Paper Info
Title
Sparse Recovery Analysis Of J-Minimization For Sparsity Promoting Functions With Monotonic Elasticity
Abstract
In this paper we theoretically study exact recovery of a sparse vector from compressed linear measurements by minimizing certain nonconvex function of the unknown vector, which can be decomposed into sum of sparsity promoting functions of the coordinates. Null space property (NSP) and restricted isometry property (RIP) are used as key theoretical tools to study recovery performance. The notion of scale function associated to a sparsity promoting function is introduced to generalize the state-of-the-art analysis technique of the lp minimization problem. Using such analysis, we derive a common general bound on the associated null space constant (NSC) which is used to find upper bounds on the restricted isometry constant (RIC) as well as the optimal sparsity, all ensuring exact recovery. The derived bounds are explicitly evaluated when the sparsity promoting function f has an associated monotonic elasticity function , defined as, psi(x) = xdf(x)/dx/f(x) . Numerical simulations are carried out to verify the efficacy of the bounds. Furthermore, interesting conclusions are drawn about the comparative performances of different sparsity promoting functions for the specific problem of 1-sparse signal recovery. (C) 2020 Elsevier B.V. All rights reserved.
Year
DOI
Venue
2021
10.1016/j.sigpro.2020.107853
SIGNAL PROCESSING
Keywords
DocType
Volume
Generalized nonconvex minimization, Sparsity promoting function, Null space property (NSP), Restricted isometry property (RIP)
Journal
180
ISSN
Citations 
PageRank 
0165-1684
0
0.34
References 
Authors
0
1
Name
Order
Citations
PageRank
Samrat Mukhopadhyay111.79