Towards a Strategy for Automatic Phase Retrieval from Noisy Fourier Intensities

Abstract

When iteratively reconstructing a two-dimensional image (or, more precisely, its image-form) from appreciably contaminated samples of the magnitude of its Fourier transform, using Fienup's hybrid input-output algorithm, it is herein demonstrated by example that the image error, which expresses the violation of the image-space constraints, exhibits pronounced fluctuations. Significantly improved final image-forms are obtained by appropriately averaging the image-forms generated at those iterations for which the image error has local minima. Reconstructions for various specimen images are shown. A technique for accelerating the convergence of Fienup's algorithm, by initially estimating the phases of low spatial frequency components of the Fourier transform, is described and illustrated by example.