• Abboud, Feriel
• Stamm, Marin
• Chouzenoux, Emilie
• Pesquet, Jean-Christophe
• Talbot, Hugues

Abstract

Optimization problems arising in signal and image processing involve an increasingly large number of variables. Inaddition to the curse of dimensionality, another difficulty to overcome is that the cost function usually reads as thesum of several loss/regularization terms, which are non-necessarily smooth and possibly composed with large-sizelinear operators. Proximal splitting approaches are fundamental tools to address such problems, with demonstratedefficiency in many applicative fields. In this paper, we present a new distributed algorithm for computing theproximity operator of a sum of non-necessarily smooth convex functions composed with arbitrary linear operators. Ouralgorithm relies on a primal-dual splitting strategy, and benefits from established convergence guaranties. Eachinvolved function is associated with a node of a hypergraph, with the ability to communicate with neighboring nodessharing the same hyperedge. Thanks to this structure, our method can be efficiently implemented on modern parallelcomputing architectures, distributing the computations on multiple nodes or machines, with controlled requirementsfor synchronization steps. Good numerical performance and scalability properties are demonstrated on a problem ofvideo sequence denoising. Our code implemented in Julia is made available at {https://github.com/MarinENSTA/distributed_julia_denoising}.

Topics

• impedance spectroscopy