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In this paper we show additional properties of the limit of the sequence produced by the subspace correction algorithm proposed by Fornasier and Schönlieb [24] for L 2 /T V-minimization problems. Inspired by the work of Vonesch and Unser [34], we adapt and specify this algorithm to the case of an orthogonal wavelet space decomposition and for deblurring(More)
In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of func-tionals formed by a discrepancy term with respect to the data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such a strategy for the nonlinear,(More)
We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the(More)
Computational problems of large-scale appearing in biomedical imaging, astronomy, art restoration, and data analysis are gaining recently a lot of attention due to better hardware , higher dimensionality of images and data sets, more parameters to be measured, and an increasing number of data acquired. In the last couple of years non-smooth minimization(More)
The minimization of a functional composed of a non-smooth and non-additive 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(More)
Introduction. The main object of study in this paper with respect to zero-cycles is a special class of Hilbert-Blumenthal surfaces X, which are defined over Q as smooth compactifications of quasi-projective varieties S/Q, more precisely, of coarse moduli schemes S that represent the moduli stack of polarized abelian surfaces with real multiplication by the(More)
In this paper non-overlapping domain decomposition methods for the pre-dual total variation minimization problem are introduced. Both parallel and sequential approaches are proposed for these methods for which convergence to a minimizer of the original problem is established. The associated subproblems are solved by a semi-smooth Newton method. Several(More)