A new direct algorithm for image reconstruction from Fourier transform magnitude

In this paper we present a new direct solution to the problem of reconstructing a two-dimensional discrete signal of finite support from knowledge of only its Fourier transform magnitude and support. Using the autocorrelation function of the unknown signal, zeros are calculated of a polynomial whose coefficients correspond to the unknown image or the image reversed. From these zeros, a set of linear equations is developed whose solution yields either the original image or the image rotated by 180°.