Image representation by one-bit Fourier phase: theory, sampling, and coherent image model

The problem of recovering an image from its Fourier-transform phase quantized to one bit, or, equivalently, finding the locations of the zero crossings of the real part of the Fourier transform, is addressed. Theoretical results are presented that set an algebraic condition under which real zero crossings uniquely specify a band-limited image. It is then shown that sampling in the frequency domain presents a major obstacle to obtaining good reconstruction results. The one-bit Fourier phase reconstruction problem is then considered when the original image is coherent, i.e. the image phase is random and highly uncorrelated. Examples are given which demonstrate that the information loss produced by frequency sampling is not as severe as that in the nonclassical problem. Motivated by digital phase-only holograms, a known random diffuser is used as the image phase and a well-known iterative reconstruction procedure is extended to incorporate the knowledge of the image phase at each stage of the iteration. This reconstruction method produces good image quality by using a few iterations, unlike its noncoherent counterpart