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 …

We propose a new first-order splitting algorithm for solving jointly the primal and dual
formulations of large-scale convex minimization problems involving the sum of a smooth …

This book presents the state of the art in sparse and multiscale image and signal processing,
covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and …

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 …

Observations in many applications consist of counts of discrete events, such as photons
hitting a detector, which cannot be effectively modeled using an additive bounded or …

The restoration of blurred images corrupted by Poisson noise is an important task in various
applications such as astronomical imaging, electronic microscopy, single particle emission …

We propose a convergence analysis of accelerated forward-backward splitting methods for
composite function minimization, when the proximity operator is not available in closed form …

This thoroughly updated new edition presents state of the art sparse and multiscale image
and signal processing. It covers linear multiscale geometric transforms, such as wavelet …

Regularization approaches have demonstrated their effectiveness for solving ill-posed
problems. However, in the context of variational restoration methods, a challenging question …

This paper describes performance bounds for compressed sensing (CS) where the
underlying sparse or compressible (sparsely approximable) signal is a vector of …