Statistical And Computational Inverse Problems: V. 160

E-Book Overview

This book develops the statistical approach to inverse problems with an emphasis on modeling and computations.  The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse problem is expressed in terms of probability densities.  The book discusses in detail the construction of prior models, the measurement noise modeling and Bayesian estimation.  Markov Chain Monte Carlo-methods as well as optimization methods are examples that are often non-trivial but easy to follow.  Besides the simple examples, the book contains problems as discretization errors, and statistical model reduction.  Furthermore, the techniques are then applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems.  The book is intended for researchers and advanced students in applied mathematics, computational physics, and engineering.  The first part of the book can be used as a text book on advanced inverse problems courses.

E-Book Content

Applied Mathematical Sciences Volume 160 Editors S.S. Antman J.E. Marsden L. Sirovich Advisors J.K. Hale P. Holmes J. Keener J. Keller B.J. Matkowsky A. Mielke C.S. Peskin K.R. Sreenivasan Jari Kaipio Erkki Somersalo Statistical and Computational Inverse Problems With 102 Figures Jari P. Kaipio Department of Applied Physics University of Kuopio 70211 Kuopio Finland [email protected] Editors: S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA [email protected] Erkki Somersalo Institute of Mathematics Helsinki University of Technology 02015 HUT Finland [email protected] J.E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA [email protected] L. Sirovich Laboratory of Applied Mathematics Department of Biomathematical Sciences Mount Sinai School of Medicine New York, NY 10029-6574 USA [email protected] Mathematics Subject Classification (2000): 15A29, 35R25, 35R30, 62F15, 62P30, 62P35, 62K05, 65C05, 65C40, 65J20, 65J22, 65F10, 65F22, 65N21, 65R30, 65R32, 78A70 Library of Congress Cataloging-in-Publication Data Kaipio, Jari. Statistical and computational inverse problems / Jari Kaipio and Erkki Somersalo. p. cm. — (Applied mathematical sciences) “April 1, 2004.” Includes bibliographical references and index. ISBN 0-387-22073-9 (alk. paper) 1. Inverse problems (Differential equations) 2. Inverse problems (Differential equations)—Numerical solutions. I. Somersalo, Erkki. II. Title. III. Applied mathematical sciences (Springer-Verlag New York, Inc.) QA377.K33 2004 515′.357—dc22 2004049181 ISBN 0-387-22073-9 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis.
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