Weighted and Reweighted Approximate Message Passing

In this paper we derive weighted and reweighted AMP algorithms for signal reconstruction from compressed sensing measurements. Weighted AMP incorporates prior support information into the AMP algorithm and iteratively solves the weighted l(1) minimization which is much faster than the usual linear programming algorithms used to solve this problem. We also introduce a reweighting scheme for regular and weighted AMP algorithms which enhances the recovery performance of both regular and weighted AMP while still maintaining the low complexity nature of AMP algorithms.