and matched well with the logging data along the wells over most
Advances in Global Full Waveform Inversion
Tromp, J.; Bozdag, E.; Lei, W.; Ruan, Y.; Lefebvre, M. P.; Modrak, R. T.; Orsvuran, R.; Smith, J. A.; Komatitsch, D.; Peter, D. B.
2017-12-01
Information about Earth's interior comes from seismograms recorded at its surface. Seismic imaging based on spectral-element and adjoint methods has enabled assimilation of this information for the construction of 3D (an)elastic Earth models. These methods account for the physics of wave excitation and propagation by numerically solving the equations of motion, and require the execution of complex computational procedures that challenge the most advanced high-performance computing systems. Current research is petascale; future research will require exascale capabilities. The inverse problem consists of reconstructing the characteristics of the medium from -often noisy- observations. A nonlinear functional is minimized, which involves both the misfit to the measurements and a Tikhonov-type regularization term to tackle inherent ill-posedness. Achieving scalability for the inversion process on tens of thousands of multicore processors is a task that offers many research challenges. We initiated global "adjoint tomography" using 253 earthquakes and produced the first-generation model named GLAD-M15, with a transversely isotropic model parameterization. We are currently running iterations for a second-generation anisotropic model based on the same 253 events. In parallel, we continue iterations for a transversely isotropic model with a larger dataset of 1,040 events to determine higher-resolution plume and slab images. A significant part of our research has focused on eliminating I/O bottlenecks in the adjoint tomography workflow. This has led to the development of a new Adaptable Seismic Data Format based on HDF5, and post-processing tools based on the ADIOS library developed by Oak Ridge National Laboratory. We use the Ensemble Toolkit for workflow stabilization & management to automate the workflow with minimal human interaction.
Sparse structure regularized ranking
Wang, Jim Jing-Yan; Sun, Yijun; Gao, Xin
2014-01-01
Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse
Regular expression containment
DEFF Research Database (Denmark)
Henglein, Fritz; Nielsen, Lasse
2011-01-01
We present a new sound and complete axiomatization of regular expression containment. It consists of the conventional axiomatiza- tion of concatenation, alternation, empty set and (the singleton set containing) the empty string as an idempotent semiring, the fixed- point rule E* = 1 + E × E......* for Kleene-star, and a general coin- duction rule as the only additional rule. Our axiomatization gives rise to a natural computational inter- pretation of regular expressions as simple types that represent parse trees, and of containment proofs as coercions. This gives the axiom- atization a Curry......-Howard-style constructive interpretation: Con- tainment proofs do not only certify a language-theoretic contain- ment, but, under our computational interpretation, constructively transform a membership proof of a string in one regular expres- sion into a membership proof of the same string in another regular expression. We...
Supersymmetric dimensional regularization
International Nuclear Information System (INIS)
Siegel, W.; Townsend, P.K.; van Nieuwenhuizen, P.
1980-01-01
There is a simple modification of dimension regularization which preserves supersymmetry: dimensional reduction to real D < 4, followed by analytic continuation to complex D. In terms of component fields, this means fixing the ranges of all indices on the fields (and therefore the numbers of Fermi and Bose components). For superfields, it means continuing in the dimensionality of x-space while fixing the dimensionality of theta-space. This regularization procedure allows the simple manipulation of spinor derivatives in supergraph calculations. The resulting rules are: (1) First do all algebra exactly as in D = 4; (2) Then do the momentum integrals as in ordinary dimensional regularization. This regularization procedure needs extra rules before one can say that it is consistent. Such extra rules needed for superconformal anomalies are discussed. Problems associated with renormalizability and higher order loops are also discussed
Regularized maximum correntropy machine
Wang, Jim Jing-Yan; Wang, Yunji; Jing, Bing-Yi; Gao, Xin
2015-01-01
In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.
Regularized maximum correntropy machine
Wang, Jim Jing-Yan
2015-02-12
In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.
A short proof of increased parabolic regularity
Directory of Open Access Journals (Sweden)
Stephen Pankavich
2015-08-01
Full Text Available We present a short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates and an inductive method, can be extended to prove analogous results for problems with time-dependent coefficients, advection-diffusion or reaction diffusion equations, and nonlinear PDEs even when other tools, such as semigroup methods or the use of explicit fundamental solutions, are unavailable.
Posterior consistency for Bayesian inverse problems through stability and regression results
International Nuclear Information System (INIS)
Vollmer, Sebastian J
2013-01-01
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes’ formula, giving rise to the posterior distribution on the unknown input. In this setting we prove posterior consistency for nonlinear inverse problems: a sequence of data is considered, with diminishing fluctuations around a single truth and it is then of interest to show that the resulting sequence of posterior measures arising from this sequence of data concentrates around the truth used to generate the data. Posterior consistency justifies the use of the Bayesian approach very much in the same way as error bounds and convergence results for regularization techniques do. As a guiding example, we consider the inverse problem of reconstructing the diffusion coefficient from noisy observations of the solution to an elliptic PDE in divergence form. This problem is approached by splitting the forward operator into the underlying continuum model and a simpler observation operator based on the output of the model. In general, these splittings allow us to conclude posterior consistency provided a deterministic stability result for the underlying inverse problem and a posterior consistency result for the Bayesian regression problem with the push-forward prior. Moreover, we prove posterior consistency for the Bayesian regression problem based on the regularity, the tail behaviour and the small ball probabilities of the prior. (paper)
Manifold Regularized Reinforcement Learning.
Li, Hongliang; Liu, Derong; Wang, Ding
2018-04-01
This paper introduces a novel manifold regularized reinforcement learning scheme for continuous Markov decision processes. Smooth feature representations for value function approximation can be automatically learned using the unsupervised manifold regularization method. The learned features are data-driven, and can be adapted to the geometry of the state space. Furthermore, the scheme provides a direct basis representation extension for novel samples during policy learning and control. The performance of the proposed scheme is evaluated on two benchmark control tasks, i.e., the inverted pendulum and the energy storage problem. Simulation results illustrate the concepts of the proposed scheme and show that it can obtain excellent performance.
Modular Regularization Algorithms
DEFF Research Database (Denmark)
Jacobsen, Michael
2004-01-01
The class of linear ill-posed problems is introduced along with a range of standard numerical tools and basic concepts from linear algebra, statistics and optimization. Known algorithms for solving linear inverse ill-posed problems are analyzed to determine how they can be decomposed into indepen...
Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data
Energy Technology Data Exchange (ETDEWEB)
Gary D. Egbert
2007-03-22
The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to the full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before
3D Inversion of SQUID Magnetic Tensor Data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...
Full waveform inversion based on scattering angle enrichment with application to real dataset
Wu, Zedong; Alkhalifah, Tariq Ali
2015-01-01
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI). However, the drawback of the existing RWI methods is inability to utilize diving waves and the extra sensitivity
An algorithm for total variation regularized photoacoustic imaging
DEFF Research Database (Denmark)
Dong, Yiqiu; Görner, Torsten; Kunis, Stefan
2014-01-01
Recovery of image data from photoacoustic measurements asks for the inversion of the spherical mean value operator. In contrast to direct inversion methods for specific geometries, we consider a semismooth Newton scheme to solve a total variation regularized least squares problem. During the iter......Recovery of image data from photoacoustic measurements asks for the inversion of the spherical mean value operator. In contrast to direct inversion methods for specific geometries, we consider a semismooth Newton scheme to solve a total variation regularized least squares problem. During...... the iteration, each matrix vector multiplication is realized in an efficient way using a recently proposed spectral discretization of the spherical mean value operator. All theoretical results are illustrated by numerical experiments....
On nonlinear periodic drift waves
International Nuclear Information System (INIS)
Kauschke, U.; Schlueter, H.
1990-09-01
Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)
Improvements in GRACE Gravity Fields Using Regularization
Save, H.; Bettadpur, S.; Tapley, B. D.
2008-12-01
The unconstrained global gravity field models derived from GRACE are susceptible to systematic errors that show up as broad "stripes" aligned in a North-South direction on the global maps of mass flux. These errors are believed to be a consequence of both systematic and random errors in the data that are amplified by the nature of the gravity field inverse problem. These errors impede scientific exploitation of the GRACE data products, and limit the realizable spatial resolution of the GRACE global gravity fields in certain regions. We use regularization techniques to reduce these "stripe" errors in the gravity field products. The regularization criteria are designed such that there is no attenuation of the signal and that the solutions fit the observations as well as an unconstrained solution. We have used a computationally inexpensive method, normally referred to as "L-ribbon", to find the regularization parameter. This paper discusses the characteristics and statistics of a 5-year time-series of regularized gravity field solutions. The solutions show markedly reduced stripes, are of uniformly good quality over time, and leave little or no systematic observation residuals, which is a frequent consequence of signal suppression from regularization. Up to degree 14, the signal in regularized solution shows correlation greater than 0.8 with the un-regularized CSR Release-04 solutions. Signals from large-amplitude and small-spatial extent events - such as the Great Sumatra Andaman Earthquake of 2004 - are visible in the global solutions without using special post-facto error reduction techniques employed previously in the literature. Hydrological signals as small as 5 cm water-layer equivalent in the small river basins, like Indus and Nile for example, are clearly evident, in contrast to noisy estimates from RL04. The residual variability over the oceans relative to a seasonal fit is small except at higher latitudes, and is evident without the need for de-striping or
Invariant models in the inversion of gravity and magnetic fields and their derivatives
Ialongo, Simone; Fedi, Maurizio; Florio, Giovanni
2014-11-01
In potential field inversion problems we usually solve underdetermined systems and realistic solutions may be obtained by introducing a depth-weighting function in the objective function. The choice of the exponent of such power-law is crucial. It was suggested to determine it from the field-decay due to a single source-block; alternatively it has been defined as the structural index of the investigated source distribution. In both cases, when k-order derivatives of the potential field are considered, the depth-weighting exponent has to be increased by k with respect that of the potential field itself, in order to obtain consistent source model distributions. We show instead that invariant and realistic source-distribution models are obtained using the same depth-weighting exponent for the magnetic field and for its k-order derivatives. A similar behavior also occurs in the gravity case. In practice we found that the depth weighting-exponent is invariant for a given source-model and equal to that of the corresponding magnetic field, in the magnetic case, and of the 1st derivative of the gravity field, in the gravity case. In the case of the regularized inverse problem, with depth-weighting and general constraints, the mathematical demonstration of such invariance is difficult, because of its non-linearity, and of its variable form, due to the different constraints used. However, tests performed on a variety of synthetic cases seem to confirm the invariance of the depth-weighting exponent. A final consideration regards the role of the regularization parameter; we show that the regularization can severely affect the depth to the source because the estimated depth tends to increase proportionally with the size of the regularization parameter. Hence, some care is needed in handling the combined effect of the regularization parameter and depth weighting.
NLSE: Parameter-Based Inversion Algorithm
Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.
Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.
Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model
Mondal, Anirban
2014-07-03
We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.
Diverse Regular Employees and Non-regular Employment (Japanese)
MORISHIMA Motohiro
2011-01-01
Currently there are high expectations for the introduction of policies related to diverse regular employees. These policies are a response to the problem of disparities between regular and non-regular employees (part-time, temporary, contract and other non-regular employees) and will make it more likely that workers can balance work and their private lives while companies benefit from the advantages of regular employment. In this paper, I look at two issues that underlie this discussion. The ...
Sparse structure regularized ranking
Wang, Jim Jing-Yan
2014-04-17
Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse structure, we assume that each multimedia object could be represented as a sparse linear combination of all other objects, and combination coefficients are regarded as a similarity measure between objects and used to regularize their ranking scores. Moreover, we propose to learn the sparse combination coefficients and the ranking scores simultaneously. A unified objective function is constructed with regard to both the combination coefficients and the ranking scores, and is optimized by an iterative algorithm. Experiments on two multimedia database retrieval data sets demonstrate the significant improvements of the propose algorithm over state-of-the-art ranking score learning algorithms.
'Regular' and 'emergency' repair
International Nuclear Information System (INIS)
Luchnik, N.V.
1975-01-01
Experiments on the combined action of radiation and a DNA inhibitor using Crepis roots and on split-dose irradiation of human lymphocytes lead to the conclusion that there are two types of repair. The 'regular' repair takes place twice in each mitotic cycle and ensures the maintenance of genetic stability. The 'emergency' repair is induced at all stages of the mitotic cycle by high levels of injury. (author)
Regularization of divergent integrals
Felder, Giovanni; Kazhdan, David
2016-01-01
We study the Hadamard finite part of divergent integrals of differential forms with singularities on submanifolds. We give formulae for the dependence of the finite part on the choice of regularization and express them in terms of a suitable local residue map. The cases where the submanifold is a complex hypersurface in a complex manifold and where it is a boundary component of a manifold with boundary, arising in string perturbation theory, are treated in more detail.
Conditioning the full-waveform inversion gradient to welcome anisotropy
Alkhalifah, Tariq Ali
2015-01-01
Multiparameter full-waveform inversion (FWI) suffers from complex nonlinearity in the objective function, compounded by the eventual trade-off between the model parameters. A hierarchical approach based on frequency and arrival time data decimation
Stochastic forward and inverse groundwater flow and solute transport modeling
Janssen, G.M.C.M.
2008-01-01
Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers
This thesis offers three new approaches that contribute
Regularizing portfolio optimization
International Nuclear Information System (INIS)
Still, Susanne; Kondor, Imre
2010-01-01
The optimization of large portfolios displays an inherent instability due to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting, which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification 'pressure'. This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade off between the two, depending on the size of the available dataset.
Regularizing portfolio optimization
Still, Susanne; Kondor, Imre
2010-07-01
The optimization of large portfolios displays an inherent instability due to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting, which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification 'pressure'. This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade off between the two, depending on the size of the available dataset.
