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Author : Muoi-Pham Quy
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (813 download)
Download or read book Sparsity Constraints and Regularization for Nonlinear Inverse Problems written by Muoi-Pham Quy and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Muoi-Pham Quy
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (813 download)
Download or read book Sparsity Constraints and Regularization for Nonlinear Inverse Problems written by Muoi-Pham Quy and published by . This book was released on 2012 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dennis Trede
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832524665
Total Pages : 137 pages
Book Rating : 4.8/5 (325 download)
Download or read book Inverse Problems with Sparsity Constraints written by Dennis Trede and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Anna Christina Brandt
Publisher : Logos Verlag Berlin
ISBN 13 : 9783832533236
Total Pages : 0 pages
Book Rating : 4.5/5 (332 download)
Download or read book Regularization of Inverse Problems for Turning Processes written by Anna Christina Brandt and published by Logos Verlag Berlin. This book was released on 2013-01-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we will focus on inverse problems appearing in ultra precise turning processes. Ultra precision turning is widely used to manufacture metallic surfaces with high surface quality. One crucial influencing factor of the surface quality is unbalances leading to vibrations of the machine structure and interaction with the cutting process. This interaction is the so-called process machine interaction. Therefore, a model is built which simulates the influence of unbalances of the machine structure and process parameters on the resulting surface of the workpiece. In order to include the process machine interaction into the model, a new force model for ultra precision turning is developed. The resulting interaction model is based on a nonlinear parameter-dependent system of ordinary differential equations. The corresponding forward model is thus described by the map connecting the input parameters to the solution of this equation system. The main part of the thesis is the inversion of the forward operator, i.e. for a given tool path on the workpiece the necessary input parameters are computed such that solving the forward model with this new input parameters results in the desired tool path. Since the forward problem is ill-posed, regularization methods with sparsity constraints are applied which promote sparse solutions. The advantage of such sparse solutions is that they limit the points of machine changes in the machine control. Two different applications are treated in detail and illustrated with various numerical examples.
Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)
Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Author : Massimo Fornasier
Publisher : Walter de Gruyter
ISBN 13 : 3110226154
Total Pages : 351 pages
Book Rating : 4.1/5 (12 download)
Download or read book Theoretical Foundations and Numerical Methods for Sparse Recovery written by Massimo Fornasier and published by Walter de Gruyter. This book was released on 2010-07-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author :
Publisher : Springer-Verlag
ISBN 13 : 3322930343
Total Pages : 199 pages
Book Rating : 4.3/5 (229 download)
Download or read book Regularization for Applied Inverse and Ill-Posed Problems written by and published by Springer-Verlag. This book was released on 2013-11-22 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas Schuster
Publisher : Walter de Gruyter
ISBN 13 : 3110255723
Total Pages : 296 pages
Book Rating : 4.1/5 (12 download)
Download or read book Regularization Methods in Banach Spaces written by Thomas Schuster and published by Walter de Gruyter. This book was released on 2012-07-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Barbara Kaltenbacher
Publisher : Walter de Gruyter
ISBN 13 : 311020827X
Total Pages : 205 pages
Book Rating : 4.1/5 (12 download)
Download or read book Iterative Regularization Methods for Nonlinear Ill-Posed Problems written by Barbara Kaltenbacher and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Author : Gerd Teschke
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (61 download)
Download or read book Accelerated Projected Steepest Descent Method for Nonlinear Inverse Problems with Sparsity Constraints written by Gerd Teschke and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Roderick Melnik
Publisher : John Wiley & Sons
ISBN 13 : 1118853857
Total Pages : 321 pages
Book Rating : 4.1/5 (188 download)
Download or read book Mathematical and Computational Modeling written by Roderick Melnik and published by John Wiley & Sons. This book was released on 2015-05-21 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and Computational Modeling Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-theart achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. The book also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, and industrial and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.
