Overview
- Presents recent research results in a consistent notation
- Contributes to two very active fields of research
- Shows that variational source condition always yields convergence rate results
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (11 chapters)
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Variational Source Conditions
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Quadratic Inverse Problems
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Sparsity Promoting Regularization
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
Book Subtitle: New Results in Modern Theory of Inverse Problems and an Application in Laser Optics
Authors: Jens Flemming
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-319-95264-2
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-95263-5Published: 18 September 2018
eBook ISBN: 978-3-319-95264-2Published: 08 September 2018
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XI, 182
Number of Illustrations: 35 b/w illustrations
Topics: Numerical Analysis, Operator Theory