Anisotropic magnetotelluric inversion using a mutual information constraint
Mandolesi, E.; Jones, A. G.
2012-12-01
In recent years, several authors pointed that the electrical conductivity of many subsurface structures cannot be described properly by a scalar field. With the development of field devices and techniques, data quality improved to the point that the anisotropy in conductivity of rocks (microscopic anisotropy) and tectonic structures (macroscopic anisotropy) cannot be neglected. Therefore a correct use of high quality data has to include electrical anisotropy and a correct interpretation of anisotropic data characterizes directly a non-negligible part of the subsurface. In this work we test an inversion routine that takes advantage of the classic Levenberg-Marquardt (LM) algorithm to invert magnetotelluric (MT) data generated from a bi-dimensional (2D) anisotropic domain. The LM method is routinely used in inverse problems due its performance and robustness. In non-linear inverse problems -such the MT problem- the LM method provides a spectacular compromise betwee quick and secure convergence at the price of the explicit computation and storage of the sensitivity matrix. Regularization in inverse MT problems has been used extensively, due to the necessity to constrain model space and to reduce the ill-posedness of the anisotropic MT problem, which makes MT inversions extremely challenging. In order to reduce non-uniqueness of the MT problem and to reach a model compatible with other different tomographic results from the same target region, we used a mutual information (MI) based constraint. MI is a basic quantity in information theory that can be used to define a metric between images, and it is routinely used in fields as computer vision, image registration and medical tomography, to cite some applications. We -thus- inverted for the model that best fits the anisotropic data and that is the closest -in a MI sense- to a tomographic model of the target area. The advantage of this technique is that the tomographic model of the studied region may be produced by any
Regular Single Valued Neutrosophic Hypergraphs
Directory of Open Access Journals (Sweden)
Muhammad Aslam Malik
2016-12-01
Full Text Available In this paper, we define the regular and totally regular single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular single valued neutrosophic hypergraphs. We also extend work on completeness of single valued neutrosophic hypergraphs.
The geometry of continuum regularization
International Nuclear Information System (INIS)
Halpern, M.B.
1987-03-01
This lecture is primarily an introduction to coordinate-invariant regularization, a recent advance in the continuum regularization program. In this context, the program is seen as fundamentally geometric, with all regularization contained in regularized DeWitt superstructures on field deformations
A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion
CUI, C.; Hou, W.
2017-12-01
Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
On inverse problem of calculus of variations
Energy Technology Data Exchange (ETDEWEB)
Tao, Z-L [College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044 (China)], E-mail: zaolingt@nuist.edu.cn
2008-02-15
Using the semi-inverse method proposed by Ji-Huan He, variational principles are established for some nonlinear equations arising in physics, including the (p, 2p)-mZK equation, Klein-Gordon equation, sine-Gordon equation, Liouville equation, Dodd- Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation.
Nonlinear variational inequalities of semilinear parabolic type
Directory of Open Access Journals (Sweden)
Park Jong-Yeoul
2001-01-01
Full Text Available The existence of solutions for the nonlinear functional differential equation governed by the variational inequality is studied. The regularity and a variation of solutions of the equation are also given.
A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging
Desmal, Abdulla
2015-03-01
A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.
An application of sparse inversion on the calculation of the inverse data space of geophysical data
Saragiotis, Christos
2011-07-01
Multiple reflections as observed in seismic reflection measurements often hide arrivals from the deeper target reflectors and need to be removed. The inverse data space provides a natural separation of primaries and surface-related multiples, as the surface multiples map onto the area around the origin while the primaries map elsewhere. However, the calculation of the inverse data is far from trivial as theory requires infinite time and offset recording. Furthermore regularization issues arise during inversion. We perform the inversion by minimizing the least-squares norm of the misfit function and by constraining the 1 norm of the solution, being the inverse data space. In this way a sparse inversion approach is obtained. We show results on field data with an application to surface multiple removal. © 2011 IEEE.
Total-variation regularization with bound constraints
International Nuclear Information System (INIS)
Chartrand, Rick; Wohlberg, Brendt
2009-01-01
We present a new algorithm for bound-constrained total-variation (TV) regularization that in comparison with its predecessors is simple, fast, and flexible. We use a splitting approach to decouple TV minimization from enforcing the constraints. Consequently, existing TV solvers can be employed with minimal alteration. This also makes the approach straightforward to generalize to any situation where TV can be applied. We consider deblurring of images with Gaussian or salt-and-pepper noise, as well as Abel inversion of radiographs with Poisson noise. We incorporate previous iterative reweighting algorithms to solve the TV portion.
Nonlinear transport of accelerator beam phase space
International Nuclear Information System (INIS)
Xie Xi; Xia Jiawen
1995-01-01
Based on the any order analytical solution of accelerator beam dynamics, the general theory for nonlinear transport of accelerator beam phase space is developed by inverse transformation method. The method is general by itself, and hence can also be applied to the nonlinear transport of various dynamic systems in physics, chemistry and biology
Annotation of Regular Polysemy
DEFF Research Database (Denmark)
Martinez Alonso, Hector
Regular polysemy has received a lot of attention from the theory of lexical semantics and from computational linguistics. However, there is no consensus on how to represent the sense of underspecified examples at the token level, namely when annotating or disambiguating senses of metonymic words...... and metonymic. We have conducted an analysis in English, Danish and Spanish. Later on, we have tried to replicate the human judgments by means of unsupervised and semi-supervised sense prediction. The automatic sense-prediction systems have been unable to find empiric evidence for the underspecified sense, even...
Regularity of Minimal Surfaces
Dierkes, Ulrich; Tromba, Anthony J; Kuster, Albrecht
2010-01-01
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is t
Regularities of radiation heredity
International Nuclear Information System (INIS)
Skakov, M.K.; Melikhov, V.D.
2001-01-01
One analyzed regularities of radiation heredity in metals and alloys. One made conclusion about thermodynamically irreversible changes in structure of materials under irradiation. One offers possible ways of heredity transmittance of radiation effects at high-temperature transformations in the materials. Phenomenon of radiation heredity may be turned to practical use to control structure of liquid metal and, respectively, structure of ingot via preliminary radiation treatment of charge. Concentration microheterogeneities in material defect structure induced by preliminary irradiation represent the genetic factor of radiation heredity [ru
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Regularization theory for ill-posed problems selected topics
Lu, Shuai
2013-01-01
Thismonograph is a valuable contribution to thehighly topical and extremly productive field ofregularisationmethods for inverse and ill-posed problems. The author is an internationally outstanding and acceptedmathematicianin this field. In his book he offers a well-balanced mixtureof basic and innovative aspects.He demonstrates new,differentiatedviewpoints, and important examples for applications. The bookdemontrates thecurrent developments inthe field of regularization theory,such as multiparameter regularization and regularization in learning theory. The book is written for graduate and PhDs
Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion
DEFF Research Database (Denmark)
Zunino, Andrea; Lange, Katrine; Melnikova, Yulia
2014-01-01
We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear...
3D inversion of full tensor magnetic gradiometry (FTMG) data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2011-01-01
Following recent advances in SQUID technology, full tensor magnetic gradiometry (FTMG) is emerging as a practical exploration method. We introduce 3D regularized focusing inversion for FTMG data. Our model studies show that inversion of magnetic tensor data can significantly improve resolution...... compared to inversion of magnetic vector data for the same model. We present a case study for the 3D inversion of GETMAG® FTMG data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D inversion agree very well with the known geology of the area....
Inverse problems of geophysics
International Nuclear Information System (INIS)
Yanovskaya, T.B.
2003-07-01
This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given
Three-dimensional gravity modeling and focusing inversion using rectangular meshes.
Energy Technology Data Exchange (ETDEWEB)
Commer, M.
2011-03-01
Rectangular grid cells are commonly used for the geophysical modeling of gravity anomalies, owing to their flexibility in constructing complex models. The straightforward handling of cubic cells in gravity inversion algorithms allows for a flexible imposition of model regularization constraints, which are generally essential in the inversion of static potential field data. The first part of this paper provides a review of commonly used expressions for calculating the gravity of a right polygonal prism, both for gravity and gradiometry, where the formulas of Plouff and Forsberg are adapted. The formulas can be cast into general forms practical for implementation. In the second part, a weighting scheme for resolution enhancement at depth is presented. Modelling the earth using highly digitized meshes, depth weighting schemes are typically applied to the model objective functional, subject to minimizing the data misfit. The scheme proposed here involves a non-linear conjugate gradient inversion scheme with a weighting function applied to the non-linear conjugate gradient scheme's gradient vector of the objective functional. The low depth resolution due to the quick decay of the gravity kernel functions is counteracted by suppressing the search directions in the parameter space that would lead to near-surface concentrations of gravity anomalies. Further, a density parameter transformation function enabling the imposition of lower and upper bounding constraints is employed. Using synthetic data from models of varying complexity and a field data set, it is demonstrated that, given an adequate depth weighting function, the gravity inversion in the transform space can recover geologically meaningful models requiring a minimum of prior information and user interaction.
A method of the asymmetric Abel's inversion in plasma diagnosis
International Nuclear Information System (INIS)
Matoba, Tohru; Funahashi, Akimasa
1975-09-01
In the case of a noncylindrical plasma, axis symmetric components are drawn from observed projected intensities of physical quantities, assuming an asymmetric form. And the radial intensity distribution is determined by Abel's inversion method. The best fitting curve is obtained analytically from measured values by the least-square estimation of nonlinear parameters. The cylindrical symmetric Abel's inversion code ( ABELIC ) and the asymmetric Abel's inversion code ( ABELILSENP 2 ) are described. (auth.)
Atmospheric inverse modeling via sparse reconstruction
Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten
2017-10-01
Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.
A primal–dual hybrid gradient method for nonlinear operators with applications to MRI
Valkonen, Tuomo
2014-05-01
We study the solution of minimax problems min xmax yG(x) + K(x), y - F*(y) in finite-dimensional Hilbert spaces. The functionals G and F* we assume to be convex, but the operator K we allow to be nonlinear. We formulate a natural extension of the modified primal-dual hybrid gradient method, originally for linear K, due to Chambolle and Pock. We prove the local convergence of the method, provided various technical conditions are satisfied. These include in particular the Aubin property of the inverse of a monotone operator at the solution. Of particular interest to us is the case arising from Tikhonov type regularization of inverse problems with nonlinear forward operators. Mainly we are interested in total variation and second-order total generalized variation priors. For such problems, we show that our general local convergence result holds when the noise level of the data f is low, and the regularization parameter α is correspondingly small. We verify the numerical performance of the method by applying it to problems from magnetic resonance imaging (MRI) in chemical engineering and medicine. The specific applications are in diffusion tensor imaging and MR velocity imaging. These numerical studies show very promising performance. © 2014 IOP Publishing Ltd.
Higher order total variation regularization for EIT reconstruction.
Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Zhang, Fan; Mueller-Lisse, Ullrich; Moeller, Knut
2018-01-08
Electrical impedance tomography (EIT) attempts to reveal the conductivity distribution of a domain based on the electrical boundary condition. This is an ill-posed inverse problem; its solution is very unstable. Total variation (TV) regularization is one of the techniques commonly employed to stabilize reconstructions. However, it is well known that TV regularization induces staircase effects, which are not realistic in clinical applications. To reduce such artifacts, modified TV regularization terms considering a higher order differential operator were developed in several previous studies. One of them is called total generalized variation (TGV) regularization. TGV regularization has been successively applied in image processing in a regular grid context. In this study, we adapted TGV regularization to the finite element model (FEM) framework for EIT reconstruction. Reconstructions using simulation and clinical data were performed. First results indicate that, in comparison to TV regularization, TGV regularization promotes more realistic images. Graphical abstract Reconstructed conductivity changes located on selected vertical lines. For each of the reconstructed images as well as the ground truth image, conductivity changes located along the selected left and right vertical lines are plotted. In these plots, the notation GT in the legend stands for ground truth, TV stands for total variation method, and TGV stands for total generalized variation method. Reconstructed conductivity distributions from the GREIT algorithm are also demonstrated.
Effective field theory dimensional regularization
International Nuclear Information System (INIS)
Lehmann, Dirk; Prezeau, Gary
2002-01-01
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed
Effective field theory dimensional regularization
Lehmann, Dirk; Prézeau, Gary
2002-01-01
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed.
Connection between Dirac and matrix Schroedinger inverse-scattering transforms
International Nuclear Information System (INIS)
Jaulent, M.; Leon, J.J.P.
1978-01-01
The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)
Eikonal-Based Inversion of GPR Data from the Vaucluse Karst Aquifer
Yedlin, M. J.; van Vorst, D.; Guglielmi, Y.; Cappa, F.; Gaffet, S.
2009-12-01
In this paper, we present an easy-to-implement eikonal-based travel time inversion algorithm and apply it to borehole GPR measurement data obtained from a karst aquifer located in the Vaucluse in Provence. The boreholes are situated with a fault zone deep inside the aquifer, in the Laboratoire Souterrain à Bas Bruit (LSBB). The measurements were made using 250 MHz MALA RAMAC borehole GPR antennas. The inversion formulation is unique in its application of a fast-sweeping eikonal solver (Zhao [1]) to the minimization of an objective functional that is composed of a travel time misfit and a model-based regularization [2]. The solver is robust in the presence of large velocity contrasts, efficient, easy to implement, and does not require the use of a sorting algorithm. The computation of sensitivities, which are required for the inversion process, is achieved by tracing rays backward from receiver to source following the gradient of the travel time field [2]. A user wishing to implement this algorithm can opt to avoid the ray tracing step and simply perturb the model to obtain the required sensitivities. Despite the obvious computational inefficiency of such an approach, it is acceptable for 2D problems. The relationship between travel time and the velocity profile is non-linear, requiring an iterative approach to be used. At each iteration, a set of matrix equations is solved to determine the model update. As the inversion continues, the weighting of the regularization parameter is adjusted until an appropriate data misfit is obtained. The inversion results, shown in the attached image, are consistent with previously obtained geological structure. Future work will look at improving inversion resolution and incorporating other measurement methodologies, with the goal of providing useful data for groundwater analysis. References: [1] H. Zhao, “A fast sweeping method for Eikonal equations,” Mathematics of Computation, vol. 74, no. 250, pp. 603-627, 2004. [2] D
2010-12-07
... FARM CREDIT SYSTEM INSURANCE CORPORATION Regular Meeting AGENCY: Farm Credit System Insurance Corporation Board. ACTION: Regular meeting. SUMMARY: Notice is hereby given of the regular meeting of the Farm Credit System Insurance Corporation Board (Board). Date and Time: The meeting of the Board will be held...
