Inverse Problem Theory and Methods for Model Parameter Estimation

Albert Tarantola

342 pages, parution le 19/04/2005

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Résumé

"Tarantola's book 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 many 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.

L'auteur - Albert Tarantola

Albert Tarantola is Professor at the Institut de Physique du Globe de Paris (University of Paris 6), where he teaches a course on inverse problems. He has published several papers on methods for interpretation of data that are well known. He is Docteur d'Etat of the University of Paris 6 and Doctor Honoris Causa of the University of Copenhagen and holds several honors from the French Academy of Sciences, the French National Science Foundation (CNRS), and professional societies.

Sommaire

Preface
The General Discrete Inverse Problem
Monte Carlo Methods
The Least-Squares Criterion
Least-Absolute-Values Criterion and Minimax Criterion
Functional Inverse Problems
Appendices
Problems
References and References for General Reading
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	SIAM: Society for Industrial and Applied Mathematics
Auteur(s)	Albert Tarantola
Parution	19/04/2005
Nb. de pages	342
Format	17,5 x 25,5
Couverture	Broché
Intérieur	Noir et Blanc
EAN13	9780898715729
ISBN13	978-0-89871-572-9