Phase recovery for two-dimensional digital objects by polynomial factorisation

Abstract

Phase retrieval for sampled, real, positive objects in two dimensions is studied from the point of view of factorisation of the z-transform. This decomposition is considered over the field of integers for noise-free autocorrelations of digital objects and the formulation provides a means of calculating all possible objects with a given autocorrelation. A brief discussion on the influence of noise is carried out using some simple examples which show theexistence of an approximate factorisation over reals. © 1986.