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.
| ISBN: | 9783319952635 |
| Publication date: | 18th September 2018 |
| Author: | Jens Flemming |
| Publisher: | Birkhauser an imprint of Springer International Publishing |
| Format: | Paperback |
| Pagination: | 182 pages |
| Series: | Frontiers in Mathematics |
| Genres: |
Numerical analysis Functional analysis and transforms |
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.
Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization features in the following genres: Numerical analysis, Functional analysis and transforms
Paperback. Not Available.
Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization was written by Jens Flemming and published by Birkhauser an imprint of Springer International Publishing
Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization has 182 pages
Yes it is part of Frontiers in Mathematics series