ENGLISH

Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion

By Per Christian Hansen

Book information

Publisher
Society for Industrial Mathematics
Year
1987
ISBN
9780898714036, 0-89871-403-6
LCC
QA218
Open Library ID
OL22340290M
Language
english
Format
PDF
Filesize
15 MB (15493532 bytes)
Series
Monographs on Mathematical Modeling and Computation
Pages
131\131
Time added
2010-04-25 21:59:20

Description

Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are exactly or nearly rank deficient. Such problems often arise in connection with noise suppression and other problems where the goal is to suppress unwanted disturbances of given measurements. Discrete ill-posed problems arise in connection with the numerical treatment of inverse problems, where one typically wants to compute information about interior properties using exterior measurements. Examples of inverse problems are image restoration and tomography, where one needs to improve blurred images or reconstruct pictures from raw data. This book describes new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed problems. The emphasis is on insight into the stabilizing properties of the algorithms and the efficiency and reliability of the computations.

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