Subspace correction methods for a class of nonsmooth and nonadditive convex variational problems with mixed L1/L2 data-fidelity in image processing
(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.
(Less)
- author
- Hintermüller, Michael and Langer, Andreas LU
- publishing date
- 2013-10-30
- 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}}, }