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
Keywordscompressed sensing, nonconvex optimization, sparse reconstruction, weighted $\ell_p$

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.

Citation Keyghadermarzy2013ncs