Wavelet decomposition method for L2/TV-image deblurring

M. Fornasier, Y. Kim, A. Langer, C.-B. Schönlieb

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Scopus)


    In this paper, we show additional properties of the limit of a sequence produced by the subspace correction algorithm proposed by Fornasier and Schönlieb [SIAM J. Numer. Anal., 47 (2009), pp. 3397--3428] for $L_2/$TV-minimization problems. An important but missing property of such a limiting sequence in that paper is the convergence to a minimizer of the original minimization problem, which was obtained in [M. Fornasier, A. Langer, and C.-B. Schönlieb, Numer. Math., 116 (2010), pp. 645--685] with an additional condition of overlapping subdomains. We can now determine when the limit is indeed a minimizer of the original problem. Inspired by the work of Vonesch and Unser [IEEE Trans. Image Process., 18 (2009), pp. 509--523], we adapt and specify this algorithm to the case of an orthogonal wavelet space decomposition for deblurring problems and provide an equivalence condition to the convergence of such a limiting sequence to a minimizer. We also provide a counterexample of a limiting sequence by the algorithm that does not converge to a minimizer, which shows the necessity of our analysis of the minimizing algorithm.

    Original languageEnglish
    Pages (from-to)857-885
    Number of pages29
    JournalSIAM Journal on Imaging Sciences
    Issue number3
    Publication statusPublished - 17 Jul 2012


    • image deblurring
    • wavelet decomposition method
    • convex optimization
    • oblique thresholding
    • total variation minimization
    • alternating minimization


    Dive into the research topics of 'Wavelet decomposition method for L2/TV-image deblurring'. Together they form a unique fingerprint.

    Cite this