This book introduces the reader to the area of inverse problems. The
study of inverse problems is of vital interest to many areas of science
and technology such as geophysical exploration, system identification,
nondestructive testing and ultrasonic tomography.
The aim of this book is twofold: in the first part, the reader is
exposed to the basic notions and difficulties encountered with ill-posed
problems. Basic properties of regularization methods for linear
ill-posed problems are studied by means of several simple analytical and
numerical examples.
The second part of the book presents two special nonlinear inverse
problems in detail - the inverse spectral problem and the inverse
scattering problem. The corresponding direct problems are studied with
respect to existence, uniqueness and continuous dependence on
parameters. Then some theoretical results as well as numerical
procedures for the inverse problems are discussed. The choice of
material and its presentation in the book are new, thus making it
particularly suitable for graduate students. Basic knowledge of real
analysis is assumed.
In this new edition, the Factorization Method is included as one of the
prominent members in this monograph. Since the Factorization Method is
particularly simple for the problem of EIT and this field has attracted
a lot of attention during the past decade a chapter on EIT has been
added in this monograph as Chapter 5 while the chapter on inverse
scattering theory is now Chapter 6.The main changes of this second
edition compared to the first edition concern only Chapters 5 and 6 and
the Appendix A. Chapter 5 introduces the reader to the inverse problem
of electrical impedance tomography.
