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

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