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

TL;DR

This paper extends the cut-pursuit algorithm to efficiently handle graph total-variation regularization for nonsmooth functions, improving its applicability to large-scale inverse and learning problems.

Contribution

The authors propose a modified cut-pursuit algorithm with convergence proofs and a heuristic for multidimensional vertex values, broadening its practical use.

Findings

Effective on large-scale inverse problems

Handles multidimensional vertex data

Extends total-variation regularization scope

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.