This book combines theory, applications, and numerical methods, and covers each of these
fields with the same weight. In order to make the book accessible to mathematicians …

We study the possibility of using the structure of the regularization error for a posteriori
choice of the regularization parameter. As a result, a rather general form of a selection …

Solving inverse problems requires the knowledge of the forward operator, but accurate
models can be computationally expensive, and hence cheaper variants that do not …

This paper is an expository survey of the basic theory of regularization for Fredholm integral
equations of the first kind and related background material on inverse problems. We begin …

We consider numerical approximations of ill-posed elliptic problems with conditional
stability. The notion of optimal error estimates is defined including both convergence with …

A nonlinear optimization method is proposed for the solution of inverse medium problems
with spatially varying properties. To avoid the prohibitively large number of unknown control …

This paper is concerned with two aspects in the convergence analysis of regularization
methods for nonlinear problems. Firstly, if a solution of the inverse problem (or its difference …

We discuss a choice of weight in penalization methods. The motivation for the use of
penalization in computational mathematics is to improve the conditioning of the numerical …

T x= y,(1) and the problem of finding a best approximate solution x†:= T† y (ie, the element of
minimal norm minimizing the residual of T x− y), where T: X→ Y is a bounded linear operator …

In this paper we investigate the regularizing properties of discretization in preimage space
for linear and nonlinear ill-posed operator equations with noisy data. We propose to choose …