Alternating direction methods for classical and ptychographic phase retrieval

In this paper, we show how the augmented Lagrangian alternating direction method (ADM) can be used to solve both the classical and ptychographic phase retrieval problems. We point out the connection between ADM and projection algorithms such as the hybrid input-output algorithm, and compare its performance against standard algorithms for phase retrieval on a number of test images. Our computational experiments show that ADM appears to be less sensitive to the choice of relaxation parameters, and it usually outperforms the existing techniques for both the classical and ptychographic phase retrieval problems.