A convergent overlapping domain decomposition method for total variation minimization

M. Fornasier, A. Langer, C.-B. Schönlieb

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Abstract

In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such a strategy for the nonlinear, nonadditive, and nonsmooth problem of total variation minimization. We provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D images in interpolation/inpainting problems, respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.
Original languageEnglish
Pages (from-to)645–685
Number of pages41
JournalNumerische Mathematik
Volume116
Early online date22 Jun 2010
DOIs
Publication statusPublished - Oct 2010
Externally publishedYes

Bibliographical note

This article is published under an open access license.

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