Workflows for Full Waveform Inversions
Boehm, Christian; Krischer, Lion; Afanasiev, Michael; van Driel, Martin; May, Dave A.; Rietmann, Max; Fichtner, Andreas
2017-04-01
Despite many theoretical advances and the increasing availability of high-performance computing clusters, full seismic waveform inversions still face considerable challenges regarding data and workflow management. While the community has access to solvers which can harness modern heterogeneous computing architectures, the computational bottleneck has fallen to these often manpower-bounded issues that need to be overcome to facilitate further progress. Modern inversions involve huge amounts of data and require a tight integration between numerical PDE solvers, data acquisition and processing systems, nonlinear optimization libraries, and job orchestration frameworks. To this end we created a set of libraries and applications revolving around Salvus (http://salvus.io), a novel software package designed to solve large-scale full waveform inverse problems. This presentation focuses on solving passive source seismic full waveform inversions from local to global scales with Salvus. We discuss (i) design choices for the aforementioned components required for full waveform modeling and inversion, (ii) their implementation in the Salvus framework, and (iii) how it is all tied together by a usable workflow system. We combine state-of-the-art algorithms ranging from high-order finite-element solutions of the wave equation to quasi-Newton optimization algorithms using trust-region methods that can handle inexact derivatives. All is steered by an automated interactive graph-based workflow framework capable of orchestrating all necessary pieces. This naturally facilitates the creation of new Earth models and hopefully sparks new scientific insights. Additionally, and even more importantly, it enhances reproducibility and reliability of the final results.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Variational analysis of regular mappings theory and applications
Ioffe, Alexander D
2017-01-01
This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, whic...
Inverse problems in systems biology
International Nuclear Information System (INIS)
Engl, Heinz W; Lu, James; Müller, Stefan; Flamm, Christoph; Schuster, Peter; Kügler, Philipp
2009-01-01
Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems' behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior. (topical review)
Selection of regularization parameter for l1-regularized damage detection
Hou, Rongrong; Xia, Yong; Bao, Yuequan; Zhou, Xiaoqing
2018-06-01
The l1 regularization technique has been developed for structural health monitoring and damage detection through employing the sparsity condition of structural damage. The regularization parameter, which controls the trade-off between data fidelity and solution size of the regularization problem, exerts a crucial effect on the solution. However, the l1 regularization problem has no closed-form solution, and the regularization parameter is usually selected by experience. This study proposes two strategies of selecting the regularization parameter for the l1-regularized damage detection problem. The first method utilizes the residual and solution norms of the optimization problem and ensures that they are both small. The other method is based on the discrepancy principle, which requires that the variance of the discrepancy between the calculated and measured responses is close to the variance of the measurement noise. The two methods are applied to a cantilever beam and a three-story frame. A range of the regularization parameter, rather than one single value, can be determined. When the regularization parameter in this range is selected, the damage can be accurately identified even for multiple damage scenarios. This range also indicates the sensitivity degree of the damage identification problem to the regularization parameter.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...
Ensemble manifold regularization.
Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng
2012-06-01
We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Celik, Hasan; Bouhrara, Mustapha; Reiter, David A.; Fishbein, Kenneth W.; Spencer, Richard G.
2013-01-01
We propose a new approach to stabilizing the inverse Laplace transform of a multiexponential decay signal, a classically ill-posed problem, in the context of nuclear magnetic resonance relaxometry. The method is based on extension to a second, indirectly detected, dimension, that is, use of the established framework of two-dimensional relaxometry, followed by projection onto the desired axis. Numerical results for signals comprised of discrete T1 and T2 relaxation components and experiments performed on agarose gel phantoms are presented. We find markedly improved accuracy, and stability with respect to noise, as well as insensitivity to regularization in quantifying underlying relaxation components through use of the two-dimensional as compared to the one-dimensional inverse Laplace transform. This improvement is demonstrated separately for two different inversion algorithms, nonnegative least squares and non-linear least squares, to indicate the generalizability of this approach. These results may have wide applicability in approaches to the Fredholm integral equation of the first kind. PMID:24035004
Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models
Elsheikh, Ahmed H.
2013-06-01
A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Extreme Nonlinear Optics An Introduction
Wegener, Martin
2005-01-01
Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...
Adaptive Regularization of Neural Classifiers
DEFF Research Database (Denmark)
Andersen, Lars Nonboe; Larsen, Jan; Hansen, Lars Kai
1997-01-01
We present a regularization scheme which iteratively adapts the regularization parameters by minimizing the validation error. It is suggested to use the adaptive regularization scheme in conjunction with optimal brain damage pruning to optimize the architecture and to avoid overfitting. Furthermo......, we propose an improved neural classification architecture eliminating an inherent redundancy in the widely used SoftMax classification network. Numerical results demonstrate the viability of the method...
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Formal solutions of inverse scattering problems. III
International Nuclear Information System (INIS)
Prosser, R.T.
1980-01-01
The formal solutions of certain three-dimensional inverse scattering problems presented in papers I and II of this series [J. Math. Phys. 10, 1819 (1969); 17 1175 (1976)] are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When the scattering data are sufficiently restricted, this mapping is shown to be a contraction, thereby establishing the existence, uniqueness, and continuous dependence on the data of these formal solutions
2010-09-02
... FARM CREDIT SYSTEM INSURANCE CORPORATION Regular Meeting AGENCY: Farm Credit System Insurance Corporation Board. SUMMARY: Notice is hereby given of the regular meeting of the Farm Credit System Insurance Corporation Board (Board). DATE AND TIME: The meeting of the Board will be held at the offices of the Farm...
Online co-regularized algorithms
Ruijter, T. de; Tsivtsivadze, E.; Heskes, T.
2012-01-01
We propose an online co-regularized learning algorithm for classification and regression tasks. We demonstrate that by sequentially co-regularizing prediction functions on unlabeled data points, our algorithm provides improved performance in comparison to supervised methods on several UCI benchmarks
Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks
Rozdeba, Paul J.
The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.
Inverse scattering problems with multi-frequencies
International Nuclear Information System (INIS)
Bao, Gang; Li, Peijun; Lin, Junshan; Triki, Faouzi
2015-01-01
This paper is concerned with computational approaches and mathematical analysis for solving inverse scattering problems in the frequency domain. The problems arise in a diverse set of scientific areas with significant industrial, medical, and military applications. In addition to nonlinearity, there are two common difficulties associated with the inverse problems: ill-posedness and limited resolution (diffraction limit). Due to the diffraction limit, for a given frequency, only a low spatial frequency part of the desired parameter can be observed from measurements in the far field. The main idea developed here is that if the reconstruction is restricted to only the observable part, then the inversion will become stable. The challenging task is how to design stable numerical methods for solving these inverse scattering problems inspired by the diffraction limit. Recently, novel recursive linearization based algorithms have been presented in an attempt to answer the above question. These methods require multi-frequency scattering data and proceed via a continuation procedure with respect to the frequency from low to high. The objective of this paper is to give a brief review of these methods, their error estimates, and the related mathematical analysis. More attention is paid to the inverse medium and inverse source problems. Numerical experiments are included to illustrate the effectiveness of these methods. (topical review)
An inverse problem in a parabolic equation
Directory of Open Access Journals (Sweden)
Zhilin Li
1998-11-01
Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.
Quasilocal energy, Komar charge and horizon for regular black holes
International Nuclear Information System (INIS)
Balart, Leonardo
2010-01-01
We study the Brown-York quasilocal energy for regular black holes. We also express the identity that relates the difference of the Brown-York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime for static and spherically symmetric black hole solutions in a convenient way which permits us to understand why this identity is not satisfied when we consider nonlinear electrodynamics. However, we give a relation between quantities evaluated at the horizon and at infinity when nonlinear electrodynamics is considered. Similar relations are obtained for more general static and spherically symmetric black hole solutions which include solutions of dilaton gravity theories.
Stochastic Gabor reflectivity and acoustic impedance inversion
Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John
2018-02-01
, obtaining bias could help the method to estimate reliable AI. To justify the effect of random noise on deterministic and stochastic inversion results, a stationary noisy trace with signal-to-noise ratio equal to 2 was used. The results highlight the inability of deterministic inversion in dealing with a noisy data set even using a high number of regularization parameters. Also, despite the low level of signal, stochastic Gabor inversion not only can estimate correctly the wavelet’s properties but also, because of bias from well logs, the inversion result is very close to the real AI. Comparing deterministic and introduced inversion results on a real data set shows that low resolution results, especially in the deeper parts of seismic sections using deterministic inversion, creates significant reliability problems for seismic prospects, but this pitfall is solved completely using stochastic Gabor inversion. The estimated AI using Gabor inversion in the time domain is much better and faster than general Gabor inversion in the frequency domain. This is due to the extra number of windows required to analyze the time-frequency information and also the amount of temporal increment between windows. In contrast, stochastic Gabor inversion can estimate trustable physical properties close to the real characteristics. Applying to a real data set could give an ability to detect the direction of volcanic intrusion and the ability of lithology distribution delineation along the fan. Comparing the inversion results highlights the efficiency of stochastic Gabor inversion to delineate lateral lithology changes because of the improved frequency content and zero phasing of the final inversion volume.
A two-way regularization method for MEG source reconstruction
Tian, Tian Siva; Huang, Jianhua Z.; Shen, Haipeng; Li, Zhimin
2012-01-01
The MEG inverse problem refers to the reconstruction of the neural activity of the brain from magnetoencephalography (MEG) measurements. We propose a two-way regularization (TWR) method to solve the MEG inverse problem under the assumptions that only a small number of locations in space are responsible for the measured signals (focality), and each source time course is smooth in time (smoothness). The focality and smoothness of the reconstructed signals are ensured respectively by imposing a sparsity-inducing penalty and a roughness penalty in the data fitting criterion. A two-stage algorithm is developed for fast computation, where a raw estimate of the source time course is obtained in the first stage and then refined in the second stage by the two-way regularization. The proposed method is shown to be effective on both synthetic and real-world examples. © Institute of Mathematical Statistics, 2012.
A two-way regularization method for MEG source reconstruction
Tian, Tian Siva
2012-09-01
The MEG inverse problem refers to the reconstruction of the neural activity of the brain from magnetoencephalography (MEG) measurements. We propose a two-way regularization (TWR) method to solve the MEG inverse problem under the assumptions that only a small number of locations in space are responsible for the measured signals (focality), and each source time course is smooth in time (smoothness). The focality and smoothness of the reconstructed signals are ensured respectively by imposing a sparsity-inducing penalty and a roughness penalty in the data fitting criterion. A two-stage algorithm is developed for fast computation, where a raw estimate of the source time course is obtained in the first stage and then refined in the second stage by the two-way regularization. The proposed method is shown to be effective on both synthetic and real-world examples. © Institute of Mathematical Statistics, 2012.
3D geophysical inversion for contact surfaces
Lelièvre, Peter; Farquharson, Colin
2014-05-01
Geologists' interpretations about the Earth typically involve distinct rock units with contacts (interfaces) between them. In contrast, standard minimum-structure volumetric inversions (performed on meshes of space-filling cells) recover smooth models inconsistent with such interpretations. There are several approaches through which geophysical inversion can help recover models with the desired characteristics. Some authors have developed iterative strategies in which several volumetric inversions are performed with regularization parameters changing to achieve sharper interfaces at automatically determined locations. Another approach is to redesign the regularization to be consistent with the desired model characteristics, e.g. L1-like norms or compactness measures. A few researchers have taken approaches that limit the recovered values to lie within particular ranges, resulting in sharp discontinuities; these include binary inversion, level set methods and clustering strategies. In most of the approaches mentioned above, the model parameterization considers the physical properties in each of the many space-filling cells within the volume of interest. The exception are level set methods, in which a higher dimensional function is parameterized and the contact surface is determined from the zero-level of that function. However, even level-set methods rely on an underlying volumetric mesh. We are researching a fundamentally different type of inversion that parameterizes the Earth in terms of the contact surfaces between rock units. 3D geological Earth models typically comprise wireframe surfaces of tessellated triangles or other polygonal planar facets. This wireframe representation allows for flexible and efficient generation of complicated geological structures. Therefore, a natural approach for representing a geophysical model in an inversion is to parameterize the wireframe contact surfaces as the coordinates of the nodes (facet vertices). The geological and
Acute puerperal uterine inversion
International Nuclear Information System (INIS)
Hussain, M.; Liaquat, N.; Noorani, K.; Bhutta, S.Z; Jabeen, T.