Author : Kazufumi Ito
Publisher : World Scientific
ISBN 13 : 9814596213
Total Pages : 330 pages
Book Rating : 4.8/5 (145 download)
Download or read book Inverse Problems: Tikhonov Theory And Algorithms written by Kazufumi Ito and published by World Scientific. This book was released on 2014-08-28 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.
Author : Richard C. Aster
Publisher : Elsevier
ISBN 13 : 0128134232
Total Pages : 406 pages
Book Rating : 4.1/5 (281 download)
Download or read book Parameter Estimation and Inverse Problems written by Richard C. Aster and published by Elsevier. This book was released on 2018-10-16 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. - Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method - Includes an online instructor's guide that helps professors teach and customize exercises and select homework problems - Covers updated information on adjoint methods that are presented in an accessible manner
Author : Torsten Hein
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832527451
Total Pages : 174 pages
Book Rating : 4.8/5 (325 download)
Download or read book Regularization in Banach Spaces - Convergence Rates Theory written by Torsten Hein and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by their successful application in image restoring and sparsity reconstruction this manuscript deals with regularization theory of linear and nonlinear inverse and ill-posed problems in Banach space settings. Whereas regularization in Hilbert spaces has been widely studied in literature for a long period the developement and investigation of regularization methods in Banach spaces have become a field of modern research. The manuscript is twofolded. The first part deals with convergence rates theory for Tikhonov regularization as classical regularization method. In particular, generalizations of well-established results in Hilbert spaces are presented in the Banach space situation. Since the numerical effort of Tikhonov regularization in applications is rather high iterative approaches were considered as alternative regularization variants in the second part. In particular, two Gradient-type methods were presented and their behaviour concerning convergence and stability is investigated. For one of the methods, additionally, a convergence rates result is formulated. All the theoretical results are illustrated by some numerical examples.
Author : Jean-Luc Starck
Publisher : Cambridge University Press
ISBN 13 : 1316483304
Total Pages : 449 pages
Book Rating : 4.3/5 (164 download)
Download or read book Sparse Image and Signal Processing written by Jean-Luc Starck and published by Cambridge University Press. This book was released on 2015-10-14 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thoroughly updated new edition presents state-of-the-art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB® and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.
Author : Jennifer L. Mueller
Publisher : SIAM
ISBN 13 : 1611972337
Total Pages : 349 pages
Book Rating : 4.6/5 (119 download)
Download or read book Linear and Nonlinear Inverse Problems with Practical Applications written by Jennifer L. Mueller and published by SIAM. This book was released on 2012-11-30 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.
Author : Edwin Lughofer
Publisher : Springer
ISBN 13 : 3642180876
Total Pages : 467 pages
Book Rating : 4.6/5 (421 download)
Download or read book Evolving Fuzzy Systems - Methodologies, Advanced Concepts and Applications written by Edwin Lughofer and published by Springer. This book was released on 2011-01-31 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: In today’s real-world applications, there is an increasing demand of integrating new information and knowledge on-demand into model building processes to account for changing system dynamics, new operating conditions, varying human behaviors or environmental influences. Evolving fuzzy systems (EFS) are a powerful tool to cope with this requirement, as they are able to automatically adapt parameters, expand their structure and extend their memory on-the-fly, allowing on-line/real-time modeling. This book comprises several evolving fuzzy systems approaches which have emerged during the last decade and highlights the most important incremental learning methods used. The second part is dedicated to advanced concepts for increasing performance, robustness, process-safety and reliability, for enhancing user-friendliness and enlarging the field of applicability of EFS and for improving the interpretability and understandability of the evolved models. The third part underlines the usefulness and necessity of evolving fuzzy systems in several online real-world application scenarios, provides an outline of potential future applications and raises open problems and new challenges for the next generation evolving systems, including human-inspired evolving machines. The book includes basic principles, concepts, algorithms and theoretic results underlined by illustrations. It is dedicated to researchers from the field of fuzzy systems, machine learning, data mining and system identification as well as engineers and technicians who apply data-driven modeling techniques in real-world systems.
