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 ℓp |
Abstract | In this paper we address the recovery conditions of weighted ℓp minimization for signal reconstruction from compressed sensing measurements when partial support in- formation is available. We show that weighted ℓp minimization with 0 < p < 1 is stable and robust under weaker sufficient conditions compared to weighted ℓ1 minimization. Moreover, the sufficient recovery conditions of weighted ℓp are weaker than those of regular ℓp minimization if at least 50% of the support estimate is accurate. We also review some algorithms which exist to solve the non-convex ℓp problem and illustrate our results with numerical experiments. |
URL | http://arxiv.org/abs/1311.3773 |
Citation Key | ghadermarzy2013ncs |