Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization
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Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization
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Author : Jens Flemming
language : en
Publisher: Springer
Release Date : 2018-09-08
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization written by Jens Flemming and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-08 with Mathematics categories.
The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.
Inverse Problems And Related Topics
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Author : Jin Cheng
language : en
Publisher: Springer Nature
Release Date : 2020-02-04
Inverse Problems And Related Topics written by Jin Cheng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-04 with Mathematics categories.
This volume contains 13 chapters, which are extended versions of the presentations at International Conference on Inverse Problems at Fudan University, Shanghai, China, October 12-14, 2018, in honor of Masahiro Yamamoto on the occasion of his 60th anniversary. The chapters are authored by world-renowned researchers and rising young talents, and are updated accounts of various aspects of the researches on inverse problems. The volume covers theories of inverse problems for partial differential equations, regularization methods, and related topics from control theory. This book addresses a wide audience of researchers and young post-docs and graduate students who are interested in mathematical sciences as well as mathematics.
An Introduction To The Mathematical Theory Of Inverse Problems
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Author : Andreas Kirsch
language : en
Publisher: Springer Nature
Release Date : 2021-02-15
An Introduction To The Mathematical Theory Of Inverse Problems written by Andreas Kirsch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-15 with Mathematics categories.
This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
New Trends In Parameter Identification For Mathematical Models
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Author : Bernd Hofmann
language : en
Publisher: Birkhäuser
Release Date : 2018-02-13
New Trends In Parameter Identification For Mathematical Models written by Bernd Hofmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-13 with Mathematics categories.
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.
Nanoscale Photonic Imaging
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Author : Tim Salditt
language : en
Publisher: Springer Nature
Release Date : 2020-06-09
Nanoscale Photonic Imaging written by Tim Salditt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-09 with Science categories.
This open access book, edited and authored by a team of world-leading researchers, provides a broad overview of advanced photonic methods for nanoscale visualization, as well as describing a range of fascinating in-depth studies. Introductory chapters cover the most relevant physics and basic methods that young researchers need to master in order to work effectively in the field of nanoscale photonic imaging, from physical first principles, to instrumentation, to mathematical foundations of imaging and data analysis. Subsequent chapters demonstrate how these cutting edge methods are applied to a variety of systems, including complex fluids and biomolecular systems, for visualizing their structure and dynamics, in space and on timescales extending over many orders of magnitude down to the femtosecond range. Progress in nanoscale photonic imaging in Göttingen has been the sum total of more than a decade of work by a wide range of scientists and mathematicians across disciplines, working together in a vibrant collaboration of a kind rarely matched. This volume presents the highlights of their research achievements and serves as a record of the unique and remarkable constellation of contributors, as well as looking ahead at the future prospects in this field. It will serve not only as a useful reference for experienced researchers but also as a valuable point of entry for newcomers.
Splitting Methods In Communication Imaging Science And Engineering
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Author : Roland Glowinski
language : en
Publisher: Springer
Release Date : 2017-01-05
Splitting Methods In Communication Imaging Science And Engineering written by Roland Glowinski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-05 with Mathematics categories.
This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.
Optimization With Sparsity Inducing Penalties
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Author : Francis Bach
language : en
Publisher:
Release Date : 2011-12-23
Optimization With Sparsity Inducing Penalties written by Francis Bach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Computers categories.
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. Optimization with Sparsity-Inducing Penalties presents optimization tools and techniques dedicated to such sparsity-inducing penalties from a general perspective. It covers proximal methods, block-coordinate descent, reweighted ?2-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provides an extensive set of experiments to compare various algorithms from a computational point of view. The presentation of Optimization with Sparsity-Inducing Penalties is essentially based on existing literature, but the process of constructing a general framework leads naturally to new results, connections and points of view. It is an ideal reference on the topic for anyone working in machine learning and related areas.
Nonlinear Ill Posed Problems
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Author : A.N. Tikhonov
language : en
Publisher: Springer
Release Date : 2014-08-23
Nonlinear Ill Posed Problems written by A.N. Tikhonov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-23 with Mathematics categories.
Inverse And Ill Posed Problems
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Author : Heinz W. Engl
language : en
Publisher:
Release Date : 1987
Inverse And Ill Posed Problems written by Heinz W. Engl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Inverse and Ill-Posed Problems.
Electromagnetic Brain Imaging
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Author : Kensuke Sekihara
language : en
Publisher: Springer
Release Date : 2015-02-20
Electromagnetic Brain Imaging written by Kensuke Sekihara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-20 with Medical categories.
This graduate level textbook provides a coherent introduction to the body of main-stream algorithms used in electromagnetic brain imaging, with specific emphasis on novel Bayesian algorithms. It helps readers to more easily understand literature in biomedical engineering and related fields and be ready to pursue research in either the engineering or the neuroscientific aspects of electromagnetic brain imaging. This textbook will not only appeal to graduate students but all scientists and engineers engaged in research on electromagnetic brain imaging.