The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees.
Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This review summarizes these major advances.
We describe the Simple Greedy Matrix Completion Algorithm providing an efficient method for restoration of low-rank matrices from incomplete corrupted entries. We provide numerical evidences that, even in the simplest implementation, the greedy approach may increase the recovery capability of existing algorithms significantly.
We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and competitive reconstruction accuracy. In the synthesis case, we also provide theoretical guarantees for the signal recovery that are on par with the existing perfect reconstruction bounds for the relaxation-based solvers and other sophisticated greedy algorithms.
Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithms
Department of Mathematics and Statistics, Concordia University（数学与统计学系，康科迪亚大学）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（应用数学与理论物理系，剑桥大学）
Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion
École Supérieure de Chimie Physique Électronique de Lyon（里昂高等化工物理电子学院）；Laboratoire Hubert Curien, UMR CNRS 5516, Université de Lyon（吕贝·居里实验室，CNRS联合研究单位5516，里昂大学）；TU Braunschweig（布伦瑞克工业大学）；Zentrum für Technomathematik, University of Bremen（不来梅大学技术数学中心）
