Global One-Bit Phase Retrieval via Sample Abundance-Including an Application to STFT Measurements

We introduce a novel technique for reconstructing signals from phaseless measurements obtained through one-bit ADCs. Our approach adopts the Sampling Kaczmarz-Motzkin algorithm to efficiently and globally optimize the phase retrieval objective. In particular, it utilizes the sample abundance provided in one-bit sensing with time-varying thresholds to overcome the limitations of traditional convex phase retrieval methods, such as costly semi-definiteness and rank constraints. Additionally, our approach eliminates the need for lifting up the unknown signal, leading to further computationally efficiency. We demonstrate the effectiveness of our technique by successfully recovering the signal of interest from one-bit sampled short-time Fourier transform magnitudes-an interesting problem that has not been adequately addressed prior to this work. The results not only demonstrate the success of our approach in the context of phase retrieval but also the potential of one-bit sampling and the associated sample abundance gains in information processing at large.