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 |
Pagination | 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 |