On the randomized Kaczmarz algorithm for phase retrieval

Abstract

We investigate a variant of the randomized Kaczmarz algorithm as a method for solving the phase retrieval problem. The main contribution of this paper is a recovery guarantee for phase retrieval from measurements perturbed with additive noise via the randomized Kaczmarz algorithm. We consider the scenario that the measurement vectors are drawn independently and uniformly at random from the unit sphere and that the number of measurements is a sufficiently large multiple of the dimension. We show that, with high probability, the randomized Kaczmarz algorithm converges to a neighborhood around the ground-truth solution whose radius depends on the noise level.