Fast Iterative Algorithms for Blind Phase Retrieval: A survey

In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem, where one has to recover both the sample and the probe (pupil) jointly from phaseless data. This survey first presents the mathematical formula of BPR, related nonlinear optimization problems and then gives a brief review of the recent iterative algorithms. It mainly consists of three types of algorithms, including the operator-splitting based first-order optimization methods, second order algorithm with Hessian,and subspace methods. The future research directions for experimental issues and theoretical analysis are further discussed.