Journal
SIAM JOURNAL ON IMAGING SCIENCES
Volume 6, Issue 4, Pages 2134-2173Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120894130
Keywords
subspace correction; domain decomposition; total variation minimization; convex optimization; image restoration; combined L-1/L-2 data-fidelity; convergence analysis; impulse noise; Gaussian noise; mixed noise
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Funding
- Austrian Science Fund FWF through the START Project [Y 305-N18]
- SFB Project [F32 04-N18]
- German Research Fund (DFG) through the Research Center MATHEON Project
- Institute for Computational Engineering and Sciences (ICES) at UT Austin, TX
- [SPP 1253]
- Austrian Science Fund (FWF) [Y 305, F 3204] Funding Source: researchfish
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The minimization of a functional composed of a nonsmooth and nonadditive regularization term and a combined L 1 and L 2 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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