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Pré-Publication, Document De Travail Année : 2020

Distributed Algorithms for Scalable Proximity Operator Computation and Application to Video Denoising

Résumé

Optimization problems arising in signal and image processing involve an increasingly large number of variables. In addition to the curse of dimensionality, another difficulty to overcome is that the cost function usually reads as the sum of several loss/regularization terms, non-necessarily smooth and possibly composed with large-size linear operators. Proximal splitting approaches are fundamental tools to address such problems, with demonstrated efficiency in many applicative fields. In this paper, we present a new distributed algorithm for computing the proximity operator of a sum of non-necessarily smooth convex functions composed with arbitrary linear operators. Our algorithm relies on a primal-dual splitting strategy, and benefits from established convergence guaranties. Each involved function is associated with a node of a hypergraph, with the ability to communicate with neighboring nodes sharing the same hyperedge. Thanks to this structure, our method can be efficiently implemented on modern parallel computing architectures, allowing to distribute computations on different nodes or machines while limiting the need for synchronization steps. Its good numerical performance and scalability properties are illustrated on a problem of video sequence denoising.
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Dates et versions

hal-03684063 , version 1 (13-12-2018)
hal-03684063 , version 2 (13-02-2020)
hal-03684063 , version 3 (01-06-2022)

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  • HAL Id : hal-03684063 , version 2

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Feriel Abboud, Emilie Chouzenoux, Jean-Christophe Pesquet, Hugues Talbot. Distributed Algorithms for Scalable Proximity Operator Computation and Application to Video Denoising. 2020. ⟨hal-03684063v2⟩
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