Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1906)
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Table of contents (19 chapters)
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Inverse and Semi-discrete Problems
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Application to 3D Doppler Tomography
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Application to the spherical mean operator
Keywords
About this book
Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions. The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the applications mentioned above.
Reviews
From the reviews:
"The powerful method of the approximate inverse is a good bunch of regularization techniques, and this monograph presents a comprehensive outline of this method. Application to 3D Doppler tomography and the spherical mean operator is then studied in details, and further results on X-ray diffractometry, thermoacoustic computerized tomography and reconstruction kernels in 3D are attached. The book is naturally recommended for computer tomographers and graduate students heading toward computer tomography, but it contains many beneficial results for researchers of Radon transforms too." (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 74, 2008)
“The book under review which deals with a particular class of regularization methods, the so called method of approximate inverse, is the result of continuous study of the author for more than a decade, by himself for his habilitation thesis and also in collaborations with many experts in the field, including A. K. Louis (his own teacher), A. Rieder and many others. … No doubt, the book is a good addition to the literature on regularization of ill-posed inverse problems.” (M. Thamban Nair, Zentralblatt MATH, Vol. 1171, 2009)
Authors and Affiliations
About the author
1990 – 1995 Study of Mathematics at Saarland University Saarbrücken (Germany)
1996 – 2004 Scientific assistant at Saarland University Saarbrücken (Germany)
1999 PhD at Saarland University Saarbrücken (Germany)
2002 – 2003 Research stay at Tufts University Medford, MA (USA)
2004 Habilitation at Saarland University Saarbrücken (Germany)
2004 – 2006 Assistant Professor at Saarland University Saarbrücken (Germany)
2007 – today Associate Professor at the Helmut Schmidt University Hamburg (Germany)
Bibliographic Information
Book Title: The Method of Approximate Inverse: Theory and Applications
Authors: Thomas Schuster
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-71227-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2007
Softcover ISBN: 978-3-540-71226-8Published: 07 May 2007
eBook ISBN: 978-3-540-71227-5Published: 26 April 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 202
Number of Illustrations: 35 b/w illustrations
Topics: Linear and Multilinear Algebras, Matrix Theory, Partial Differential Equations, Integral Equations, Numerical Analysis