2004-01-01
Objective: To determine the frequency, causes, clinical presentations, management and maternal mortality associated with acute puerperal inversion of the uterus. Materials and Methods: All the patients who developed acute puerperal inversion of the uterus either in or outside the JPMC were included in the study. Patients of chronic uterine inversion were not included in the present study. Abdominal and vaginal examination was done to confirm and classify inversion into first, second or third degrees. Results: 57036 deliveries and 36 acute uterine inversions occurred during the study period, so the frequency of uterine inversion was 1 in 1584 deliveries. Mismanagement of third stage of labour was responsible for uterine inversion in 75% of patients. Majority of the patients presented with shock, either hypovolemic (69%) or neurogenic (13%) in origin. Manual replacement of the uterus under general anaesthesia with 2% halothane was successfully done in 35 patients (97.5%). Abdominal hysterectomy was done in only one patient. There were three maternal deaths due to inversion. Conclusion: Proper education and training regarding placental delivery, diagnosis and management of uterine inversion must be imparted to the maternity care providers especially to traditional birth attendants and family physicians to prevent this potentially life-threatening condition. (author)
Inverse problem in hydrogeology
Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.
2005-03-01
The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le
"Plug-and-play" edge-preserving regularization
DEFF Research Database (Denmark)
Chen, Donghui; Kilmer, Misha E.; Hansen, Per Christian
2014-01-01
In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated algorithms are complex and require a good knowledge of large...... cosine transform.hence the term "plug-and-play" . We do not attempt to improve on TV reconstructions, but rather provide an easy-to-use approach to computing reconstructions with similar properties....
Regularization and error estimates for nonhomogeneous backward heat problems
Directory of Open Access Journals (Sweden)
Duc Trong Dang
2006-01-01
Full Text Available In this article, we study the inverse time problem for the non-homogeneous heat equation which is a severely ill-posed problem. We regularize this problem using the quasi-reversibility method and then obtain error estimates on the approximate solutions. Solutions are calculated by the contraction principle and shown in numerical experiments. We obtain also rates of convergence to the exact solution.
Continuum-regularized quantum gravity
International Nuclear Information System (INIS)
Chan Huesum; Halpern, M.B.
1987-01-01
The recent continuum regularization of d-dimensional Euclidean gravity is generalized to arbitrary power-law measure and studied in some detail as a representative example of coordinate-invariant regularization. The weak-coupling expansion of the theory illustrates a generic geometrization of regularized Schwinger-Dyson rules, generalizing previous rules in flat space and flat superspace. The rules are applied in a non-trivial explicit check of Einstein invariance at one loop: the cosmological counterterm is computed and its contribution is included in a verification that the graviton mass is zero. (orig.)
Efficient multidimensional regularization for Volterra series estimation
Birpoutsoukis, Georgios; Csurcsia, Péter Zoltán; Schoukens, Johan
2018-05-01
This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. To avoid the excessive memory needs in case of long measurements or large number of estimated parameters, a practical gradient-based estimation method is also provided, leading to the same numerical results as the proposed Volterra estimation method. Moreover, the transient effects in the simulated output are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Combining the proposed methodologies, the nonparametric Volterra models of the cascaded water tanks benchmark are presented in this paper. The results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series with and without transient removal are compared and studied. It is clear that the obtained models capture the system dynamics when tested on a validation dataset, and their performance is comparable with the white-box (physical) models.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
3D CSEM data inversion using Newton and Halley class methods
Amaya, M.; Hansen, K. R.; Morten, J. P.
2016-05-01
For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those
Image processing with a cellular nonlinear network
International Nuclear Information System (INIS)
Morfu, S.
2005-01-01
A cellular nonlinear network (CNN) based on uncoupled nonlinear oscillators is proposed for image processing purposes. It is shown theoretically and numerically that the contrast of an image loaded at the nodes of the CNN is strongly enhanced, even if this one is initially weak. An image inversion can be also obtained without reconfiguration of the network whereas a gray levels extraction can be performed with an additional threshold filtering. Lastly, an electronic implementation of this CNN is presented
Laplacian embedded regression for scalable manifold regularization.
Chen, Lin; Tsang, Ivor W; Xu, Dong
2012-06-01
Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real
Inverse problems basics, theory and applications in geophysics
Richter, Mathias
2016-01-01
The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.
Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations
Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril
2011-01-01
We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the loc...
New regular black hole solutions
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zanchin, Vilson T.
2011-01-01
In the present work we consider general relativity coupled to Maxwell's electromagnetism and charged matter. Under the assumption of spherical symmetry, there is a particular class of solutions that correspond to regular charged black holes whose interior region is de Sitter, the exterior region is Reissner-Nordstroem and there is a charged thin-layer in-between the two. The main physical and geometrical properties of such charged regular black holes are analyzed.
Regular variation on measure chains
Czech Academy of Sciences Publication Activity Database
Řehák, Pavel; Vitovec, J.
2010-01-01
Roč. 72, č. 1 (2010), s. 439-448 ISSN 0362-546X R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : regularly varying function * regularly varying sequence * measure chain * time scale * embedding theorem * representation theorem * second order dynamic equation * asymptotic properties Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://www.sciencedirect.com/science/article/pii/S0362546X09008475
Manifold Regularized Correlation Object Tracking
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2017-01-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped fr...
On geodesics in low regularity
Sämann, Clemens; Steinbauer, Roland
2018-02-01
We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle interrelation with solutions of the geodesic equations. Then we turn to the initial value problem for geodesics for locally Lipschitz continuous metrics and generalize recent results on existence, regularity and uniqueness of solutions in the sense of Filippov.
Inverse logarithmic potential problem
Cherednichenko, V G
1996-01-01
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Inverse Kinematics using Quaternions
DEFF Research Database (Denmark)
Henriksen, Knud; Erleben, Kenny; Engell-Nørregård, Morten
In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection....
Support Minimized Inversion of Acoustic and Elastic Wave Scattering
Safaeinili, Ali
Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging. In many applications, it is common to have a bias toward a solution with minimum (L^2)^2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing "Minimum Support" functional instead of the minimum (L^2)^2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world. We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable. An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time. The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work
Variational regularization of 3D data experiments with Matlab
Montegranario, Hebert
2014-01-01
Variational Regularization of 3D Data provides an introduction to variational methods for data modelling and its application in computer vision. In this book, the authors identify interpolation as an inverse problem that can be solved by Tikhonov regularization. The proposed solutions are generalizations of one-dimensional splines, applicable to n-dimensional data and the central idea is that these splines can be obtained by regularization theory using a trade-off between the fidelity of the data and smoothness properties.As a foundation, the authors present a comprehensive guide to the necessary fundamentals of functional analysis and variational calculus, as well as splines. The implementation and numerical experiments are illustrated using MATLAB®. The book also includes the necessary theoretical background for approximation methods and some details of the computer implementation of the algorithms. A working knowledge of multivariable calculus and basic vector and matrix methods should serve as an adequat...
Kaltenbacher, Barbara; Klassen, Andrej
2018-05-01
In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called the method of quasi solutions) with some versions of the discrepancy principle for choosing the regularization parameter, and Morozov regularization (also called the method of the residuals). After motivating nonequivalence with Tikhonov regularization by means of an example, we prove well-definedness of the Ivanov and the Morozov method, convergence in the sense of regularization, as well as convergence rates under variational source conditions. Finally, we apply these results to some linear and nonlinear parameter identification problems in elliptic boundary value problems.
Particle Swarm Optimization and Uncertainty Assessment in Inverse Problems
Directory of Open Access Journals (Sweden)
José L. G. Pallero
2018-01-01
Full Text Available Most inverse problems in the industry (and particularly in geophysical exploration are highly underdetermined because the number of model parameters too high to achieve accurate data predictions and because the sampling of the data space is scarce and incomplete; it is always affected by different kinds of noise. Additionally, the physics of the forward problem is a simplification of the reality. All these facts result in that the inverse problem solution is not unique; that is, there are different inverse solutions (called equivalent, compatible with the prior information that fits the observed data within similar error bounds. In the case of nonlinear inverse problems, these equivalent models are located in disconnected flat curvilinear valleys of the cost-function topography. The uncertainty analysis consists of obtaining a representation of this complex topography via different sampling methodologies. In this paper, we focus on the use of a particle swarm optimization (PSO algorithm to sample the region of equivalence in nonlinear inverse problems. Although this methodology has a general purpose, we show its application for the uncertainty assessment of the solution of a geophysical problem concerning gravity inversion in sedimentary basins, showing that it is possible to efficiently perform this task in a sampling-while-optimizing mode. Particularly, we explain how to use and analyze the geophysical models sampled by exploratory PSO family members to infer different descriptors of nonlinear uncertainty.
Unwrapped phase inversion with an exponential damping
Choi, Yun Seok
2015-07-28
Full-waveform inversion (FWI) suffers from the phase wrapping (cycle skipping) problem when the frequency of data is not low enough. Unless we obtain a good initial velocity model, the phase wrapping problem in FWI causes a result corresponding to a local minimum, usually far away from the true solution, especially at depth. Thus, we have developed an inversion algorithm based on a space-domain unwrapped phase, and we also used exponential damping to mitigate the nonlinearity associated with the reflections. We construct the 2D phase residual map, which usually contains the wrapping discontinuities, especially if the model is complex and the frequency is high. We then unwrap the phase map and remove these cycle-based jumps. However, if the phase map has several residues, the unwrapping process becomes very complicated. We apply a strong exponential damping to the wavefield to eliminate much of the residues in the phase map, thus making the unwrapping process simple. We finally invert the unwrapped phases using the back-propagation algorithm to calculate the gradient. We progressively reduce the damping factor to obtain a high-resolution image. Numerical examples determined that the unwrapped phase inversion with a strong exponential damping generated convergent long-wavelength updates without low-frequency information. This model can be used as a good starting model for a subsequent inversion with a reduced damping, eventually leading to conventional waveform inversion.
Bounded Perturbation Regularization for Linear Least Squares Estimation
Ballal, Tarig
2017-10-18
This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.
An inverse problem approach to pattern recognition in industry
Directory of Open Access Journals (Sweden)
Ali Sever
2015-01-01
Full Text Available Many works have shown strong connections between learning and regularization techniques for ill-posed inverse problems. A careful analysis shows that a rigorous connection between learning and regularization for inverse problem is not straightforward. In this study, pattern recognition will be viewed as an ill-posed inverse problem and applications of methods from the theory of inverse problems to pattern recognition are studied. A new learning algorithm derived from a well-known regularization model is generated and applied to the task of reconstruction of an inhomogeneous object as pattern recognition. Particularly, it is demonstrated that pattern recognition can be reformulated in terms of inverse problems defined by a Riesz-type kernel. This reformulation can be employed to design a learning algorithm based on a numerical solution of a system of linear equations. Finally, numerical experiments have been carried out with synthetic experimental data considering a reasonable level of noise. Good recoveries have been achieved with this methodology, and the results of these simulations are compatible with the existing methods. The comparison results show that the Regularization-based learning algorithm (RBA obtains a promising performance on the majority of the test problems. In prospects, this method can be used for the creation of automated systems for diagnostics, testing, and control in various fields of scientific and applied research, as well as in industry.
On a new series of integrable nonlinear evolution equations
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.
1980-10-01
Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)
BOOK REVIEW: Inverse Problems. Activities for Undergraduates
Yamamoto, Masahiro
2003-06-01
This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight
Rosas-Carbajal, M.; Linde, N.; Kalscheuer, T.; Vrugt, J.A.
2014-01-01
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space
Incorporating a Spatial Prior into Nonlinear D-Bar EIT Imaging for Complex Admittivities.
Hamilton, Sarah J; Mueller, J L; Alsaker, M
2017-02-01
Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.
Regularization ambiguities in loop quantum gravity
International Nuclear Information System (INIS)
Perez, Alejandro
2006-01-01
One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem--the existence of well-behaved regularization of the constraints--is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the SU(2) unitary representation used in the diffeomorphism covariant 'point-splitting' regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer m and, here, it is referred to as the m ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study 2+1 gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in 2+1 loop quantum gravity. We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in 3+1 dimensions - due to the difficulties associated to the definition of the physical inner product - it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find
International Nuclear Information System (INIS)
Burkhard, N.R.
1979-01-01
The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables
Metric regularity and subdifferential calculus
International Nuclear Information System (INIS)
Ioffe, A D
2000-01-01
The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces
Manifold Regularized Correlation Object Tracking.
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2018-05-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions. Thus, the final classifier in our method is trained with positive, negative, and unlabeled base samples, which is a semisupervised learning framework. A block optimization strategy is further introduced to learn a manifold regularization-based correlation filter for efficient online tracking. Experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state-of-the-art tracking approaches.
Nonlinear Fourier transform for dual-polarization optical communication system
DEFF Research Database (Denmark)
Gaiarin, Simone
communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...
Dimensional regularization in configuration space
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1995-09-01
Dimensional regularization is introduced in configuration space by Fourier transforming in D-dimensions the perturbative momentum space Green functions. For this transformation, Bochner theorem is used, no extra parameters, such as those of Feynman or Bogoliubov-Shirkov are needed for convolutions. The regularized causal functions in x-space have ν-dependent moderated singularities at the origin. They can be multiplied together and Fourier transformed (Bochner) without divergence problems. The usual ultraviolet divergences appear as poles of the resultant functions of ν. Several example are discussed. (author). 9 refs
Regular algebra and finite machines
Conway, John Horton
2012-01-01
World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians.His topics cover Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Additional subjects include event classes and operator classes, some regulator algebras, context-free languages, communicative regular alg
Matrix regularization of 4-manifolds
Trzetrzelewski, M.
2012-01-01
We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...
National Research Council Canada - National Science Library
Haji-saeed, Bahareh; Khoury, Jed; Woods, Charles L; Kierstead, John
2008-01-01
...) for facial recognition is proposed. In order to avoid spectral overlap and nonlinear crosstalk, superposition of rotationally variant sets of inverse filter Fourier-transformed Radon-processed templates is used to generate the SDF...
Full-waveform inversion with reflected waves for 2D VTI media
Pattnaik, Sonali; Tsvankin, Ilya; Wang, Hui; Alkhalifah, Tariq
2016-01-01
Full-waveform inversion in anisotropic media using reflected waves suffers from the strong non-linearity of the objective function and trade-offs between model parameters. Estimating long-wavelength model components by fixing parameter perturbations
International Nuclear Information System (INIS)
Rosenwald, J.-C.
