Inverse Problems With Sparsity Constraints

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Inverse Problems with Sparsity Constraints

Dennis Trede
Inverse Problems with Sparsity Constraints Book PDF

Author : Dennis Trede
Publisher : Logos Verlag Berlin GmbH
Page : 137 pages
File Size : 40,6 Mb
Release : 2010
Category : Computers
ISBN : 9783832524661

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Inverse Problems with Sparsity Constraints by Dennis Trede Pdf

This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.

Frontiers in PDE-Constrained Optimization

Harbir Antil,Drew P. Kouri,Martin-D. Lacasse,Denis Ridzal
Frontiers in PDE Constrained Optimization Book PDF

Author : Harbir Antil,Drew P. Kouri,Martin-D. Lacasse,Denis Ridzal
Publisher : Springer
Page : 434 pages
File Size : 40,5 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9781493986361

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Frontiers in PDE-Constrained Optimization by Harbir Antil,Drew P. Kouri,Martin-D. Lacasse,Denis Ridzal Pdf

This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs)​. As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.

Theoretical Foundations and Numerical Methods for Sparse Recovery

Massimo Fornasier
Theoretical Foundations and Numerical Methods for Sparse Recovery Book PDF

Author : Massimo Fornasier
Publisher : Walter de Gruyter
Page : 351 pages
File Size : 43,5 Mb
Release : 2010-07-30
Category : Mathematics
ISBN : 9783110226157

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Theoretical Foundations and Numerical Methods for Sparse Recovery by Massimo Fornasier Pdf

The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock

Mathematical Methods for Curves and Surfaces

Morten Dæhlen,Michael S. Floater,Tom Lyche,Jean-Louis Merrien,Knut Morken,Larry L. Schumaker
Mathematical Methods for Curves and Surfaces Book PDF

Author : Morten Dæhlen,Michael S. Floater,Tom Lyche,Jean-Louis Merrien,Knut Morken,Larry L. Schumaker
Publisher : Springer
Page : 453 pages
File Size : 49,8 Mb
Release : 2010-02-12
Category : Computers
ISBN : 9783642116209

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Mathematical Methods for Curves and Surfaces by Morten Dæhlen,Michael S. Floater,Tom Lyche,Jean-Louis Merrien,Knut Morken,Larry L. Schumaker Pdf

This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008, held in Tønsberg, Norway, in June/July 2008. The 28 revised full papers presented were carefully reviewed and selected from 129 talks presented at the conference. The topics addressed by the papers range from mathematical analysis of various methods to practical implementation on modern graphics processing units.

Scale Space and Variational Methods in Computer Vision

Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie
Scale Space and Variational Methods in Computer Vision Book PDF

Author : Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie
Publisher : Springer Science & Business Media
Page : 882 pages
File Size : 45,9 Mb
Release : 2009-05-25
Category : Computers
ISBN : 9783642022555

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Scale Space and Variational Methods in Computer Vision by Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie Pdf

This book constitutes the refereed proceedings of the Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2009, emanated from the joint edition of the 5th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2009 and the 7th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2009, held in Voss, Norway in June 2009. The 71 revised full papers presented were carefully reviewed and selected numerous submissions. The papers are organized in topical sections on segmentation and detection; image enhancement and reconstruction; motion analysis, optical flow, registration and tracking; surfaces and shapes; scale space and feature extraction.

Extraction of Quantifiable Information from Complex Systems

Stephan Dahlke,Wolfgang Dahmen,Michael Griebel,Wolfgang Hackbusch,Klaus Ritter,Reinhold Schneider,Christoph Schwab,Harry Yserentant
Extraction of Quantifiable Information from Complex Systems Book PDF

Author : Stephan Dahlke,Wolfgang Dahmen,Michael Griebel,Wolfgang Hackbusch,Klaus Ritter,Reinhold Schneider,Christoph Schwab,Harry Yserentant
Publisher : Springer
Page : 446 pages
File Size : 43,7 Mb
Release : 2014-11-13
Category : Mathematics
ISBN : 9783319081595

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Extraction of Quantifiable Information from Complex Systems by Stephan Dahlke,Wolfgang Dahmen,Michael Griebel,Wolfgang Hackbusch,Klaus Ritter,Reinhold Schneider,Christoph Schwab,Harry Yserentant Pdf

In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.

