2013/02/03 by Siddhartha Satpathi, Rajib Lochan Das, Mrityunjoy Chakraborty · 30 citations
Computer Science · Engineering · Mathematics · #Compressed sensing #Constant (computer programming) #Greedy algorithm #Isometry (Riemannian geometry) #Matching pursuit #Matrix (chemical analysis) #Matrix Theory and Algorithms #Restricted isometry property #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Upper and lower bounds #cs.IT #math.IT
paper · pdf · doi:10.1109/lsp.2013.2279977
published in IEEE Signal Processing Letters 20(11), 1074-1077 (Institute of Electrical and Electronics Engineers) · 8 pages, 1 figure
arxiv created 2013/02/03 · openalex publication_date 2013/08/29 · arxiv updated 2015/06/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The generalized Orthogonal Matching Pursuit (gOMP) is a recently proposed compressive sensing greedy recovery algorithm which generalizes the OMP algorithm by selecting N( ≥ 1) atoms in each iteration. In this letter, we demonstrate that the gOMP can successfully reconstruct a K-sparse signal from a compressed measurement y=Φx by a maximum of K iterations if the sensing matrix Φ satisfies the Restricted Isometry Property (RIP) of order NK, with the RIP constant δNKsatisfying δNKNK. We also show that by increasing the RIP order just by one (i.e., NK+1 from NK), it is possible to refine the bound further to δNK+1K+1in OMP.