Phase retrieval via Sparse Wirtinger Flow

Abstract

Phase retrieval (PR) problem is an inverse problem which arises in various applications. Based on the Wirtinger flow method, an algorithm utilizing the sparsity priority called SWF (Sparse Wirtinger Flow) is proposed in this paper to deal with the PR problem. Firstly, the support of the signal is estimated besides the initialization is evaluated based on this support. Then the evaluation is updated by the hard-thresholding method from this initialization. We prove that for any k -sparse signal with length n , SWF has a linear convergence with O ( k 2 log n ) phaseless Gaussian random measurements. To get ε accuracy, the computational complexity of SWF is O ( k 3 n log n log 1 ε ) . Numerical tests also demonstrate that SWF has a higher recovery rate than other algorithms compared especially when we have no prior information about sparsity k . Moreover, SWF is robust to the noise.