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20 November 2001 Krylov subspace iterative methods for nonsymmetric discrete ill-posed problems in image restoration
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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.
© (2001) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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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