Optimization methods are at the core of many problems in signal/image processing,
computer vision, and machine learning. For a long time, it has been recognized that looking …

This article reviews the use of first order convex optimization schemes to solve the
discretized dynamic optimal transport problem, initially proposed by Benamou and Brenier …

A large number of imaging problems reduce to the optimization of a cost function, with
typical structural properties. The aim of this paper is to describe the state of the art in …

This monograph is about a class of optimization algorithms called proximal algorithms. Much
like Newton's method is a standard tool for solving unconstrained smooth optimization …

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 …

This paper introduces a generalized forward-backward splitting algorithm for finding a zero
of a sum of maximal monotone operators B+i=1^nA_i, where B is cocoercive. It involves the …

Algorithms for signal denoising that combine wavelet-domain sparsity and total variation
(TV) regularization are relatively free of artifacts, such as pseudo-Gibbs oscillations …

The easy-to-compute Anscombe transform offers a conversion of a Poisson random variable
into a variance stabilized Gaussian one, thus becoming handy in various Poisson-noisy …

The ℓ 1/ℓ 2 ratio regularization function has shown good performance for retrieving sparse
signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits …

This paper addresses signal denoising when large-amplitude coefficients form clusters
(groups). The L1-norm and other separable sparsity models do not capture the tendency of …