Jean-Christophe Pesquet

Abstract: The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems, has recently been introduced in the arena of signal processing, where it has become increasingly important. In this paper, we review the basic properties of proximity operators which are relevant to signal processing and present optimization methods based on these operators. These proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. Applications of proximal methods in signal recovery and synthesis are discussed.

TL;DR: The basic properties of proximity operators which are relevant to signal processing and optimization methods based on these operators are reviewed and proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework.

TL;DR: A decomposition method based on the Douglas-Rachford algorithm for monotone operator-splitting for signal recovery problems and applications to non-Gaussian image denoising in a tight frame are demonstrated.

TL;DR: This work addresses the time-invariance problem for orthonormal wavelet transforms and proposes an extension to wavelet packet decompositions to achieve time invariance and preserve the orthonormality.

TL;DR: A primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators was proposed in this paper.