Statistical and Computational Inverse Problems
The 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 th
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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.
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SPIN 10980149
(MP)
To Eerika, Paula, Maija and Noora
VII
Between the idea And the reality Between the motion And the act Falls the Shadow T.S. Eliot
Preface
This book is aimed at postgraduate students in applied mathematics as well as at engineering and physics students with a firm background in mathematics. The first four chapters can be used as the material for a first course on inverse problems with a focus on computational and statistical aspects. On the other hand, Chapters 3 and 4, which discuss statistical and nonstationary inversion methods, can be used by students already having knowldege of classical inversi
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