Large Scale Inverse Problems

Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl
Large Scale Inverse Problems Book PDF

Author : Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl
Publisher : Walter de Gruyter
Page : 216 pages
File Size : 54,7 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9783110282269

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Large Scale Inverse Problems by Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl Pdf

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

Regularization of Inverse Problems and Inexact Operator Evaluations

Thomas Bonesky
Regularization of Inverse Problems and Inexact Operator Evaluations Book PDF

Author : Thomas Bonesky
Publisher : Unknown
Page : 0 pages
File Size : 40,5 Mb
Release : 2009
Category : Electronic
ISBN : 3832523103

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Regularization of Inverse Problems and Inexact Operator Evaluations by Thomas Bonesky Pdf

This thesis contributes to the field of inverse problems with sparsity constraints. In recent years this has been a rapidly developing field within the theory of inverse and ill-posed problems. It turned out that solutions of many inverse problems have a sparse structure, which means that they can be represented using only a finite number of elements of a suitable basis or frame. To reconstruct these solutions, Tikhonov-type regularization schemes have been investigated intensively within the last years. The minimization schemes for the related Tikhonov functionals require the evaluation of the underlying operators and their adjoints. One of the main topics of this thesis is the investigation of such a minimization scheme assuming that the necessary operator evaluations are not calculated exactly, but are computed via an adaptive scheme. A second major part is the coupling of Morozov's discrepancy principle and Tikhonov regularization, where the classical quadratic penalty term has been substituted by a more general convex functional. Finally, a non-trivial inverse heat conduction problem from steel production is solved by a combination of iterated soft-shrinkage and an adaptive finite element method.

Regularization Methods in Banach Spaces

Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski
Regularization Methods in Banach Spaces Book PDF

Author : Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski
Publisher : Walter de Gruyter
Page : 296 pages
File Size : 54,9 Mb
Release : 2012-07-30
Category : Mathematics
ISBN : 9783110255720

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Regularization Methods in Banach Spaces by Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski Pdf

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.

Algorithms for Sparsity-Constrained Optimization

Sohail Bahmani
Algorithms for Sparsity Constrained Optimization Book PDF

Author : Sohail Bahmani
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 43,8 Mb
Release : 2013-10-07
Category : Technology & Engineering
ISBN : 9783319018812

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Algorithms for Sparsity-Constrained Optimization by Sohail Bahmani Pdf

This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a "greedy" algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.

Advances in Imaging and Electron Physics

Anonim
Advances in Imaging and Electron Physics Book PDF

Author : Anonim
Publisher : Academic Press
Page : 281 pages
File Size : 53,9 Mb
Release : 2011-09-06
Category : Technology & Engineering
ISBN : 9780080569123

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Advances in Imaging and Electron Physics by Anonim Pdf

Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. Publication of this 150th volume is an event to be celebrated and, to mark the occasion, the editor has brought together leaders of some of the main themes of past and hopefully of future volumes: electron microscopy, since Ladislaus Marton was one of the pioneers; mathematical morphology, which has often appeared in this series and also fills a supplement, so often cited that it usually appears just as “Academic Press, 1994 (H.J.A.M. Heijmans, Morphological Image Operators, Supplement 25, 1994) with no mention of the Advances; ptychography, a highly original approach to the phase problem, the latter also the subject of a much cited Supplement (W.O. Saxton, ‘Computer Techniques for Image Processing in Electron Microscopy’, Supplement 10, 1978); and wavelets, which have become a subject in their own right, not just a tool in image processing. Updated with contributions from leading international scholars and industry experts Discusses hot topic areas and presents current and future research trends Invaluable reference and guide for physicists, engineers and mathematicians

