A convergent overlapping domain decomposition method for total variation minimization

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

doi:10.1007/s00211-010-0314-7

A convergent overlapping domain decomposition method for total variation minimization

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

Austrian Academy of Sciences
University of Göttingen

Research output: Contribution to journal › Article › peer-review

41 Citations (Scopus)

110 Downloads (Pure)

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 language	English
Pages (from-to)	645–685
Number of pages	41
Journal	Numerische Mathematik
Volume	116
Early online date	22 Jun 2010
DOIs	https://doi.org/10.1007/s00211-010-0314-7
Publication status	Published - Oct 2010
Externally published	Yes

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AB - 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.

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A convergent overlapping domain decomposition method for total variation minimization

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