Fast 2D Phase Retrieval using Bandlimited Masks

We propose a new phase retrieval algorithm for recovering 2D discrete signals from the squared magnitudes of their short-time Fourier transform measurements. The algorithm works by efficiently inverting (in FFT–time) a Fourier-based, physics-driven, and highly structured linear system to obtain relative phase information. The missing phases are subsequently recovered through the use of an eigenvector-based angular synchronization procedure. In addition to providing a deterministic measurement mask construction, the efficiency and robustness of the proposed method are demonstrated through numerical experiments.