2008-01-01
The lecture addressed the following topics: Optimizing radiotherapy dose distribution; IMRT contributes to optimization of energy deposition; Inverse vs direct planning; Main steps of IMRT; Background of inverse planning; General principle of inverse planning; The 3 main components of IMRT inverse planning; The simplest cost function (deviation from prescribed dose); The driving variable : the beamlet intensity; Minimizing a 'cost function' (or 'objective function') - the walker (or skier) analogy; Application to IMRT optimization (the gradient method); The gradient method - discussion; The simulated annealing method; The optimization criteria - discussion; Hard and soft constraints; Dose volume constraints; Typical user interface for definition of optimization criteria; Biological constraints (Equivalent Uniform Dose); The result of the optimization process; Semi-automatic solutions for IMRT; Generalisation of the optimization problem; Driving and driven variables used in RT optimization; Towards multi-criteria optimization; and Conclusions for the optimization phase. (P.A.)
Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco
2015-04-01
The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Clason, Christian
2012-01-01
This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
Electron dose map inversion based on several algorithms
International Nuclear Information System (INIS)
Li Gui; Zheng Huaqing; Wu Yican; Fds Team
2010-01-01
The reconstruction to the electron dose map in radiation therapy was investigated by constructing the inversion model of electron dose map with different algorithms. The inversion model of electron dose map based on nonlinear programming was used, and this model was applied the penetration dose map to invert the total space one. The realization of this inversion model was by several inversion algorithms. The test results with seven samples show that except the NMinimize algorithm, which worked for just one sample, with great error,though,all the inversion algorithms could be realized to our inversion model rapidly and accurately. The Levenberg-Marquardt algorithm, having the greatest accuracy and speed, could be considered as the first choice in electron dose map inversion.Further tests show that more error would be created when the data close to the electron range was used (tail error). The tail error might be caused by the approximation of mean energy spectra, and this should be considered to improve the method. The time-saving and accurate algorithms could be used to achieve real-time dose map inversion. By selecting the best inversion algorithm, the clinical need in real-time dose verification can be satisfied. (authors)
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.; Pimentel, Edgard
2015-01-01
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Energy Technology Data Exchange (ETDEWEB)
Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)
2014-10-15
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
International Nuclear Information System (INIS)
Agaltsov, A. D.; Novikov, R. G.
2014-01-01
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given
Regularization of Nonmonotone Variational Inequalities
International Nuclear Information System (INIS)
Konnov, Igor V.; Ali, M.S.S.; Mazurkevich, E.O.
2006-01-01
In this paper we extend the Tikhonov-Browder regularization scheme from monotone to rather a general class of nonmonotone multivalued variational inequalities. We show that their convergence conditions hold for some classes of perfectly and nonperfectly competitive economic equilibrium problems
Lattice regularized chiral perturbation theory
International Nuclear Information System (INIS)
Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.
2004-01-01
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term
2011-01-20
... Meeting SUMMARY: Notice is hereby given of the regular meeting of the Farm Credit System Insurance Corporation Board (Board). Date and Time: The meeting of the Board will be held at the offices of the Farm... meeting of the Board will be open to the [[Page 3630
Forcing absoluteness and regularity properties
Ikegami, D.
2010-01-01
For a large natural class of forcing notions, we prove general equivalence theorems between forcing absoluteness statements, regularity properties, and transcendence properties over L and the core model K. We use our results to answer open questions from set theory of the reals.
Globals of Completely Regular Monoids
Institute of Scientific and Technical Information of China (English)
Wu Qian-qian; Gan Ai-ping; Du Xian-kun
2015-01-01
An element of a semigroup S is called irreducible if it cannot be expressed as a product of two elements in S both distinct from itself. In this paper we show that the class C of all completely regular monoids with irreducible identity elements satisfies the strong isomorphism property and so it is globally determined.
Fluid queues and regular variation
Boxma, O.J.
1996-01-01
This paper considers a fluid queueing system, fed by N independent sources that alternate between silence and activity periods. We assume that the distribution of the activity periods of one or more sources is a regularly varying function of index ¿. We show that its fat tail gives rise to an even
Fluid queues and regular variation
O.J. Boxma (Onno)
1996-01-01
textabstractThis paper considers a fluid queueing system, fed by $N$ independent sources that alternate between silence and activity periods. We assume that the distribution of the activity periods of one or more sources is a regularly varying function of index $zeta$. We show that its fat tail
Empirical laws, regularity and necessity
Koningsveld, H.
1973-01-01
In this book I have tried to develop an analysis of the concept of an empirical law, an analysis that differs in many ways from the alternative analyse's found in contemporary literature dealing with the subject.
1 am referring especially to two well-known views, viz. the regularity and
Interval matrices: Regularity generates singularity
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří; Shary, S.P.
2018-01-01
Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016
Regularization in Matrix Relevance Learning
Schneider, Petra; Bunte, Kerstin; Stiekema, Han; Hammer, Barbara; Villmann, Thomas; Biehl, Michael
A In this paper, we present a regularization technique to extend recently proposed matrix learning schemes in learning vector quantization (LVQ). These learning algorithms extend the concept of adaptive distance measures in LVQ to the use of relevance matrices. In general, metric learning can
On the MSE Performance and Optimization of Regularized Problems
Alrashdi, Ayed
2016-11-01
The amount of data that has been measured, transmitted/received, and stored in the recent years has dramatically increased. So, today, we are in the world of big data. Fortunately, in many applications, we can take advantages of possible structures and patterns in the data to overcome the curse of dimensionality. The most well known structures include sparsity, low-rankness, block sparsity. This includes a wide range of applications such as machine learning, medical imaging, signal processing, social networks and computer vision. This also led to a specific interest in recovering signals from noisy compressed measurements (Compressed Sensing (CS) problem). Such problems are generally ill-posed unless the signal is structured. The structure can be captured by a regularizer function. This gives rise to a potential interest in regularized inverse problems, where the process of reconstructing the structured signal can be modeled as a regularized problem. This thesis particularly focuses on finding the optimal regularization parameter for such problems, such as ridge regression, LASSO, square-root LASSO and low-rank Generalized LASSO. Our goal is to optimally tune the regularizer to minimize the mean-squared error (MSE) of the solution when the noise variance or structure parameters are unknown. The analysis is based on the framework of the Convex Gaussian Min-max Theorem (CGMT) that has been used recently to precisely predict performance errors.
Solving probabilistic inverse problems rapidly with prior samples
Käufl, Paul; Valentine, Andrew P.; de Wit, Ralph W.; Trampert, Jeannot
2016-01-01
Owing to the increasing availability of computational resources, in recent years the probabilistic solution of non-linear, geophysical inverse problems by means of sampling methods has become increasingly feasible. Nevertheless, we still face situations in which a Monte Carlo approach is not
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...
Morozov-type discrepancy principle for nonlinear ill-posed problems ...
Indian Academy of Sciences (India)
For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement of the Lipschitz ...
Morozov-type discrepancy principle for nonlinear ill-posed problems ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement ...
Regular and conformal regular cores for static and rotating solutions
Energy Technology Data Exchange (ETDEWEB)
Azreg-Aïnou, Mustapha
2014-03-07
Using a new metric for generating rotating solutions, we derive in a general fashion the solution of an imperfect fluid and that of its conformal homolog. We discuss the conditions that the stress–energy tensors and invariant scalars be regular. On classical physical grounds, it is stressed that conformal fluids used as cores for static or rotating solutions are exempt from any malicious behavior in that they are finite and defined everywhere.
Regular and conformal regular cores for static and rotating solutions
International Nuclear Information System (INIS)
Azreg-Aïnou, Mustapha
2014-01-01
Using a new metric for generating rotating solutions, we derive in a general fashion the solution of an imperfect fluid and that of its conformal homolog. We discuss the conditions that the stress–energy tensors and invariant scalars be regular. On classical physical grounds, it is stressed that conformal fluids used as cores for static or rotating solutions are exempt from any malicious behavior in that they are finite and defined everywhere.
Trimming and procrastination as inversion techniques
Backus, George E.
1996-12-01
By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.
Analog fault diagnosis by inverse problem technique
Ahmed, Rania F.
2011-12-01
A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.
The neural substrates of impaired finger tapping regularity after stroke.
Calautti, Cinzia; Jones, P Simon; Guincestre, Jean-Yves; Naccarato, Marcello; Sharma, Nikhil; Day, Diana J; Carpenter, T Adrian; Warburton, Elizabeth A; Baron, Jean-Claude
2010-03-01
Not only finger tapping speed, but also tapping regularity can be impaired after stroke, contributing to reduced dexterity. The neural substrates of impaired tapping regularity after stroke are unknown. Previous work suggests damage to the dorsal premotor cortex (PMd) and prefrontal cortex (PFCx) affects externally-cued hand movement. We tested the hypothesis that these two areas are involved in impaired post-stroke tapping regularity. In 19 right-handed patients (15 men/4 women; age 45-80 years; purely subcortical in 16) partially to fully recovered from hemiparetic stroke, tri-axial accelerometric quantitative assessment of tapping regularity and BOLD fMRI were obtained during fixed-rate auditory-cued index-thumb tapping, in a single session 10-230 days after stroke. A strong random-effect correlation between tapping regularity index and fMRI signal was found in contralesional PMd such that the worse the regularity the stronger the activation. A significant correlation in the opposite direction was also present within contralesional PFCx. Both correlations were maintained if maximal index tapping speed, degree of paresis and time since stroke were added as potential confounds. Thus, the contralesional PMd and PFCx appear to be involved in the impaired ability of stroke patients to fingertap in pace with external cues. The findings for PMd are consistent with repetitive TMS investigations in stroke suggesting a role for this area in affected-hand movement timing. The inverse relationship with tapping regularity observed for the PFCx and the PMd suggests these two anatomically-connected areas negatively co-operate. These findings have implications for understanding the disruption and reorganization of the motor systems after stroke. Copyright (c) 2009 Elsevier Inc. All rights reserved.
Creation and annihilation of solitons in the string nonlinear equation
International Nuclear Information System (INIS)
Aguero G, M.A.; Espinosa G, A.A.; Martinez O, J.
1997-01-01
Starting from the cubic-quintic Schroedinger equation it is obtained the nonlinear string equation. This system supports regular and singular solitons. It is shown that two singular solitons could be generated after the interaction of two regular solitons and viceversa. (Author)
Nonlinear anisotropic parabolic equations in Lm
Directory of Open Access Journals (Sweden)
Fares Mokhtari
2014-01-01
Full Text Available In this paper, we give a result of regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with lower-order term when the right-hand side is an Lm function, with m being ”small”. This work generalizes some results given in [2] and [3].
Modelling and inversion of local magnetic anomalies
International Nuclear Information System (INIS)
Quesnel, Y; Langlais, B; Sotin, C; Galdéano, A
2008-01-01
We present a method—named as MILMA for modelling and inversion of local magnetic anomalies—that combines forward and inverse modelling of aeromagnetic data to characterize both magnetization properties and location of unconstrained local sources. Parameters of simple-shape magnetized bodies (cylinder, prism or sphere) are first adjusted by trial and error to predict the signal. Their parameters provide a priori information for inversion of the measurements. Here, a generalized nonlinear approach with a least-squares criterion is adopted to seek the best parameters of the sphere (dipole). This inversion step allows the model to be more objectively adjusted to fit the magnetic signal. The validity of the MILMA method is demonstrated through synthetic and real cases using aeromagnetic measurements. Tests with synthetic data reveal accurate results in terms of depth source, whatever be the number of sources. The MILMA method is then used with real measurements to constrain the properties of the magnetized units of the Champtoceaux complex (France). The resulting parameters correlate with the crustal structure and properties revealed by other geological and geophysical surveys in the same area. The MILMA method can therefore be used to investigate the properties of poorly constrained lithospheric magnetized sources
Inverse boundary element calculations based on structural modes
DEFF Research Database (Denmark)
Juhl, Peter Møller
2007-01-01
The inverse problem of calculating the flexural velocity of a radiating structure of a general shape from measurements in the field is often solved by combining a Boundary Element Method with the Singular Value Decomposition and a regularization technique. In their standard form these methods sol...
The inverse problem for Schwinger pair production
Directory of Open Access Journals (Sweden)
F. Hebenstreit
2016-02-01
Full Text Available The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.
Use of regularization method in the determination of ring parameters and orbit correction
International Nuclear Information System (INIS)
Tang, Y.N.; Krinsky, S.
1993-01-01
We discuss applying the regularization method of Tikhonov to the solution of inverse problems arising in accelerator operations. This approach has been successfully used for orbit correction on the NSLS storage rings, and is presently being applied to the determination of betatron functions and phases from the measured response matrix. The inverse problem of differential equation often leads to a set of integral equations of the first kind which are ill-conditioned. The regularization method is used to combat the ill-posedness
The Volterra's integral equation theory for accelerator single-freedom nonlinear components
International Nuclear Information System (INIS)
Wang Sheng; Xie Xi
1996-01-01
The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed
Solving inversion problems with neural networks
Kamgar-Parsi, Behzad; Gualtieri, J. A.
1990-01-01
A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.
Variational structure of inverse problems in wave propagation and vibration
Energy Technology Data Exchange (ETDEWEB)
Berryman, J.G.
1995-03-01
Practical algorithms for solving realistic inverse problems may often be viewed as problems in nonlinear programming with the data serving as constraints. Such problems are most easily analyzed when it is possible to segment the solution space into regions that are feasible (satisfying all the known constraints) and infeasible (violating some of the constraints). Then, if the feasible set is convex or at least compact, the solution to the problem will normally lie on the boundary of the feasible set. A nonlinear program may seek the solution by systematically exploring the boundary while satisfying progressively more constraints. Examples of inverse problems in wave propagation (traveltime tomography) and vibration (modal analysis) will be presented to illustrate how the variational structure of these problems may be used to create nonlinear programs using implicit variational constraints.
