A Fast Fixed Point Continuation Algorithm with Application to Compressed Sensing

Fixed point continuation (FPC) algorithm is a developed version of convex optimization algorithm, which is an important research method for reconstruction of Compressed Sensing (CS). In this paper, a fast FPC (FFPC) algorithm is proposed to accelerate the convergence speed of FPC algorithm. It is introduced into an efficient shifting step, and its current iteration is updated by using special linear combination of two previous iterations. Therefore the accuracy of each iteration is improved, and the convergence speed is accelerated. In the numerical experiments, the convergence of FFPC algorithm is proven, the convergence speed of FFPC algorithm is obviously improved compared with the standard FPC algorithm, and the reconstruction quality is better than other algorithms.