A STOCHASTIC ALTERNATING MINIMIZATION METHOD FOR SPARSE PHASE RETRIEVAL

Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a stochastic alternating minimization method for sparse phase retrieval (StormSpar) algorithm which empirically is able to recover n-dimensional s-sparse signals from only O(s log n) measurements without a desired initial value required by many existing methods. In StormSpar, the hard-thresholding pursuit (HTP) algorithm is employed to solve the sparse constrained least-square sub-problems. The main competitive feature of StormSpar is that it converges globally requiring optimal order of number of samples with random initialization. Extensive numerical experiments are given to validate the proposed algorithm.