Krylov subspace iterative methods for nonsymmetric discrete ill-posed problems in image restoration

Daniela Calvetti; Bryan Lewis; Lothar Reichel

doi:10.1117/12.448653

20 November 2001 Krylov subspace iterative methods for nonsymmetric discrete ill-posed problems in image restoration

Daniela Calvetti, Bryan Lewis, Lothar Reichel

Proceedings Volume 4474, Advanced Signal Processing Algorithms, Architectures, and Implementations XI; (2001) https://doi.org/10.1117/12.448653
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

The BiCG and QMR methods are well-known Krylov subspace iterative methods for the solution of linear systems of equations with a large nonsymmetric, nonsingular matrix. However, little is known of the performance of these methods when they are applied to the computation of approximate solutions of linear systems of equations with a matrix of ill-determined rank. Such linear systems are known as linear discrete ill-posed problems. We describe an application of the BiCG and QMR methods to the solution of linear discrete ill-posed problems that arise in image restoration, and compare these methods to the conjugate gradient method applied to the associated normal equations and to total variation-penalized Tikhonov regularization.

Citation Download Citation

Daniela Calvetti, Bryan Lewis, and Lothar Reichel "Krylov subspace iterative methods for nonsymmetric discrete ill-posed problems in image restoration", Proc. SPIE 4474, Advanced Signal Processing Algorithms, Architectures, and Implementations XI, (20 November 2001); https://doi.org/10.1117/12.448653

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