Related papers: Fast L1-L2 minimization via a proximal operator

The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…

This paper considers a class of structured fractional minimization problems. The numerator consists of a differentiable function, a simple nonconvex nonsmooth function, a concave nonsmooth function, and a convex nonsmooth function composed…

Longest Common Subsequence ($LCS$) deals with the problem of measuring similarity of two strings. While this problem has been analyzed for decades, the recent interest stems from a practical observation that considering single characters is…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

We present a new approach to solve the sparse approximation or best subset selection problem, namely find a $k$-sparse vector ${\bf x}\in\mathbb{R}^d$ that minimizes the $\ell_2$ residual $\lVert A{\bf x}-{\bf y} \rVert_2$. We consider a…

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…

In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on…

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely…

This paper introduces a nonconvex approach for sparse signal recovery, proposing a novel model termed the $\tau_2$-model, which utilizes the squared $\ell_1/\ell_2$ norms for this purpose. Our model offers an advancement over the $\ell_0$…

Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…

We discuss how to evaluate the proximal operator of a convex and increasing function of a nuclear norm, which forms the key computational step in several first-order optimization algorithms such as (accelerated) proximal gradient descent…

Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation…

In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be…

Sparse signal recovery based on nonconvex and nonsmooth optimization problems has significant applications and demonstrates superior performance in signal processing and machine learning. This work deals with a scale-invariant…

A popular robust alternative of the classic principal component analysis (PCA) is the $\ell_1$-norm PCA (L1-PCA), which aims to find a subspace that captures the most variation in a dataset as measured by the $\ell_1$-norm. L1-PCA has shown…

We develop a Recursive $\mathcal{L}_1$-Regularized Least Squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight…

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…

Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision or biomedical imaging. One of the main challenges to perform this task is to design efficient numerical…

We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We prove its convergence and we estimate its local rate. We show how the algorithm can be…