The Method of Approximate Inverse: Theory and Applications / Edition 1

The Method of Approximate Inverse: Theory and Applications / Edition 1

by Thomas Schuster
Pub. Date:
Springer Berlin Heidelberg

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The Method of Approximate Inverse: Theory and Applications / Edition 1

This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.

Product Details

ISBN-13: 9783540712268
Publisher: Springer Berlin Heidelberg
Publication date: 06/12/2007
Series: Lecture Notes in Mathematics Series , #1906
Edition description: 2007
Pages: 202
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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.

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