Variance-Reduced Randomized Kaczmarz Algorithm In Xfel Single-Particle Imaging Phase Retrieval.

In this paper, we propose the Variance Reduced Randomized Kaczmarz (VR-RK) algorithm for XFEL signal particle imaging phase retrieval. The VR-RK algorithm is inspired by the randomized Kaczmarz algorithm and the variance reduction in stochastic gradient methods. The formulations of the VR-RK algorithm under the L-1 and L-2 constraints are also presented. Numerical simulations demonstrate that the VR-RK method has a faster convergence rate compared with the randomized Kaczmarz method. Tests on the synthetic signal particle imaging data and the PR772 XFEL real imaging data show that the VR-RK algorithm can recover information with higher accuracy. It is useful for biological data processing.