Table of contents
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.
inverse problem ill-posedness variational source condition quadratic inverse problem autoconvolution nonlinear inverse problem sparsity Tikhonov regularization source condition Banach space convergence rate
- DOI https://doi.org/10.1007/978-3-319-95264-2
- Copyright Information Springer Nature Switzerland AG 2018
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-95263-5
- Online ISBN 978-3-319-95264-2
- Series Print ISSN 1660-8046
- Series Online ISSN 1660-8054
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