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°.
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Izraelevitz et al. (1987) studied this question.
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