Non-Convex Compressed Sensing Using Partial Support Information

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