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

Flemming, Jens

Softcover

ISBN 10: 3319952633 ISBN 13: 9783319952635

Publisher: Birkhäuser, 2018

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2018
• Language: English
• ISBN 10: 3319952633
• ISBN 13: 9783319952635
• Binding: Paperback
• Edition number: 1
• Number of pages: 193