Open AccessSufficient condition for exact support recovery of sparse signals through greedy block coordinate descent
Author(s) -
Li Haifeng,
Liu Guoqi,
Zou Jian
Publication year - 2019
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2018.5123
Subject(s) - coordinate descent , greedy algorithm , block (permutation group theory) , computer science , descent (aeronautics) , algorithm , mathematical optimization , artificial intelligence , mathematics , combinatorics , engineering , aerospace engineering
In the underdetermined modelY ^= A X + N , where X is a K ‐group sparse matrix (i.e. it has no more than K non‐zero rows), the matrix A may be also perturbed. Theoretically, a more relaxed condition means that fewer measurements are required to ensure sparse recovery. In this study, a relaxed sufficient condition is proposed for greedy block coordinate descent (GBCD) under total perturbations based on the restricted isometry property in order to guarantee that the support of X is recovered. We also show that GBCD fails in a more general case when 1 / ( K + 1 ) ≤ δ K + 1 < 1 .