On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation

Tony Chan*, Ke Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a 'local' non-stationary minimum of the solution, which is usually believed to be 'non-smooth'. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.

Original languageEnglish (US)
Pages (from-to)387-411
Number of pages25
JournalNumerical Algorithms
Volume41
Issue number4
DOIs
StatePublished - Apr 1 2006

Keywords

  • Image restoration
  • Nonlinear solvers
  • Primal relaxation
  • Regularisation
  • Total variation

ASJC Scopus subject areas

  • Applied Mathematics

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