An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration

M. Hintermüller, Georg Stadler

Research output: Contribution to journalArticle

Abstract

In this paper, a primal-dual algorithm for total bounded variation (TV)-type image restoration is analyzed and tested. Analytically it turns out that employing a global Lsregularization, with 1 < s ≤ 2, in the dual problem results in a local smoothing of the TVregularization term in the primal problem. The local smoothing can alternatively be obtained as the inflmal convolution of the ℓr-norm, with r-1 + s -1 = 1, and a smooth function. In the case r = s = 2, this results in Gauss-TV-type image restoration. The globalized primal-dual algorithm introduced in this paper works with generalized derivatives, converges locally at a superlinear rate, and is stable with respect to noise in the data. In addition, it utilizes a projection technique which reduces the size of the linear system that has to be solved per iteration. A comprehensive numerical study ends the paper.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalSIAM Journal on Scientific Computing
Volume28
Issue number1
DOIs
StatePublished - 2006

Fingerprint

Inf-convolution
Local Smoothing
Primal-dual Algorithm
Bounded variation
Image Restoration
Image reconstruction
Convolution
Generalized Derivatives
Dual Problem
Smooth function
Gauss
Linear systems
Numerical Study
Linear Systems
Projection
Derivatives
Converge
Iteration
Norm
Term

Keywords

  • Fenchel duality
  • Generalized newton-type methods
  • Image restoration
  • Total bounded variation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

An infeasible primal-dual algorithm for total bounded variation-based inf-convolution-type image restoration. / Hintermüller, M.; Stadler, Georg.

In: SIAM Journal on Scientific Computing, Vol. 28, No. 1, 2006, p. 1-23.

Research output: Contribution to journalArticle

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