Fourier Phase Retrieval with Side Information Using Generative Prior

Classical methods for phase retrieval rely on prior knowledge about the support and positivity of the images. In recent years, sparse, low-rank, and generative models with spectral initialization have been proposed for various phase retrieval problems. Despite the progress, phase retrieval with structured measurements, still remains a challenging problem. In particular, Fourier phase retrieval is sensitive to the initialization and comes with inherent ambiguities about shift and flip on images. In this paper, we propose to use additional side information about the signal to initialize and regularize the phase retrieval problem. In particular, we assume that a part of the signal is known. We use the known part to initialize the estimate and incorporate the support knowledge as an additional constraint while solving the phase retrieval problem. We empirically demonstrate that our proposed method provides significant improvement over Fourier phase retrieval without side information.