Non-convex compressed sensing using partial support information

TitleNon-convex compressed sensing using partial support information
Publication TypeJournal Article
Year of Publication2014
AuthorsNavid Ghadermarzy, Hassan Mansour, Ozgur Yilmaz
JournalJournal of Sampling Theory in Signal and Image Processing
Volume13
Pagination249-270
Keywordscompressed sensing, nonconvex optimization, sparse reconstruction, weighted $\ell_p$
Abstract

In this paper we address the recovery conditions of weighted $\ell_p$ minimization for signal reconstruction from compressed sensing measurements when partial support in- formation is available. We show that weighted $\ell_p$ minimization with 0 < p < 1 is stable and robust under weaker sufficient conditions compared to weighted $\ell_1$ minimization. Moreover, the sufficient recovery conditions of weighted $\ell_p$ are weaker than those of regular $\ell_p$ minimization if at least 50% of the support estimate is accurate. We also review some algorithms which exist to solve the non-convex $\ell_p$ problem and illustrate our results with numerical experiments.

URLhttp://arxiv.org/abs/1311.3773
Citation Keyghadermarzy2013ncs