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

Hugo Raguet , Loic Landrieu (1)

1 MATIS - Méthodes d'Analyses pour le Traitement d'Images et la Stéréorestitution

We present an extension of the cut-pursuit algorithm, introduced by Landrieu & 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.

Domaines: Machine Learning [stat.ML]

Hugo Raguet, Loic Landrieu. Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation. Thirty-sixth International Conference on Machine Learning ( ICM 2019 )L, Jun 2019, Long Beach, United States. ⟨hal-03481168⟩