Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Weighted toeplitz regularized least squares computation for image restoration

Language

English

Abstract

The main aim of this paper is to develop a fast algorithm for solving weighted Toeplitz regularized least squares problems arising from image restoration. Based on augmented system formulation, we develop new Hermitian and skew-Hermitian splitting (HSS) preconditioners for solving such linear systems. The advantage of the proposed preconditioner is that the blurring matrix, weighting matrix, and regularization matrix can be decoupled such that the resulting preconditioner is not expensive to use. We show that for a preconditioned system that is derived from a saddle point structure of size (m+n)×(m+n), the preconditioned matrix has an eigenvalue at 1 with multiplicity n and the other m eigenvalues of the form 1 λ with |λ| > 1. We also study how to choose the HSS parameter to minimize the magnitude of λ, and therefore the Krylov subspace method applied to solving the preconditioned system converges very quickly. Experimental results for image restoration problems are reported to demonstrate that the performance of the proposed preconditioner is better than the other testing preconditioners. © 2014 Society for Industrial and Applied Mathematics.

Keywords

Colored noise, Image restoration, Least squares problems, Preconditioners, Splitting, Weighted Toeplitz matrices

Publication Date

2014

Source Publication Title

SIAM Journal on Scientific Computing

Volume

36

Issue

1

Start Page

B94

End Page

B121

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/120888776

Link to Publisher's Edition

http://dx.doi.org/10.1137/120888776

ISSN (print)

10648275

ISSN (electronic)

10957197

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