A self-adaptive proximal point algorithm for signal reconstruction in compressive sensing

Compressive sensing (CS) is a new framework for simulations sensing and compressive. How to reconstruct a sparse signal from limited measurements is the key problem in CS. For solving the reconstruction problem of a sparse signal, we proposed a self-adaptive proximal point algorithm (PPA). This algorithm can handle the sparse signal reconstruction by solving a substituted problem — ℓ1 problem. At last, the numerical results shows that the proposed method is more effective compared with the compressive sampling matching pursuit (CoSaMP).