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Subspace correction methods for a class of nonsmooth and nonadditive convex variational problems with mixed L1/L2 data-fidelity in image processing

Hintermüller, Michael and Langer, Andreas LU (2013) In SIAM Journal on Imaging Sciences 6(4). p.2134-2173
Abstract

The minimization of a functional composed of a nonsmooth and nonadditive regularization term and a combined L1 and L2 data-fidelity term is proposed. It is shown analytically and numerically that the new model has noticeable advantages over popular models in image processing tasks. For the numerical minimization of the new objective, subspace correction methods are introduced which guarantee the convergence and monotone decay of the associated energy along the iterates. Moreover, an estimate of the distance between the outcome of the subspace correction method and the global minimizer of the nonsmooth objective is derived. This estimate and numerical experiments for image denoising, inpainting, and deblurring... (More)

The minimization of a functional composed of a nonsmooth and nonadditive regularization term and a combined L1 and L2 data-fidelity term is proposed. It is shown analytically and numerically that the new model has noticeable advantages over popular models in image processing tasks. For the numerical minimization of the new objective, subspace correction methods are introduced which guarantee the convergence and monotone decay of the associated energy along the iterates. Moreover, an estimate of the distance between the outcome of the subspace correction method and the global minimizer of the nonsmooth objective is derived. This estimate and numerical experiments for image denoising, inpainting, and deblurring indicate that in practice the proposed subspace correction methods indeed approach the global solution of the underlying minimization problem.

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author
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publishing date
type
Contribution to journal
publication status
published
subject
keywords
Combined L/L data-fidelity, Convergence analysis, Convex optimization, Domain decomposition, Gaussian noise, Image restoration, Impulse noise, Mixed noise, Subspace correction, Total variation minimization
in
SIAM Journal on Imaging Sciences
volume
6
issue
4
pages
40 pages
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • scopus:84891116294
ISSN
1936-4954
DOI
10.1137/120894130
language
English
LU publication?
no
additional info
Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
id
5a8c77e6-45f1-47ba-9655-7796eced5396
date added to LUP
2021-03-15 22:33:01
date last changed
2022-03-19 00:02:48
@article{5a8c77e6-45f1-47ba-9655-7796eced5396,
  abstract     = {{<p>The minimization of a functional composed of a nonsmooth and nonadditive regularization term and a combined L<sup>1</sup> and L<sup>2</sup> data-fidelity term is proposed. It is shown analytically and numerically that the new model has noticeable advantages over popular models in image processing tasks. For the numerical minimization of the new objective, subspace correction methods are introduced which guarantee the convergence and monotone decay of the associated energy along the iterates. Moreover, an estimate of the distance between the outcome of the subspace correction method and the global minimizer of the nonsmooth objective is derived. This estimate and numerical experiments for image denoising, inpainting, and deblurring indicate that in practice the proposed subspace correction methods indeed approach the global solution of the underlying minimization problem.</p>}},
  author       = {{Hintermüller, Michael and Langer, Andreas}},
  issn         = {{1936-4954}},
  keywords     = {{Combined L/L data-fidelity; Convergence analysis; Convex optimization; Domain decomposition; Gaussian noise; Image restoration; Impulse noise; Mixed noise; Subspace correction; Total variation minimization}},
  language     = {{eng}},
  month        = {{10}},
  number       = {{4}},
  pages        = {{2134--2173}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Imaging Sciences}},
  title        = {{Subspace correction methods for a class of nonsmooth and nonadditive convex variational problems with mixed L<sup>1</sup>/L<sup>2</sup> data-fidelity in image processing}},
  url          = {{http://dx.doi.org/10.1137/120894130}},
  doi          = {{10.1137/120894130}},
  volume       = {{6}},
  year         = {{2013}},
}