Subspace Correction Methods for a Class of Nonsmooth and Nonadditive Convex Variational Problems with Mixed L1/L2 Data-Fidelity in Image Processing
Subspace Correction Methods for a Class of Nonsmooth and Nonadditive Convex Variational Problems with Mixed L1/L2 Data-Fidelity in Image Processing
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DOI：
10.1137/120894130
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发表时间：
2013-01-01
影响因子：
2.1
通讯作者：
Langer, Andreas
中科院分区：
文献类型：
--
作者：
Hintermueller, Michael;Langer, Andreas
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.
