Stable ptychographic phase retrieval via lost subspace completion

In this paper, we consider a special case of the phase retrieval problem called ptychography. Its is a popular technique of imaging, based on local illuminations of a specimen and further reconstruction from the far field diffraction patterns. The stability and success of the recovery process is heavily based on the choice of the illumination function commonly called a window. It describes the distribution of the light along the measured region. While for some windows the conditioning can be controlled, many important classes of windows, such as Gaussian windows, were not covered. We present a subspace completion method, which allows for a well-conditioned reconstruction for a much wider choice of windows, including Gaussian windows.