On connections between Amplitude Flow and Error Reduction for phase retrieval and ptychography

Abstract In this paper, we consider two iterative algorithms for the phase retrieval problem: well-known Error Reduction method and Amplitude Flow algorithm, which performs minimization of amplitude-based squared loss via gradient descent. We show that can be interpreted as a scaled applied to minimize same loss, allows establish its convergence properties. Moreover, class measurement scenarios, such ptychography, both methods have computational complexity sometimes even coincide.