Sparse Representation, Modeling and Learning in Visual Recognition

Hong Cheng
Sparse Representation Modeling and Learning in Visual Recognition Book PDF

Author : Hong Cheng
Publisher : Springer
Page : 257 pages
File Size : 44,6 Mb
Release : 2015-05-25
Category : Computers
ISBN : 9781447167143

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Sparse Representation, Modeling and Learning in Visual Recognition by Hong Cheng Pdf

This unique text/reference presents a comprehensive review of the state of the art in sparse representations, modeling and learning. The book examines both the theoretical foundations and details of algorithm implementation, highlighting the practical application of compressed sensing research in visual recognition and computer vision. Topics and features: describes sparse recovery approaches, robust and efficient sparse representation, and large-scale visual recognition; covers feature representation and learning, sparsity induced similarity, and sparse representation and learning-based classifiers; discusses low-rank matrix approximation, graphical models in compressed sensing, collaborative representation-based classification, and high-dimensional nonlinear learning; includes appendices outlining additional computer programming resources, and explaining the essential mathematics required to understand the book.

Scale Space and Variational Methods in Computer Vision

Fiorella Sgallari,Almerico Murli
Scale Space and Variational Methods in Computer Vision Book PDF

Author : Fiorella Sgallari,Almerico Murli
Publisher : Springer Science & Business Media
Page : 946 pages
File Size : 52,7 Mb
Release : 2007-05-24
Category : Computers
ISBN : 9783540728221

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Scale Space and Variational Methods in Computer Vision by Fiorella Sgallari,Almerico Murli Pdf

This book constitutes the refereed proceedings of the First International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2007, emanated from the joint edition of the 4th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2007 and the 6th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2007, held in Ischia Italy, May/June 2007.

Sparse Image and Signal Processing

Jean-Luc Starck,Fionn Murtagh,Jalal M. Fadili
Sparse Image and Signal Processing Book PDF

Author : Jean-Luc Starck,Fionn Murtagh,Jalal M. Fadili
Publisher : Cambridge University Press
Page : 351 pages
File Size : 44,6 Mb
Release : 2010-05-10
Category : Computers
ISBN : 9780521119139

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Sparse Image and Signal Processing by Jean-Luc Starck,Fionn Murtagh,Jalal M. Fadili Pdf

This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Matlab and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research available for download at the associated Web site.

New Trends in Parameter Identification for Mathematical Models

Bernd Hofmann,Antonio Leitão,Jorge P. Zubelli
New Trends in Parameter Identification for Mathematical Models Book PDF

Author : Bernd Hofmann,Antonio Leitão,Jorge P. Zubelli
Publisher : Birkhäuser
Page : 347 pages
File Size : 45,9 Mb
Release : 2018-02-13
Category : Mathematics
ISBN : 9783319708249

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New Trends in Parameter Identification for Mathematical Models by Bernd Hofmann,Antonio Leitão,Jorge P. Zubelli Pdf

The Proceedings volume contains 16 contributions to the IMPA conference “New Trends in Parameter Identification for Mathematical Models”, Rio de Janeiro, Oct 30 – Nov 3, 2017, integrating the “Chemnitz Symposium on Inverse Problems on Tour”. This conference is part of the “Thematic Program on Parameter Identification in Mathematical Models” organized at IMPA in October and November 2017. One goal is to foster the scientific collaboration between mathematicians and engineers from the Brazialian, European and Asian communities. Main topics are iterative and variational regularization methods in Hilbert and Banach spaces for the stable approximate solution of ill-posed inverse problems, novel methods for parameter identification in partial differential equations, problems of tomography , solution of coupled conduction-radiation problems at high temperatures, and the statistical solution of inverse problems with applications in physics.