Facies Constrained Elastic Full Waveform Inversion
Zhang, Z.
2017-05-26
Current efforts to utilize full waveform inversion (FWI) as a tool beyond acoustic imaging applications, for example for reservoir analysis, face inherent limitations on resolution and also on the potential trade-off between elastic model parameters. Adding rock physics constraints does help to mitigate these issues. However, current approaches to add such constraints are based on averaged type rock physics regularization terms. Since the true earth model consists of different facies, averaging over those facies naturally leads to smoothed models. To overcome this, we propose a novel way to utilize facies based constraints in elastic FWI. A so-called confidence map is calculated and updated at each iteration of the inversion using both the inverted models and the prior information. The numerical example shows that the proposed method can reduce the cross-talks and also can improve the resolution of inverted elastic properties.
Facies Constrained Elastic Full Waveform Inversion
Zhang, Z.; Zabihi Naeini, E.; Alkhalifah, Tariq Ali
2017-01-01
Current efforts to utilize full waveform inversion (FWI) as a tool beyond acoustic imaging applications, for example for reservoir analysis, face inherent limitations on resolution and also on the potential trade-off between elastic model parameters. Adding rock physics constraints does help to mitigate these issues. However, current approaches to add such constraints are based on averaged type rock physics regularization terms. Since the true earth model consists of different facies, averaging over those facies naturally leads to smoothed models. To overcome this, we propose a novel way to utilize facies based constraints in elastic FWI. A so-called confidence map is calculated and updated at each iteration of the inversion using both the inverted models and the prior information. The numerical example shows that the proposed method can reduce the cross-talks and also can improve the resolution of inverted elastic properties.
Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
Directory of Open Access Journals (Sweden)
Chunlong Sun
2017-01-01
Full Text Available The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data give good approximations to the exact order demonstrating the efficiency of the inversion algorithm and numerical stability of the inversion problem.
Physical model of dimensional regularization
Energy Technology Data Exchange (ETDEWEB)
Schonfeld, Jonathan F.
2016-12-15
We explicitly construct fractals of dimension 4-ε on which dimensional regularization approximates scalar-field-only quantum-field theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and we argue that there probably is no Lorentz-invariant fractal of dimension greater than 2. We derive dimensional regularization's power-law screening first for fractals obtained by removing voids from 3-dimensional Euclidean space. The derivation applies techniques from elementary dielectric theory. Surprisingly, fractal geometry by itself does not guarantee the appropriate power-law behavior; boundary conditions at fractal voids also play an important role. We then extend the derivation to 4-dimensional Minkowski space. We comment on generalization to non-scalar fields, and speculate about implications for quantum gravity. (orig.)
Maximum mutual information regularized classification
Wang, Jim Jing-Yan
2014-09-07
In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reducing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradient descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization.
Maximum mutual information regularized classification
Wang, Jim Jing-Yan; Wang, Yi; Zhao, Shiguang; Gao, Xin
2014-01-01
In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reducing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradient descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization.
Regularized strings with extrinsic curvature
International Nuclear Information System (INIS)
Ambjoern, J.; Durhuus, B.
1987-07-01
We analyze models of discretized string theories, where the path integral over world sheet variables is regularized by summing over triangulated surfaces. The inclusion of curvature in the action is a necessity for the scaling of the string tension. We discuss the physical properties of models with extrinsic curvature terms in the action and show that the string tension vanishes at the critical point where the bare extrinsic curvature coupling tends to infinity. Similar results are derived for models with intrinsic curvature. (orig.)
Circuit complexity of regular languages
Czech Academy of Sciences Publication Activity Database
Koucký, Michal
2009-01-01
Roč. 45, č. 4 (2009), s. 865-879 ISSN 1432-4350 R&D Projects: GA ČR GP201/07/P276; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : regular languages * circuit complexity * upper and lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.726, year: 2009
Inverse scale space decomposition
DEFF Research Database (Denmark)
Schmidt, Marie Foged; Benning, Martin; Schönlieb, Carola-Bibiane
2018-01-01
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and even and positively one-homogeneous regularisation functionals, can decompose data represented...... by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums...... of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range...
The Lorentz integral transform and its inversion
International Nuclear Information System (INIS)
Barnea, N.; Efros, V.D.; Leidemann, W.; Orlandini, G.
2010-01-01
The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due to a historical misconception. In this connection standard regularization procedures for the solution of the integral transform problem are presented. In particular a recent one is considered in detail and critical comments on it are provided. In addition a general remark concerning the concept of the Lorentz integral transform as a method with a controlled resolution is made. (author)
Inverse Ising Inference Using All the Data
Aurell, Erik; Ekeberg, Magnus
2012-03-01
We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l1 regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.
Generalized inverses theory and computations
Wang, Guorong; Qiao, Sanzheng
2018-01-01
This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.
Some results on inverse scattering
International Nuclear Information System (INIS)
Ramm, A.G.
2008-01-01
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: (1) Property C and applications, (2) Stable inversion of fixed-energy 3D scattering data and its error estimate, (3) Inverse scattering with 'incomplete' data, (4) Inverse scattering for inhomogeneous Schroedinger equation, (5) Krein's inverse scattering method, (6) Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion methods, (7) The Newton-Sabatier and Cox-Thompson procedures are not inversion methods, (8) Resonances: existence, location, perturbation theory, (9) Born inversion as an ill-posed problem, (10) Inverse obstacle scattering with fixed-frequency data, (11) Inverse scattering with data at a fixed energy and a fixed incident direction, (12) Creating materials with a desired refraction coefficient and wave-focusing properties. (author)
Application of the kernel method to the inverse geosounding problem.
Hidalgo, Hugo; Sosa León, Sonia; Gómez-Treviño, Enrique
2003-01-01
Determining the layered structure of the earth demands the solution of a variety of inverse problems; in the case of electromagnetic soundings at low induction numbers, the problem is linear, for the measurements may be represented as a linear functional of the electrical conductivity distribution. In this paper, an application of the support vector (SV) regression technique to the inversion of electromagnetic data is presented. We take advantage of the regularizing properties of the SV learning algorithm and use it as a modeling technique with synthetic and field data. The SV method presents better recovery of synthetic models than Tikhonov's regularization. As the SV formulation is solved in the space of the data, which has a small dimension in this application, a smaller problem than that considered with Tikhonov's regularization is produced. For field data, the SV formulation develops models similar to those obtained via linear programming techniques, but with the added characteristic of robustness.
Inverse problem in radionuclide transport
International Nuclear Information System (INIS)
Yu, C.
1988-01-01
The disposal of radioactive waste must comply with the performance objectives set forth in 10 CFR 61 for low-level waste (LLW) and 10 CFR 60 for high-level waste (HLW). To determine probable compliance, the proposed disposal system can be modeled to predict its performance. One of the difficulties encountered in such a study is modeling the migration of radionuclides through a complex geologic medium for the long term. Although many radionuclide transport models exist in the literature, the accuracy of the model prediction is highly dependent on the model parameters used. The problem of using known parameters in a radionuclide transport model to predict radionuclide concentrations is a direct problem (DP); whereas the reverse of DP, i.e., the parameter identification problem of determining model parameters from known radionuclide concentrations, is called the inverse problem (IP). In this study, a procedure to solve IP is tested, using the regression technique. Several nonlinear regression programs are examined, and the best one is recommended. 13 refs., 1 tab
Inverse Problems and Uncertainty Quantification
Litvinenko, Alexander
2014-01-06
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Inverse Problems and Uncertainty Quantification
Litvinenko, Alexander; Matthies, Hermann G.
2014-01-01
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Inverse problems and uncertainty quantification
Litvinenko, Alexander
2013-12-18
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)— the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Apiñaniz, Estibaliz; Mendioroz, Arantza; Salazar, Agustín; Celorrio, Ricardo
2010-09-01
We analyze the ability of the Tikhonov regularization to retrieve different shapes of in-depth thermal conductivity profiles, usually encountered in hardened materials, from surface temperature data. Exponential, oscillating, and sigmoidal profiles are studied. By performing theoretical experiments with added white noises, the influence of the order of the Tikhonov functional and of the parameters that need to be tuned to carry out the inversion are investigated. The analysis shows that the Tikhonov regularization is very well suited to reconstruct smooth profiles but fails when the conductivity exhibits steep slopes. We check a natural alternative regularization, the total variation functional, which gives much better results for sigmoidal profiles. Accordingly, a strategy to deal with real data is proposed in which we introduce this total variation regularization. This regularization is applied to the inversion of real data corresponding to a case hardened AISI1018 steel plate, giving much better anticorrelation of the retrieved conductivity with microindentation test data than the Tikhonov regularization. The results suggest that this is a promising way to improve the reliability of local inversion methods.
Manifold Based Low-rank Regularization for Image Restoration and Semi-supervised Learning
Lai, Rongjie; Li, Jia
2017-01-01
Low-rank structures play important role in recent advances of many problems in image science and data science. As a natural extension of low-rank structures for data with nonlinear structures, the concept of the low-dimensional manifold structure has been considered in many data processing problems. Inspired by this concept, we consider a manifold based low-rank regularization as a linear approximation of manifold dimension. This regularization is less restricted than the global low-rank regu...
Fu, Y. B.; Ogden, R. W.
2001-05-01
This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
Sun, Chunlong; Li, Gongsheng; Jia, Xianzheng
2017-01-01
The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short) from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data...
Inversion assuming weak scattering
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus
2013-01-01
due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...
Less is more: regularization perspectives on large scale machine learning
CERN. Geneva
2017-01-01
Deep learning based techniques provide a possible solution at the expanse of theoretical guidance and, especially, of computational requirements. It is then a key challenge for large scale machine learning to devise approaches guaranteed to be accurate and yet computationally efficient. In this talk, we will consider a regularization perspectives on machine learning appealing to classical ideas in linear algebra and inverse problems to scale-up dramatically nonparametric methods such as kernel methods, often dismissed because of prohibitive costs. Our analysis derives optimal theoretical guarantees while providing experimental results at par or out-performing state of the art approaches.
Bayesian seismic AVO inversion
Energy Technology Data Exchange (ETDEWEB)
Buland, Arild
2002-07-01
A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S
SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS
Desmal, Abdulla
2015-07-29
A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Parameter choice in Banach space regularization under variational inequalities
International Nuclear Information System (INIS)
Hofmann, Bernd; Mathé, Peter
2012-01-01
The authors study parameter choice strategies for the Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depends on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices under consideration include an a priori choice, the discrepancy principle as well as the Lepskii principle. For the convenience of the reader, the authors review in an appendix a few instances where the validity of a variational inequality can be established. (paper)
Poisson image reconstruction with Hessian Schatten-norm regularization.
Lefkimmiatis, Stamatios; Unser, Michael
2013-11-01
Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupted by Poisson noise. In this paper, we propose an efficient framework for Poisson image reconstruction, under a regularization approach, which depends on matrix-valued regularization operators. In particular, the employed regularizers involve the Hessian as the regularization operator and Schatten matrix norms as the potential functions. For the solution of the problem, we propose two optimization algorithms that are specifically tailored to the Poisson nature of the noise. These algorithms are based on an augmented-Lagrangian formulation of the problem and correspond to two variants of the alternating direction method of multipliers. Further, we derive a link that relates the proximal map of an l(p) norm with the proximal map of a Schatten matrix norm of order p. This link plays a key role in the development of one of the proposed algorithms. Finally, we provide experimental results on natural and biological images for the task of Poisson image deblurring and demonstrate the practical relevance and effectiveness of the proposed framework.
Optimal Tikhonov Regularization in Finite-Frequency Tomography
Fang, Y.; Yao, Z.; Zhou, Y.
2017-12-01
The last decade has witnessed a progressive transition in seismic tomography from ray theory to finite-frequency theory which overcomes the resolution limit of the high-frequency approximation in ray theory. In addition to approximations in wave propagation physics, a main difference between ray-theoretical tomography and finite-frequency tomography is the sparseness of the associated sensitivity matrix. It is well known that seismic tomographic problems are ill-posed and regularizations such as damping and smoothing are often applied to analyze the tradeoff between data misfit and model uncertainty. The regularizations depend on the structure of the matrix as well as noise level of the data. Cross-validation has been used to constrain data uncertainties in body-wave finite-frequency inversions when measurements at multiple frequencies are available to invert for a common structure. In this study, we explore an optimal Tikhonov regularization in surface-wave phase-velocity tomography based on minimization of an empirical Bayes risk function using theoretical training datasets. We exploit the structure of the sensitivity matrix in the framework of singular value decomposition (SVD) which also allows for the calculation of complete resolution matrix. We compare the optimal Tikhonov regularization in finite-frequency tomography with traditional tradeo-off analysis using surface wave dispersion measurements from global as well as regional studies.
Regularized Statistical Analysis of Anatomy
DEFF Research Database (Denmark)
Sjöstrand, Karl
2007-01-01
This thesis presents the application and development of regularized methods for the statistical analysis of anatomical structures. Focus is on structure-function relationships in the human brain, such as the connection between early onset of Alzheimer’s disease and shape changes of the corpus...... and mind. Statistics represents a quintessential part of such investigations as they are preluded by a clinical hypothesis that must be verified based on observed data. The massive amounts of image data produced in each examination pose an important and interesting statistical challenge...... efficient algorithms which make the analysis of large data sets feasible, and gives examples of applications....
