Restoration of images with spatially variant blur by the GMRES method

Daniela Calvetti; Bryan Lewis; Lothar Reichel

doi:10.1117/12.406515

13 November 2000 Restoration of images with spatially variant blur by the GMRES method

Daniela Calvetti, Bryan Lewis, Lothar Reichel

Proceedings Volume 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X; (2000) https://doi.org/10.1117/12.406515
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

The GMRES method is a popular iterative method for the solution of linear systems of equations with a large nonsymmetric nonsingular matrix. However, little is known about the performance of the GMRES method when the matrix of the linear system is of ill-determined rank, i.e., when the matrix has many singular values of different orders of magnitude close to the origin. Linear systems with such matrices arise, for instance, in image restoration, when the image to be restored is contaminated by noise and blur. We describe how the GMRES method can be applied to the restoration of such images. The GMRES method is compared to the conjugate gradient method applied to the normal equations associated with the given linear system of equations. The numerical examples show the GMRES method to require less computational work and to give restored images of higher quality than the conjugate gradient method.

Citation Download Citation

Daniela Calvetti, Bryan Lewis, and Lothar Reichel "Restoration of images with spatially variant blur by the GMRES method", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); https://doi.org/10.1117/12.406515

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