Consider the phase retrieval problem with many outliers. Without outliers and with a small fraction of outliers, PhaseLift is known to recover a vector exactly, with high probability, under a linear number of Gaussian measurements. In the present paper, we study the robustness of PhaseLift to significant corruptions in the scenario where the majority of measurements are outliers, and where each outlier is above or below its true value with equal probability. We prove that PhaseLift can tolerate noise and arbitrarily small values of the fraction of uncorrupted measurements.
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