Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
New Results in Modern Theory of Inverse Problems and an Application in Laser Optics
Authors: Flemming, Jens
Free Preview- 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
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- About this book
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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.
- Table of contents (11 chapters)
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Inverse Problems, Ill-Posedness, Regularization
Pages 3-14
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Variational Source Conditions Yield Convergence Rates
Pages 15-20
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Existence of Variational Source Conditions
Pages 21-28
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What Are Quadratic Inverse Problems?
Pages 31-53
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Tikhonov Regularization
Pages 55-57
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Table of contents (11 chapters)
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Bibliographic Information
- Bibliographic Information
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- 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
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- Jens Flemming
- Series Title
- Frontiers in Mathematics
- Copyright
- 2018
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-319-95264-2
- DOI
- 10.1007/978-3-319-95264-2
- Softcover ISBN
- 978-3-319-95263-5
- Series ISSN
- 1660-8046
- Edition Number
- 1
- Number of Pages
- XI, 182
- Number of Illustrations
- 35 b/w illustrations
- Topics
