Open AccessRobust GNC approach for quantised compressed sensing
Author(s) -
Elleuch I.,
Abdelkefi F.,
Siala M.,
Hamila R.,
AlDahir N.
Publication year - 2017
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
ISSN - 1350-911X
DOI - 10.1049/el.2017.0925
Subject(s) - compressed sensing , convexity , sequence (biology) , convergence (economics) , consistency (knowledge bases) , regular polygon , distortion (music) , range (aeronautics) , algorithm , scale (ratio) , computer science , mathematical optimization , path (computing) , mathematics , artificial intelligence , engineering , amplifier , computer network , physics , geometry , bandwidth (computing) , quantum mechanics , aerospace engineering , biology , financial economics , economics , genetics , programming language , economic growth
Practical acquisition of compressed sensing measurements involves a finite‐range finite‐precision quantisation step. To solve the sparse recovery problem and handle the quantisation distortion, this Letter proposes a non‐smooth graduated‐non‐convexity approach that follows a path of gradually improved solutions along a sequence of non‐smooth non‐convex optimisation problems that progressively promote quantisation consistency (QC) and sparsity. We consider two classes of multi‐scale continuous approximation functions to depict intermediate QC degrees and sparsity‐inducing strengths, respectively, and apply recent proximal splitting methods to solve the resulting subproblem at each refinement scale. The simulations demonstrate the convergence of intermediate solutions to a nearly optimal estimation, in terms of accuracy and support recovery.