On convergence of Ptychographic Iterative Engine for STFT phase retrieval

Abstract

We consider a recovery from ptychographic measurements also known as the Short-Time Fourier Transform (STFT) phase retrieval. That is the unknown object of interest has to be reconstructed from as a set of diffraction patterns resulting from a series of localized illuminations. In this paper we study Ptychographic Iterative Engine (PIE), a popular iterative algorithm among practitioners, which uses the measurements corresponding to a single illumination at the time. We show that PIE is the stochastic gradient descent applied to the amplitude-based squared loss and derive its sublinear convergence guarantees.