Preconditioned iterative methods for algebraic systems from multiplicative half-quadratic regularization image restorations

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, i.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the preconditioned conjugate gradient method, incorporated with a constraint preconditioner, is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived, which can be used to estimate the convergence speed of the preconditioned conjugate gradient method. We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.

Original languageEnglish
Pages (from-to)461-474
Number of pages14
JournalNumerical Mathematics
Volume3
Issue number4
DOIs
Publication statusPublished - Nov 2010

Scopus Subject Areas

  • Modelling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Constraint preconditioner
  • Edge-preserving
  • Eigenvalue bounds
  • Image restoration
  • Multiplicative half-quadratic regularization
  • Newton method
  • Preconditioned conjugate gradient method

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