Numerical Methods for Inverse Problems [Hardcover]

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system.

The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications.

This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

Preface ix

Part 1. Introduction and Examples 1

Chapter 1. Overview of Inverse Problems  3

1.1. Direct and inverse problems 3

1.2. Well-posed and ill-posed problems 4

Chapter 2. Examples of Inverse Problems  9

2.1. Inverse problems in heat transfer 10

2.2. Inverse problems in hydrogeology 13

2.3. Inverse problems in seismic exploration 16

2.4. Medical imaging 21

2.5. Other examples 25

Part 2. Linear Inverse Problems 29

Chapter 3. Integral Operators and Integral Equations  31

3.1. Definition and first properties 31

3.2. Discretization of integral equations 36

3.2.1. Discretization by quadrature–collocation 36

3.2.2. Discretization by the Galerkin method 39

3.3. Exercises 42