Academic Training Lecture - Regular Programme
PH Department
2011-01-01
Regular Lecture Programme 9 May 2011 ACT Lectures on Detectors - Inner Tracking Detectors by Pippa Wells (CERN) 10 May 2011 ACT Lectures on Detectors - Calorimeters (2/5) by Philippe Bloch (CERN) 11 May 2011 ACT Lectures on Detectors - Muon systems (3/5) by Kerstin Hoepfner (RWTH Aachen) 12 May 2011 ACT Lectures on Detectors - Particle Identification and Forward Detectors by Peter Krizan (University of Ljubljana and J. Stefan Institute, Ljubljana, Slovenia) 13 May 2011 ACT Lectures on Detectors - Trigger and Data Acquisition (5/5) by Dr. Brian Petersen (CERN) from 11:00 to 12:00 at CERN ( Bldg. 222-R-001 - Filtration Plant )
Bardeen regular black hole with an electric source
Rodrigues, Manuel E.; Silva, Marcos V. de S.
2018-06-01
If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work, we show that the Bardeen model may also be interpreted as a solution of Einstein equations in the presence of an electric source, whose electric field does not behave as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions.
Traveling waves of the regularized short pulse equation
International Nuclear Information System (INIS)
Shen, Y; Horikis, T P; Kevrekidis, P G; Frantzeskakis, D J
2014-01-01
The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by a finite sum of hyperbolic secants powers. The dependence of the soliton's parameters (height, width, etc) to the parameters of the equation is also investigated. Second, by developing a multiple scale reduction of the RSPE to the nonlinear Schrödinger equation, we are able to construct (both standing and traveling) envelope wave breather type solutions of the former, based on the solitary wave structures of the latter. Both the regular and the breathing traveling wave solutions identified are found to be robust and should thus be amenable to observations in the form of few optical cycle pulses. (paper)
Approximate 2D inversion of airborne TEM data
DEFF Research Database (Denmark)
Christensen, N.B.; Wolfgram, Peter
2006-01-01
We propose an approximate two-dimensional inversion procedure for transient electromagnetic data. The method is a two-stage procedure, where data are first inverted with 1D multi-layer models. The 1D model section is then considered as data for the next inversion stage that produces the 2D model...... section. For moving platform data there is translational invariance and the second part of the inversion becomes a deconvolution. The convolution kernels are computed by perturbing one model element in an otherwise homogeneous 2D section and calculating full nonlinear responses. These responses...... are then inverted with 1D models to produce a 1D model section. This section is the convolution kernel for the deconvolution. Within its limitations, the approximate 2D inversion performs well. Theoretical modeling shows that it delivers model sections that are a definite improvement over 1D model sections...
Reducing errors in the GRACE gravity solutions using regularization
Save, Himanshu; Bettadpur, Srinivas; Tapley, Byron D.
2012-09-01
The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth's monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003-Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4
Thermodynamic Product Relations for Generalized Regular Black Hole
International Nuclear Information System (INIS)
Pradhan, Parthapratim
2016-01-01
We derive thermodynamic product relations for four-parametric regular black hole (BH) solutions of the Einstein equations coupled with a nonlinear electrodynamics source. The four parameters can be described by the mass (m), charge (q), dipole moment (α), and quadrupole moment (β), respectively. We study its complete thermodynamics. We compute different thermodynamic products, that is, area product, BH temperature product, specific heat product, and Komar energy product, respectively. Furthermore, we show some complicated function of horizon areas that is indeed mass-independent and could turn out to be universal.
Multi-task feature learning by using trace norm regularization
Directory of Open Access Journals (Sweden)
Jiangmei Zhang
2017-11-01
Full Text Available Multi-task learning can extract the correlation of multiple related machine learning problems to improve performance. This paper considers applying the multi-task learning method to learn a single task. We propose a new learning approach, which employs the mixture of expert model to divide a learning task into several related sub-tasks, and then uses the trace norm regularization to extract common feature representation of these sub-tasks. A nonlinear extension of this approach by using kernel is also provided. Experiments conducted on both simulated and real data sets demonstrate the advantage of the proposed approach.
Analytic semigroups and optimal regularity in parabolic problems
Lunardi, Alessandra
2012-01-01
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in p
Voxel inversion of airborne electromagnetic data for improved model integration
Fiandaca, Gianluca; Auken, Esben; Kirkegaard, Casper; Vest Christiansen, Anders
2014-05-01
Inversion of electromagnetic data has migrated from single site interpretations to inversions including entire surveys using spatial constraints to obtain geologically reasonable results. Though, the model space is usually linked to the actual observation points. For airborne electromagnetic (AEM) surveys the spatial discretization of the model space reflects the flight lines. On the contrary, geological and groundwater models most often refer to a regular voxel grid, not correlated to the geophysical model space, and the geophysical information has to be relocated for integration in (hydro)geological models. We have developed a new geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which then allows for informing directly geological/hydrogeological models. The new voxel model space defines the soil properties (like resistivity) on a set of nodes, and the distribution of the soil properties is computed everywhere by means of an interpolation function (e.g. inverse distance or kriging). Given this definition of the voxel model space, the 1D forward responses of the AEM data are computed as follows: 1) a 1D model subdivision, in terms of model thicknesses, is defined for each 1D data set, creating "virtual" layers. 2) the "virtual" 1D models at the sounding positions are finalized by interpolating the soil properties (the resistivity) in the center of the "virtual" layers. 3) the forward response is computed in 1D for each "virtual" model. We tested the new inversion scheme on an AEM survey carried out with the SkyTEM system close to Odder, in Denmark. The survey comprises 106054 dual mode AEM soundings, and covers an area of approximately 13 km X 16 km. The voxel inversion was carried out on a structured grid of 260 X 325 X 29 xyz nodes (50 m xy spacing), for a total of 2450500 inversion parameters. A classical spatially constrained inversion (SCI) was carried out on the same data set, using 106054
Wave-equation reflection traveltime inversion
Zhang, Sanzong
2011-01-01
The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.
Regularized Label Relaxation Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung; Fang, Bingwu
2018-04-01
Linear regression (LR) and some of its variants have been widely used for classification problems. Most of these methods assume that during the learning phase, the training samples can be exactly transformed into a strict binary label matrix, which has too little freedom to fit the labels adequately. To address this problem, in this paper, we propose a novel regularized label relaxation LR method, which has the following notable characteristics. First, the proposed method relaxes the strict binary label matrix into a slack variable matrix by introducing a nonnegative label relaxation matrix into LR, which provides more freedom to fit the labels and simultaneously enlarges the margins between different classes as much as possible. Second, the proposed method constructs the class compactness graph based on manifold learning and uses it as the regularization item to avoid the problem of overfitting. The class compactness graph is used to ensure that the samples sharing the same labels can be kept close after they are transformed. Two different algorithms, which are, respectively, based on -norm and -norm loss functions are devised. These two algorithms have compact closed-form solutions in each iteration so that they are easily implemented. Extensive experiments show that these two algorithms outperform the state-of-the-art algorithms in terms of the classification accuracy and running time.
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
Nonlinear optical studies of organic monolayers
International Nuclear Information System (INIS)
Shen, Y.R.
1988-02-01
Second-order nonlinear optical effects are forbidden in a medium with inversion symmetry, but are necessarily allowed at a surface where the inversion summary is broken. They are often sufficiently strong so that a submonolayer perturbation of the surface can be readily detected. They can therefore be used as effective tools to study monolayers adsorbed at various interfaces. We discuss here a number of recent experiments in which optical second harmonic generation (SHG) and sum-frequency generation (SFG) are employed to probe and characterize organic monolayers. 15 refs., 5 figs
Electrochemically driven emulsion inversion
Johans, Christoffer; Kontturi, Kyösti
2007-09-01
It is shown that emulsions stabilized by ionic surfactants can be inverted by controlling the electrical potential across the oil-water interface. The potential dependent partitioning of sodium dodecyl sulfate (SDS) was studied by cyclic voltammetry at the 1,2-dichlorobenzene|water interface. In the emulsion the potential control was achieved by using a potential-determining salt. The inversion of a 1,2-dichlorobenzene-in-water (O/W) emulsion stabilized by SDS was followed by conductometry as a function of added tetrapropylammonium chloride. A sudden drop in conductivity was observed, indicating the change of the continuous phase from water to 1,2-dichlorobenzene, i.e. a water-in-1,2-dichlorobenzene emulsion was formed. The inversion potential is well in accordance with that predicted by the hydrophilic-lipophilic deviation if the interfacial potential is appropriately accounted for.
DEFF Research Database (Denmark)
Gale, A.S.; Surlyk, Finn; Anderskouv, Kresten
2013-01-01
Evidence from regional stratigraphical patterns in Santonian−Campanian chalk is used to infer the presence of a very broad channel system (5 km across) with a depth of at least 50 m, running NNW−SSE across the eastern Isle of Wight; only the western part of the channel wall and fill is exposed. W......−Campanian chalks in the eastern Isle of Wight, involving penecontemporaneous tectonic inversion of the underlying basement structure, are rejected....
Reactivity in inverse micelles
International Nuclear Information System (INIS)
Brochette, Pascal
1987-01-01
This research thesis reports the study of the use of micro-emulsions of water in oil as reaction support. Only the 'inverse micelles' domain of the ternary mixing (water/AOT/isooctane) has been studied. The main addressed issues have been: the micro-emulsion disturbance in presence of reactants, the determination of reactant distribution and the resulting kinetic theory, the effect of the interface on electron transfer reactions, and finally protein solubilization [fr
Nonlinear electron transport in magnetized laser plasmas
International Nuclear Information System (INIS)
Kho, T.H.; Haines, M.G.
1986-01-01
Electron transport in a magnetized plasma heated by inverse bremsstrahlung is studied numerically using a nonlinear Fokker--Planck model with self-consistent E and B fields. The numerical scheme is described. Nonlocal transport is found to alter many of the transport coefficients derived from linear transport theory, in particular, the Nernst and Righi--Leduc effects, in addition to the perpendicular heat flux q/sub perpendicular/, are substantially reduced near critical surface. The magnetic field, however, remains strongly coupled to the nonlinear q/sub perpendicular/ and, as has been found in hydrosimulations, convective amplification of the magnetic field occurs in the overdense plasma
International Nuclear Information System (INIS)
Steinhauer, L.C.; Romea, R.D.; Kimura, W.D.
1997-01-01
A new method for laser acceleration is proposed based upon the inverse process of transition radiation. The laser beam intersects an electron-beam traveling between two thin foils. The principle of this acceleration method is explored in terms of its classical and quantum bases and its inverse process. A closely related concept based on the inverse of diffraction radiation is also presented: this concept has the significant advantage that apertures are used to allow free passage of the electron beam. These concepts can produce net acceleration because they do not satisfy the conditions in which the Lawson-Woodward theorem applies (no net acceleration in an unbounded vacuum). Finally, practical aspects such as damage limits at optics are employed to find an optimized set of parameters. For reasonable assumptions an acceleration gradient of 200 MeV/m requiring a laser power of less than 1 GW is projected. An interesting approach to multi-staging the acceleration sections is also presented. copyright 1997 American Institute of Physics
Intersections, ideals, and inversion
International Nuclear Information System (INIS)
Vasco, D.W.
1998-01-01
Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly one dimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons
Intersections, ideals, and inversion
Energy Technology Data Exchange (ETDEWEB)
Vasco, D.W.
1998-10-01
Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.
Frequency-domain waveform inversion using the unwrapped phase
Choi, Yun Seok
2011-01-01
Phase wrapping in the frequency-domain (or cycle skipping in the time-domain) is the major cause of the local minima problem in the waveform inversion. The unwrapped phase has the potential to provide us with a robust and reliable waveform inversion, with reduced local minima. We propose a waveform inversion algorithm using the unwrapped phase objective function in the frequency-domain. The unwrapped phase, or what we call the instantaneous traveltime, is given by the imaginary part of dividing the derivative of the wavefield with respect to the angular frequency by the wavefield itself. As a result, the objective function is given a traveltime-like function, which allows us to smooth it and reduce its nonlinearity. The gradient of the objective function is computed using the back-propagation algorithm based on the adjoint-state technique. We apply both our waveform inversion algorithm using the unwrapped phase and the conventional waveform inversion and show that our inversion algorithm gives better convergence to the true model than the conventional waveform inversion. © 2011 Society of Exploration Geophysicists.
The attitude inversion method of geostationary satellites based on unscented particle filter
Du, Xiaoping; Wang, Yang; Hu, Heng; Gou, Ruixin; Liu, Hao
2018-04-01
The attitude information of geostationary satellites is difficult to be obtained since they are presented in non-resolved images on the ground observation equipment in space object surveillance. In this paper, an attitude inversion method for geostationary satellite based on Unscented Particle Filter (UPF) and ground photometric data is presented. The inversion algorithm based on UPF is proposed aiming at the strong non-linear feature in the photometric data inversion for satellite attitude, which combines the advantage of Unscented Kalman Filter (UKF) and Particle Filter (PF). This update method improves the particle selection based on the idea of UKF to redesign the importance density function. Moreover, it uses the RMS-UKF to partially correct the prediction covariance matrix, which improves the applicability of the attitude inversion method in view of UKF and the particle degradation and dilution of the attitude inversion method based on PF. This paper describes the main principles and steps of algorithm in detail, correctness, accuracy, stability and applicability of the method are verified by simulation experiment and scaling experiment in the end. The results show that the proposed method can effectively solve the problem of particle degradation and depletion in the attitude inversion method on account of PF, and the problem that UKF is not suitable for the strong non-linear attitude inversion. However, the inversion accuracy is obviously superior to UKF and PF, in addition, in the case of the inversion with large attitude error that can inverse the attitude with small particles and high precision.
