Quantization and Greed are Good: One bit Phase Retrieval, Robustness and Greedy Refinements

Abstract: In this paper, we study the problem of robust phase recovery. We investigate a novel approach based on extremely quantized (one-bit) phase-less measurements and a corresponding recovery scheme. The proposed approach has surprising robustness and stability properties and, unlike currently available methods, allows to efficiently perform phase recovery from measurements affected by severe (possibly unknown) non-linear perturbations, such as distortions (e.g. clipping). Beyond robustness, we show how our approach can be used within greedy approaches based on alternating minimization. In particular, we propose novel initialization schemes for the alternating minimization achieving favorable convergence properties with improved sample complexity.