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

M. Hintermüller, A. Langer

    Research output: Contribution to journalArticlepeer-review

    46 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)2134-2173
    Number of pages40
    JournalSIAM Journal on Imaging Sciences
    Volume6
    Issue number4
    DOIs
    Publication statusPublished - 30 Oct 2013

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