An accelerated iteration algorithm for reconstructing sparse compressed sensing data

The variable stepsize methods are effective to accelerate many iteration algorithms, one aim of them is to construct an adaptive stepsize, which has more simple and efficient format. The purpose of this paper is to introduce a new simpler variable stepsize for the CQ (Convexes C and Q) algorithm and to reconstruct the sparse compressed sensing data from noise. In order to solve the split feasibility problem with faster CQ algorithm, through analysing the former adaptive stepsizes, the paper proposed a much more simpler stepsize format, which can avoid to compute the objective function. Then, the convergence of to the new modified CQ algorithm is proved. In the experiment of reconstruct compressed sensing data, satisfied results not only show that the proposed modified stepsize can accelerate CQ algorithm better, but also give out a new method to reconstruct the sparse signal.