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Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation

Hugo Raguet (hugo.raguet***at***lilo.org)
Landrieu Loc (Loic.Landrieu***at***ign.fr)

Abstract: We present an extension of the cut-pursuit algorithm, introduced by Landrieu and Obozinski (2017), to the graph total-variation regularization of functions with a separable nondifferentiable part. We propose a modified algorithmic scheme as well as adapted proofs of convergence. We also present a heuristic approach for handling the cases in which the values associated to each vertex of the graph are multidimensional. The performance of our algorithm, which we demonstrate on difficult, ill-conditioned large-scale inverse and learning problems, is such that it may in practice extend the scope of application of the total-variation regularization.

Keywords: total variation; nonsmooth optimization; graph cut; brain source identification;

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Applications -- Science and Engineering (Biomedical Applications )

Category 3: Applications -- Science and Engineering (Data-Mining )

Citation: 2018

Download: [PDF]

Entry Submitted: 02/11/2018
Entry Accepted: 02/11/2018
Entry Last Modified: 10/25/2018

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