"Tarantola's book on inverse problem theory is undoubtedly the most important work on probabilistic inverse theory. It presents a complete theory where a physical parameter is represented, not by a number, but by a probability distribution."
-- Klaus Mosegaard, Niels Bohr Institute.
While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.
Prompted by recent developments in inverse theory, Inverse Problem Theory and Methods for Model Parameter Estimation is a completely rewritten version of a 1987 book by the same author. In this version there are lots of algorithmic details for Monte Carlo methods, least-squares discrete problems, and least-squares problems involving functions. In addition, some notions are clarified, the role of optimization techniques is underplayed, and Monte Carlo methods are taken much more seriously. The first part of the book deals exclusively with discrete inverse problems with a finite number of parameters while the second part of the book deals with general inverse problems.
The book is directed to all scientists, including applied mathematicians, facing the problem of quantitative interpretation of experimental data in fields such as physics, chemistry, biology, image processing, and information sciences. Considerable effort has been made so that this book can serve either as a reference manual for researchers or as a textbook in a course for undergraduate or graduate students.
Chapter 1: The General Discrete Inverse Problem; Chapter 2: Monte Carol Methods; Chapter 3: The Least-Squares Criterion; Chapter 4: Least-Absolute Values Criterion and Minimax Criterion; Chapter 5: Functional Inverse Problems; Chapter 6: Appendices; Chapter 7: Problems; References; Index.
2005 / xii + 342 pages / Softcover / ISBN-13: 978-0-898715-72-9 / ISBN-10: 0-89871-572-5 /
List Price $101.50 / Member Price $71.05 / Order Code OT89