Flexible GMRES for Total Variation regularization

Research output: Contribution to journalArticle

Abstract

This paper presents a novel approach to the regularization of linear problems involving total variation (TV) penalization, with a particular emphasis on image deblurring applications. The starting point of the new strategy is an approximation of the non-differentiable TV regularization term by a sequence of quadratic terms, expressed as iteratively reweighted 2-norms of the gradient of the solution. The resulting problem is then reformulated as a Tikhonov regularization problem in standard form, and solved by an efficient Krylov subspace method. Namely, flexible GMRES is considered in order to incorporate new weights into the solution subspace as soon as a new approximate solution is computed. The new method is dubbed TV-FGMRES. Theoretical insight is given, and computational details are carefully unfolded. Numerical experiments and comparisons with other algorithms for TV image deblurring, as well as other algorithms based on Krylov subspace methods, are provided to validate TV-FGMRES.
Original languageEnglish
Pages (from-to)721-746
Number of pages26
JournalBIT Numerical Mathematics
Volume59
Issue number3
Early online date2 Apr 2019
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • Flexible GMRES
  • Image deblurring
  • Smoothing-norm preconditioning
  • TV regularization

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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