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 paper reviews the state-of-the-art in denoising methods for biological microscopy
images and introduces a new and original sparsity-based algorithm. The proposed method …

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 …

The nuclear norm is widely used to induce low-rank solutions for many optimization
problems with matrix variables. Recently, it has been shown that the augmented Lagrangian …

Much research has been devoted to the problem of restoring Poissonian images, namely for
medical and astronomical applications. However, the restoration of these images using state …

We consider the linearly constrained separable convex minimization problem whose
objective function is separable into m individual convex functions with nonoverlapping …

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 …

Multiplicative noise (also known as speckle noise) models are central to the study of
coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and …

We propose a new plug-and-play image restoration method based on primal-dual splitting.
Existing plug-and-play image restoration methods interpret any off-the-shelf Gaussian …

In this paper, we study alternating direction methods for solving constrained total-variation
image restoration and reconstruction problems. Alternating direction methods can be …