Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization: New Results in Modern Theory of Inverse Problems and an ... in Laser Optics (Frontiers in Mathematics) - Softcover
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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.
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- VerlagBirkhäuser
- Erscheinungsdatum2018
- ISBN 10 3319952633
- ISBN 13 9783319952635
- EinbandTapa blanda
- Auflage1
- Anzahl der Seiten196
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Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization : New Results in Modern Theory of Inverse Problems and an Application in Laser Optics
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Springer International Publishing
(2018)
ISBN 10: 3319952633
ISBN 13: 9783319952635
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Buchbeschreibung Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The book collects and contributes new results on the theory and practice of ill-posed inverseproblems.Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems arediscussed 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 ofapplicability. It is shown that the tool known as variational source condition always yieldsconvergence rate results.A theory for nonlinear inverse problems with quadratic structure is developed as well ascorresponding regularization methods. The new methods are applied to a difficult inverse problemfrom laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensiveconvergence analysis reveals new insights into the behavior of Tikhonov-type regularization withsparsity enforcing penalty. Artikel-Nr. 9783319952635
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