title: Phase retrieval with random phase illumination.
abstract: This paper presents a detailed numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio σ=4 determines a unique phasing solution up to a global phase factor. Under this condition, the standard phasing algorithms converge rapidly to the true solution without stagnation. Excellent approximation is achieved after a small number of iterations, not just with high resolution but also low resolution RPI in the presence of additive as well multiplicative noises. It is shown that RPI with σ=2 is sufficient for phasing complex-valued images under a sector condition and σ=1 for phasing nonnegative images. The error-reduction algorithm with RPI is proved to converge to the true solution under proper conditions.
authors.affiliation: Department of Mathematics, University of California, Davis, California 95616, USA. fannjiang@math.ucdavis.edu
authors.forename: Albert
authors.initials: A
authors.lastname: Fannjiang
authors.forename: Wenjing
authors.initials: W
authors.lastname: Liao