Non-Convex Compressed Sensing Using Partial Support Information

摘要

In this paper we address the recovery conditions of weighted ℓ_p minimization for signal reconstruction from compressed sensing measurements when partial support in­formation is available. We show that weighted ℓ_p minimization with 0 ＜ p ＜ 1 is stable and robust under weaker sufficient conditions compared to weighted ℓ_1 minimization. Moreover, the sufficient recovery conditions of weighted ℓ_p are weaker than those of regular ℓ_p minimization if at least 50% of the support estimate is accurate. We also review some algorithms which exist to solve the non-convex l_p problem and illustrate our results with numerical experiments.