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Frontiers in Mathematics

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

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  • 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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eBook 46,00 €
price for Spain (gross)
  • ISBN 978-3-319-95264-2
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  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-95263-5
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  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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)

Table of contents (11 chapters)

Buy this book

eBook 46,00 €
price for Spain (gross)
  • ISBN 978-3-319-95264-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-95263-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

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
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