A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models

Qia Li, Charles A. Micchelli, Lixin Shen, Yuesheng Xu

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


Our goal in this paper is to improve the computational performance of the proximity algorithms for the L1/TV denoising model. This leads us to a new characterization of all solutions to the L1/TV model via fixed-point equations expressed in terms of the proximity operators. Based upon this observation we develop an algorithm for solving the model and establish its convergence. Furthermore, we demonstrate that the proposed algorithm can be accelerated through the use of the componentwise Gauss-Seidel iteration so that the CPU time consumed is significantly reduced. Numerical experiments using the proposed algorithm for impulsive noise removal are included, with a comparison to three recently developed algorithms. The numerical results show that while the proposed algorithm enjoys a high quality of the restored images, as the other three known algorithms do, it performs significantly better in terms of computational efficiency measured in the CPU time consumed.

Original languageEnglish (US)
Article number095003
JournalInverse Problems
Issue number9
StatePublished - Sep 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


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