Blind deconvolution and phase retrieval using point zeros

The Fourier transform of a signal or image of compact support is an entire function of exponential type which can be represented in terms of their zeros by means of a product of factors each encoding a zero of the function. In more than one dimensional problems, an entire function is generally not factorizable into an infinite product of terms, but is irreducible, [1,2] from which it follows that there is a unique phase to be associated with its power spectrum, in principle.