Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization : New Results in Modern Theory of Inverse Problems and an Application in Laser Optics

Flemming, Jens

ISBN 10: 3319952633 / ISBN 13: 9783319952635

Published by Springer (India) Private Limited, 2018

About this Item

Seller Inventory # 18376473739

Bibliographic Details

• Title: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization : New Results in Modern Theory of Inverse Problems and an Application in Laser Optics
• Publisher: Springer (India) Private Limited
• Publication Date: 2018
• Language: English
• ISBN 10: 3319952633
• ISBN 13: 9783319952635
• Binding: Soft cover
• Condition: New

About this title

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.