Phase retrieval from multiple FRFT measurements based on nonconvex low-rank minimization

Phase retrieval (PR) problems aim to recover the phase from intensity measurements and are relevant in many applications such as X-ray crystallography and diffraction imaging. Most existing phase retrieval algorithms apply mask-based Fourier transform (FT) measurements to provide redundant information for signal reconstruction. This gives rise to a series of problems with masks such as the choice of suitable masks. In this work, we prove the rationality of multiple fractional Fourier transform (MFRFT) measurements, which can be applied to replace mask-based FT measurements. In addition, based on the low rank property (rank-1) of the desired matrix, we present a new low-rank model for PR problems using truncated nuclear norm regularization (TNNR), called TNNR-MFRFT. Extensive experiments validate the superiority of our approach over the state-of-the-art algorithms.