Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison

A detailed comparison of the original Gerchberg–Saxton and the Yang–Gu algorithms for the reconstruction of model images from two intensity measurements in a nonunitary transform system is presented. The Yang–Gu algorithm is a generalization of the Gerchberg–Saxton algorithm and is effective in solving the general amplitude–phase-retrieval problem in any linear unitary or nonunitary transform system. For a unitary transform system the Yang–Gu algorithm is identical to the Gerchberg–Saxton algorithm. The reconstruction of images from data corrupted with random noise is also investigated. The simulation results show that the Yang–Gu algorithm is relatively insensitive to the presence of noise in data. In all cases studied the Yang–Gu algorithm always resulted in a highly accurate recovered phase.