Block-triangular Preconditioners for Systems Arising From Edge-preserving Image Restoration

Zhong Zhi Bai*, Yu Mei Huang, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)


Signal and image restoration problems are often solved by minimizing a cost function consisting of an ℓ2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-described signal and image restoration problems with the half-quadratic regularization technique by making use of the Newton method. At each iteration of the Newton method, the Newton equation is a structured system of linear equations of a symmetric positive definite coefficient matrix, and may be efficiently solved by the preconditioned conjugate gradient method accelerated with the modified block SSOR preconditioner. Our experimental results show that the modified block-SSOR preconditioned conjugate gradient method is feasible and effective for further improving the numerical performance of the half-quadratic regularization approach.

Original languageEnglish
Pages (from-to)848-863
Number of pages16
JournalJournal of Computational Mathematics
Issue number6
Publication statusPublished - Dec 2010

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Block system of equations
  • Edge-preserving
  • Half-quadratic regularization
  • Image restoration
  • Matrix preconditioner


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