Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (Monographs on Mathematical Modeling and Computation, Series Number 4) - Softcover

Hansen, Per Christian

Softcover

ISBN 10: 0898714036 ISBN 13: 9780898714036

Publisher: Society for Industrial and Applied Mathematics, 1987

Synopsis

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.

About this title

Book 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, tomography, seismology, astronomy, and other areas.

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 1987
• Language: English
• ISBN 10: 0898714036
• ISBN 13: 9780898714036
• Binding: Paperback
• Number of pages: 263