The Method of Approximate Inverse

Theory and Applications

Thomas Schuster

$114.95 $91.82

Paperback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Springer Verlag
01 May 2007

Mathematics & Sciences; Algebra

Series: Lecture Notes in Mathematics

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.

By: Thomas Schuster
Imprint: Springer Verlag
Country of Publication: Germany
Volume: v. 1906
Dimensions: Height: 235mm, Width: 155mm, Spine: 13mm
Weight: 454g
ISBN: 9783540712268
ISBN 10: 3540712267
Series: Lecture Notes in Mathematics
Pages: 216
Publication Date: 01 May 2007
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Inverse and Semi-discrete Problems.- Ill-posed problems and regularization methods.- Approximate inverse in L 2-spaces.- Approximate inverse in Hilbert spaces.- Approximate inverse in distribution spaces.- Conclusion and perspectives.- Application to 3D Doppler Tomography.- A semi-discrete setup for Doppler tomography.- Solving the semi-discrete problem.- Convergence and stability.- Approaches for defect correction.- Conclusion and perspectives.- Application to the spherical mean operator.- The spherical mean operator.- Design of a mollifier.- Computation of reconstruction kernels.- Numerical experiments.- Conclusion and perspectives.- Further Applications.- Approximate inverse and X-ray diffractometry.- A filtered backprojection algorithm.- Computation of reconstruction kernels in 3D computerized tomography.- Conclusion and perspectives.

1990 -- 1995 Study of Mathematics at Saarland University Saarbrucken (Germany) 1996 -- 2004 Scientific assistant at Saarland University Saarbrucken (Germany) 1999 PhD at Saarland University Saarbrucken (Germany) 2002 -- 2003 Research stay at Tufts University Medford, MA (USA) 2004 Habilitation at Saarland University Saarbrucken (Germany) 2004 -- 2006 Assistant Professor at Saarland University Saarbrucken (Germany) 2007 -- today Associate Professor at the Helmut Schmidt University Hamburg (Germany)

Reviews for The Method of Approximate Inverse: Theory and Applications

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. ( rpad 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)