In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both shape and scale parameters, making it very flexible. theoretical analysis results in terms of null space property, spherical section property restricted invertibility factor are established for constrained unconstrained models. practical algorithms via ...

In this paper, we study the solving of gridless sparse optimization problem and its application to 3D image deconvolution. Based on recent works (Denoyelle et al, 2019) introducing Sliding Frank-Wolfe algorithm solve Beurling LASSO problem, introduce an accelerated algorithm, denoted BSFW, that preserves convergence properties, while removing most costly local descents. Besides, as BLASSO still...

Compressed Sensing (CS) is a signal acquisition approach aiming to reduce the number of measurements required to capture a sparse (or, more generally, compressible) signal. Several works have shown significant performance advantages over conventional sampling techniques, through both theoretical analyses and experimental results, and have established CS as an efficient way to acquire and recons...

For Gaussian sampling matrices, we provide bounds on the minimal number of measurements m required to achieve robust weighted sparse recovery guarantees in terms of how well a given prior model for the sparsity support aligns with the true underlying support. Our main contribution is that for a sparse vector x ∈ R supported on an unknown set S ⊂ {1, 2, . . . , N} with |S| ≤ k, if S has weighted...

We consider the following k-sparse recovery problem: design a distribution of m× n matrix A, such that for any signal x, given Ax with high probability we can efficiently recover x̂ satisfying ‖x− x̂‖1 ≤ C mink-sparse x′ ‖x− x‖1. It is known that there exist such distributions with m = O(k log(n/k)) rows; in this thesis, we show that this bound is tight. We also introduce the set query algorithm,...

Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitive algorithm for sparse recovery. Recent developments have shown that OMP guarantees exact recovery of K-sparse signals in K iterations if the observation matrix Φ satisfies the Restricted Isometry Property (RIP) with Restricted Isometry Constant (RIC) δK+1 < 1