Iterative Regularization Methods for Nonlinear Ill-Posed Problems

Barbara Kaltenbacher, Andreas Neubauer, and Otmar Scherzer, Iterative Regularization Methods for Nonlinear Ill-Posed Problems, Radon Series on Computational and Applied Mathematics, de Gruyter, Berlin, 2008.
ISBN 978-3-11-020420-9

Table of Contents

1. Introduction
1.1. Regularization methods
1.2. Iterative regularization methods
2. Nonlinear Landweber iteration
2.1. Basic conditions
2.2. Convergence of the Landweber iteration
2.3. Convergence rates
2.4. An example
3. Modified Landweber methods
3.1. Landweber iteration in Hilbert scales
3.2. Iteratively regularized Landweber iteration
3.3. A derivative free approach
3.4. Steepest descent and minimal error method
3.5. The Landweber--Kaczmarz method
4 .Newton type methods
4.1. Levenberg--Marquardt method
4.2. Iteratively regularized Gauss--Newton method
4.3. Generalizations of the iteratively regularized Gauss--Newton method
4.4. Broyden's method for ill-posed problems
5. Multilevel methods
5.1. Regularization by discretization
5.2. Multigrid methods
6. Level set methods
6.1. Continuous regularization
6.2. Level set regularization
7. Applications
7.1. Reconstruction of transducer pressure fields from Schlieren images
7.2. Identification of B-H curves in nonlinear magnetics