# Non-convex compressed sensing using partial support information

 Title Non-convex compressed sensing using partial support information Publication Type Journal Article Year of Publication 2014 Authors Navid Ghadermarzy, Hassan Mansour, Ozgur Yilmaz Journal Journal of Sampling Theory in Signal and Image Processing Volume 13 Number 3 Page 249-270 Keywords compressed 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. URL http://arxiv.org/abs/1311.3773 Citation Key ghadermarzy2013ncs