Cut-pursuit algorithm for regularizing nonsmooth functionals with graph total variation

Date(s) : 22/06/2018   iCal
14 h 00 min - 15 h 00 min

I will 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.

This is a joint work with Loïc Landrieu (IGN, LaSTIG MATIS).

Landrieu, L. and Obozinski, G. « [Cut pursuit: Fast algorithms to learn piecewise
constant functions on general weighted graphs->] ». SIAM Journal on Imaging
Sciences, 10(4):1724–1766, 2017.

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