Talk "Gradient Methods for Blind Ptychography" at AIP 2023
Abstract
Ptychography is an imaging technique, the goal of which is to reconstruct the object of interest from a set of diffraction patterns obtained by illuminating its small regions. When the distribution of light within the region is known, the recovery of the object from ptychographic measurements becomes a special case of the phase retrieval problem. In the other case, also known as blind ptychography, the recovery of both the object and the distribution is necessary. One of the well-known reconstruction methods for blind ptychography is extended Ptychographic Iterative Engine. Despite its popularity, there was no known analysis of its performance. Based on the fact that it is a stochastic gradient descent method, we derive its convergence guarantees if the step sizes are chosen sufficiently small. The second considered method is a generalization of the Amplitude Flow algorithm for phase retrieval, a gradient descent scheme for the minimization of the amplitude-based squared loss. By applying an alternating minimization procedure, the blind ptychography is reduced to phase retrieval subproblems, which can be solved by performing a few steps of Amplitude Flow. The resulting procedure converges to a critical point at a sublinear rate.
