Single-Shot Fractional Fourier Phase Retrieval

Traditional phase retrieval is generally concerned with recovering a signal from its Fourier magnitude measurements whose inherent ambiguities make this problem especially difficult. In this work, we present an efficient phase retrieval technique from the single fractional Fourier transform (FrFT) magnitude measurement. Specifically, the FrFT measurement can be well-combined with signal priors via a generalized alternating projection framework, which can effectively alleviate the ambiguities of phase retrieval and the stagnation problem of numerical iterative processes. Through numerical simulations, we demonstrate that reconstructing an image from the single FrFT measurement leads to a significant performance improvement over that from the Fourier transform magnitude by using the proposed method. The source code is available at https://github.com/Yixiao-Yang/SFrFPR.