The goal of this article is to promote the use of fixed point strategies in data science by
showing that they provide a simplifying and unifying framework to model, analyze, and solve …

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-
convexity modulus. Such regularizers give rise to variational denoisers that minimize a …

This paper presents a novel framework for sparse robust signal recovery integrating the
sparse recovery using the minimax concave (MC) penalty and robust regression called …

We present an efficient mathematical framework to derive promising methods that enjoy
“enhanced” desirable properties. The popular minimax concave penalty for sparse modeling …

Recently, several nonconvex sparse regularizers which can preserve the convexity of the
cost function have received increasing attention. This article proposes a general class of …

We propose a robust approach to recovering jointly sparse signals in the presence of
outliers. The robust recovery task is cast as a convex optimization problem involving a …

We propose an efficient regression method which is highly robust against outliers and stable
even in the severely noisy situations. The robustness here comes from the adoption of the …

In this paper, we address a nonconvexly constrained nonsmooth optimization problem
involving the composition of a weakly convex function and a smooth mapping. To find a …

For the sparsity-rank-aware least squares estimations, the LiGME (Linearly involved
Generalized Moreau Enhanced) model was established recently in [Abe, Yamagishi …

In this paper, we propose a unified algebraic design of the generalized Moreau
enhancement matrix (GME matrix) for the Linearly involved Generalized-Moreau-Enhanced …