Testing earthquake source inversion methodologies
Page, Morgan T.; Mai, Paul Martin; Schorlemmer, Danijel
2011-01-01
Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data
From inactive to regular jogger
DEFF Research Database (Denmark)
Lund-Cramer, Pernille; Brinkmann Løite, Vibeke; Bredahl, Thomas Viskum Gjelstrup
study was conducted using individual semi-structured interviews on how a successful long-term behavior change had been achieved. Ten informants were purposely selected from participants in the DANO-RUN research project (7 men, 3 women, average age 41.5). Interviews were performed on the basis of Theory...... of Planned Behavior (TPB) and The Transtheoretical Model (TTM). Coding and analysis of interviews were performed using NVivo 10 software. Results TPB: During the behavior change process, the intention to jogging shifted from a focus on weight loss and improved fitness to both physical health, psychological......Title From inactive to regular jogger - a qualitative study of achieved behavioral change among recreational joggers Authors Pernille Lund-Cramer & Vibeke Brinkmann Løite Purpose Despite extensive knowledge of barriers to physical activity, most interventions promoting physical activity have proven...
Source Estimation by Full Wave Form Inversion
Energy Technology Data Exchange (ETDEWEB)
Sjögreen, Björn [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Petersson, N. Anders [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
2013-08-07
Given time-dependent ground motion recordings at a number of receiver stations, we solve the inverse problem for estimating the parameters of the seismic source. The source is modeled as a point moment tensor source, characterized by its location, moment tensor components, the start time, and frequency parameter (rise time) of its source time function. In total, there are 11 unknown parameters. We use a non-linear conjugate gradient algorithm to minimize the full waveform misfit between observed and computed ground motions at the receiver stations. An important underlying assumption of the minimization problem is that the wave propagation is accurately described by the elastic wave equation in a heterogeneous isotropic material. We use a fourth order accurate finite difference method, developed in [12], to evolve the waves forwards in time. The adjoint wave equation corresponding to the discretized elastic wave equation is used to compute the gradient of the misfit, which is needed by the non-linear conjugated minimization algorithm. A new source point moment source discretization is derived that guarantees that the Hessian of the misfit is a continuous function of the source location. An efficient approach for calculating the Hessian is also presented. We show how the Hessian can be used to scale the problem to improve the convergence of the non-linear conjugated gradient algorithm. Numerical experiments are presented for estimating the source parameters from synthetic data in a layer over half-space problem (LOH.1), illustrating rapid convergence of the proposed approach.
Tessellating the Sphere with Regular Polygons
Soto-Johnson, Hortensia; Bechthold, Dawn
2004-01-01
Tessellations in the Euclidean plane and regular polygons that tessellate the sphere are reviewed. The regular polygons that can possibly tesellate the sphere are spherical triangles, squares and pentagons.
On the equivalence of different regularization methods
International Nuclear Information System (INIS)
Brzezowski, S.
1985-01-01
The R-circunflex-operation preceded by the regularization procedure is discussed. Some arguments are given, according to which the results may depend on the method of regularization, introduced in order to avoid divergences in perturbation calculations. 10 refs. (author)
The uniqueness of the regularization procedure
International Nuclear Information System (INIS)
Brzezowski, S.
1981-01-01
On the grounds of the BPHZ procedure, the criteria of correct regularization in perturbation calculations of QFT are given, together with the prescription for dividing the regularized formulas into the finite and infinite parts. (author)
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
indicate that a certain class of initial waves approach asymptotically these exact solutions of the KP equation. The author discusses an application of the theory to the problem of the resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall, known as the Mach reflection problem in shallow water. A beautiful explanation of the problem was presented in a swimming pool experiment during NEEDS 2009. Smooth and peaked solitons of the CH equation Holm and Ivanov [4] discuss the relations between smooth and peaked soliton solutions for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. They first present the derivation of the soliton solution for the CH equation by means of inverse scattering transform (IST); the solution is obtained in a form that admits the peakon limit. The canonical Hamiltonian formulation of the CH equation in action-angle variables is recovered using the scattering data. The authors review some of the geometric properties of the CH equation and conclude their review with the higher dimensional generalization of the dispersionless CH equation, known as EPDiff. They also consider the possible extensions of their approach in three open problems. Regular contributions to this issue cover a wide range of topics related to integrable systems. Let us briefly illustrate some of the topics covered by this issue. One of the main topics is the study of hierarchies of integrable equations. The multifaceted idea of integrability of a particular PDE includes an approach whose aim is to find an infinite set of independent conserved quantities, much in the spirit of Liouville integrability in classical mechanics. The existence of these conserved quantities in involution, or of the corresponding infinite set of commuting symmetries, leads to an infinite set of commuting flows; i.e., to the construction of a hierarchy of compatible PDEs with respect to an infinite set of times. Obviously
3D first-arrival traveltime tomography with modified total variation regularization
Jiang, Wenbin; Zhang, Jie
2018-02-01
Three-dimensional (3D) seismic surveys have become a major tool in the exploration and exploitation of hydrocarbons. 3D seismic first-arrival traveltime tomography is a robust method for near-surface velocity estimation. A common approach for stabilizing the ill-posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a 3D first-arrival traveltime tomography method with modified total variation (MTV) regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. To solve the minimization problem of the new traveltime tomography method, we decouple the original optimization problem into two following subproblems: a standard traveltime tomography problem with the traditional Tikhonov regularization and a L2 total variation problem. We apply the conjugate gradient method and split-Bregman iterative method to solve these two subproblems, respectively. Our synthetic examples show that the new method produces higher resolution models than the conventional traveltime tomography with Tikhonov regularization. We apply the technique to field data. The stacking section shows significant improvements with static corrections from the MTV traveltime tomography.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
Apagyi, B; Scheid, W
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
International Nuclear Information System (INIS)
Apagyi, Barnabas; Harman, Zoltan; Scheid, Werner
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure
Nonlinear approaches for phase retrieval in the Fresnel region for hard X-ray imaging
International Nuclear Information System (INIS)
Davidoiu, Valentina
2013-01-01
projection operators on the convergence properties of the method. In the second part of this thesis, we investigate the resolution of the linear inverse problem with an iterative thresholding algorithm in wavelet coordinates. In the following, the two former algorithms are combined and compared with another nonlinear approach based on sparsity regularization and a fixed point algorithm. The performance of theses algorithms are evaluated on simulated data for different noise levels. Finally the algorithms were adapted to process real data sets obtained in phase CT at the ESRF at Grenoble. (author)
Asymptotic inverse periods of reflected reactors above prompt critical
International Nuclear Information System (INIS)
Spriggs, G.D.; Busch, R.D.
1995-01-01
It is commonly assumed that the kinetic behavior of reflected and unreflected reactors is identical. In particular, it is often accepted that a given reactivity change in either type of system will result in an identical asymptotic inverse period. This is generally true for reactivities below prompt critical. For reactivities above prompt critical, however, the asymptotic inverse period can vary in a highly nonlinear fashion with system reactivity depending on the reflector return fraction, the neutron lifetime in the core, and the neutron lifetime in the reflector
Regularization Techniques for Linear Least-Squares Problems
Suliman, Mohamed
2016-04-01
method deals with discrete ill-posed problems when the singular values of the linear transformation matrix are decaying very fast to a significantly small value. For the both proposed algorithms, the regularization parameter is obtained as a solution of a non-linear characteristic equation. We provide a details study for the general properties of these functions and address the existence and uniqueness of the root. To demonstrate the performance of the derivations, the first proposed COPRA method is applied to estimate different signals with various characteristics, while the second proposed COPRA method is applied to a large set of different real-world discrete ill-posed problems. Simulation results demonstrate that the two proposed methods outperform a set of benchmark regularization algorithms in most cases. In addition, the algorithms are also shown to have the lowest run time.
A variational regularization of Abel transform for GPS radio occultation
Directory of Open Access Journals (Sweden)
T.-K. Wee
2018-04-01
Full Text Available In the Global Positioning System (GPS radio occultation (RO technique, the inverse Abel transform of measured bending angle (Abel inversion, hereafter AI is the standard means of deriving the refractivity. While concise and straightforward to apply, the AI accumulates and propagates the measurement error downward. The measurement error propagation is detrimental to the refractivity in lower altitudes. In particular, it builds up negative refractivity bias in the tropical lower troposphere. An alternative to AI is the numerical inversion of the forward Abel transform, which does not incur the integration of error-possessing measurement and thus precludes the error propagation. The variational regularization (VR proposed in this study approximates the inversion of the forward Abel transform by an optimization problem in which the regularized solution describes the measurement as closely as possible within the measurement's considered accuracy. The optimization problem is then solved iteratively by means of the adjoint technique. VR is formulated with error covariance matrices, which permit a rigorous incorporation of prior information on measurement error characteristics and the solution's desired behavior into the regularization. VR holds the control variable in the measurement space to take advantage of the posterior height determination and to negate the measurement error due to the mismodeling of the refractional radius. The advantages of having the solution and the measurement in the same space are elaborated using a purposely corrupted synthetic sounding with a known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison to nearby radiosonde observations shows that VR attains considerably smaller random and systematic errors compared to AI. A noteworthy finding is that in the heights and areas that the measurement bias is supposedly small, VR follows AI very closely in the
A variational regularization of Abel transform for GPS radio occultation
Wee, Tae-Kwon
2018-04-01
In the Global Positioning System (GPS) radio occultation (RO) technique, the inverse Abel transform of measured bending angle (Abel inversion, hereafter AI) is the standard means of deriving the refractivity. While concise and straightforward to apply, the AI accumulates and propagates the measurement error downward. The measurement error propagation is detrimental to the refractivity in lower altitudes. In particular, it builds up negative refractivity bias in the tropical lower troposphere. An alternative to AI is the numerical inversion of the forward Abel transform, which does not incur the integration of error-possessing measurement and thus precludes the error propagation. The variational regularization (VR) proposed in this study approximates the inversion of the forward Abel transform by an optimization problem in which the regularized solution describes the measurement as closely as possible within the measurement's considered accuracy. The optimization problem is then solved iteratively by means of the adjoint technique. VR is formulated with error covariance matrices, which permit a rigorous incorporation of prior information on measurement error characteristics and the solution's desired behavior into the regularization. VR holds the control variable in the measurement space to take advantage of the posterior height determination and to negate the measurement error due to the mismodeling of the refractional radius. The advantages of having the solution and the measurement in the same space are elaborated using a purposely corrupted synthetic sounding with a known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison to nearby radiosonde observations shows that VR attains considerably smaller random and systematic errors compared to AI. A noteworthy finding is that in the heights and areas that the measurement bias is supposedly small, VR follows AI very closely in the mean refractivity
Application of Turchin's method of statistical regularization
Zelenyi, Mikhail; Poliakova, Mariia; Nozik, Alexander; Khudyakov, Alexey
2018-04-01
During analysis of experimental data, one usually needs to restore a signal after it has been convoluted with some kind of apparatus function. According to Hadamard's definition this problem is ill-posed and requires regularization to provide sensible results. In this article we describe an implementation of the Turchin's method of statistical regularization based on the Bayesian approach to the regularization strategy.
Regular extensions of some classes of grammars
Nijholt, Antinus
Culik and Cohen introduced the class of LR-regular grammars, an extension of the LR(k) grammars. In this report we consider the analogous extension of the LL(k) grammers, called the LL-regular grammars. The relations of this class of grammars to other classes of grammars are shown. Every LL-regular
On the evolution equations, solvable through the inverse scattering method
International Nuclear Information System (INIS)
Gerdjikov, V.S.; Khristov, E.Kh.
1979-01-01
The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation
Westra, H.J.R.
2012-01-01
In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like
Robust 1D inversion and analysis of helicopter electromagnetic (HEM) data
DEFF Research Database (Denmark)
Tølbøll, R.J.; Christensen, N.B.
2006-01-01
but can resolve layer boundary to a depth of more than 100 m. Modeling experiments also show that the effect of altimeter errors on the inversion results is serious. We suggest a new interpretation scheme for HEM data founded solely on full nonlinear 1D inversion and providing layered-earth models...... supported by datamisfit parameters and a quantitative model-parameter analysis. The backbone of the scheme is the removal of cultural coupling effects followed by a multilayer inversion that in turn provides reliable starting models for a subsequent few-layer inversion. A new procedure for correlation...
Application of optical deformation analysis system on wedge splitting test and its inverse analysis
DEFF Research Database (Denmark)
Skocek, Jan; Stang, Henrik
2010-01-01
. Results of the inverse analysis are compared with traditional inverse analysis based on clip gauge data. Then the optically measured crack profile and crack tip position are compared with predictions done by the non-linear hinge model and a finite element analysis. It is shown that the inverse analysis...... based on the optically measured data can provide material parameters of the fictitious crack model matching favorably those obtained by classical inverse analysis based on the clip gauge data. Further advantages of using of the optical deformation analysis lie in identification of such effects...
Multi-resolution inversion algorithm for the attenuated radon transform
Barbano, Paolo Emilio
2011-09-01
We present a FAST implementation of the Inverse Attenuated Radon Transform which incorporates accurate collimator response, as well as artifact rejection due to statistical noise and data corruption. This new reconstruction procedure is performed by combining a memory-efficient implementation of the analytical inversion formula (AIF [1], [2]) with a wavelet-based version of a recently discovered regularization technique [3]. The paper introduces all the main aspects of the new AIF, as well numerical experiments on real and simulated data. Those display a substantial improvement in reconstruction quality when compared to linear or iterative algorithms. © 2011 IEEE.
On the inverse Magnus effect in free molecular flow
Weidman, Patrick D.; Herczynski, Andrzej
2004-02-01
A Newton-inspired particle interaction model is introduced to compute the sideways force on spinning projectiles translating through a rarefied gas. The simple model reproduces the inverse Magnus force on a sphere reported by Borg, Söderholm and Essén [Phys. Fluids 15, 736 (2003)] using probability theory. Further analyses given for cylinders and parallelepipeds of rectangular and regular polygon section point to a universal law for this class of geometric shapes: when the inverse Magnus force is steady, it is proportional to one-half the mass M of gas displaced by the body.