Phase retrieval via randomized block Kaczmarz by averaging with heavy ball momentum

Abstract

We propose a variant of the randomized Kaczmarz method for solving phase retrieval problems called randomized block Kaczmarz with heavy ball momentum (RBK-HB). It achieves effective acceleration compared to the Kaczmarz methods by combining block and heavy ball momentum techniques. In the theoretical part, by assuming that the loss function is strongly convex near the true solution, the RBK-HB method converges linearly with high probability. Numerical experiments show that compared with the Kaczmarz methods, the RBK-HB method is less sensitive to the initial point, the number of measurements required for successful recovery is less and has a faster convergence rate.