Fast algorithms for l1 norm/mixed l1 and l2 norms for image restoration

Haoying Fu, Michael K. Ng, Mila Nikolova, Jesse Barlow, Wai Ki Ching

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations

Abstract

Image restoration problems are often solved by finding the minimizer of a suitable objective function. Usually this function consists of a data-fitting term and a regularization term. For the least squares solution, both the data-fitting and the regularization terms are in the ℓ2 norm. In this paper, we consider the least absolute deviation (LAD) solution and the least mixed norm (LMN) solution. For the LAD solution, both the data-fitting and the regularization terms are in the ℓ1 norm. For the LMN solution, the regularization term is in the ℓ1 norm but the data-fitting term is in the ℓ2 norm. The LAD and the LMN solutions are formulated as the solutions of a linear and a quadratic programming problems respectively, and solved by interior point methods. At each iteration of the interior point method, a structured linear system must be solved. The preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to such structured inner systems. Experimental results are used to demonstrate the effectiveness of our approach. We also show the quality of the restored images using the minimization of ℓ1 norm/mixed ℓ1 and ℓ2 norms is better than that using ℓ2 norm approach.

Original languageEnglish (US)
Pages (from-to)843-851
Number of pages9
JournalLecture Notes in Computer Science
Volume3483
Issue numberIV
DOIs
StatePublished - 2005
EventInternational Conference on Computational Science and Its Applications - ICCSA 2005 - , Singapore
Duration: May 9 2005May 12 2005

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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