Open AccessBlock‐sparse compressed sensing with partially known signal support via non‐convex minimisation
Author(s) -
He Shiying,
Wang Yao,
Wang Jianjun,
Xu Zongben
Publication year - 2016
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.2015.0425
Subject(s) - restricted isometry property , compressed sensing , minimisation (clinical trials) , signal recovery , mathematics , algorithm , a priori and a posteriori , gaussian , regular polygon , basis pursuit , sparse approximation , upper and lower bounds , norm (philosophy) , computer science , statistics , mathematical analysis , matching pursuit , geometry , physics , philosophy , epistemology , quantum mechanics , political science , law
The mixed l 2 / l p (0 < p ≤ 1) norm minimisation method with partially known support for recovering block‐sparse signals is studied. The authors mainly extend this work on block‐sparse compressed sensing by incorporating some known part of the block support information as a priori and establish sufficient restricted p ‐isometry property ( p ‐RIP) conditions for exact and robust recovery. The authors’ theoretical results show it is possible to recover the block‐sparse signals via l 2 / l p minimisation from reduced number of measurements by applying the partially known support. The authors also derive a lower bound on necessary random Gaussian measurements for the p ‐RIP conditions to hold with high possibility. Finally, a series of numerical experiments are carried out to illustrate that fewer measurements with smaller p are needed to reconstruct the signal.