CONVERGENCE ANALYSIS ON A FAST ITERATIVE PHASE RETRIEVAL ALGORITHM WITHOUT INDEPENDENCE ASSUMPTION

摘要

Phase retrieval has been an attractive problem, and many algorithms have been proposed. Randomized Kaczmarz method is a fast iterative method with good performance in both convergence rate and computational cost with theoretical analysis. However, they all assume that the iteratively updated variables and the original data are independent, which is not true in reality. In this paper, we study for the first time the convergence analysis of this method in the real case, where only a finite number of measurements are available. Specifically, we theoretically prove the linear rate of convergence for the phase retrieval via randomized Kaczmarz algorithm without independence assumption.