Image Representation by One-Bit Fourier Phase: Theory, Sampling, and Coherent Image Model

In this paper, we concern ourselves with the problem of recovering an image from its Fourier transform phase quantized to 1 bit, or, equivalently, the locations of the zero crossings of the real part of the Fourier transform. We first present new theoretical results that set an algebraic condition under which real zero crossings uniquely specify a band limited image. We then show through a large-scale set of experiments that sampling in the frequency domain presents a major obstacle to obtaining good reconstruction results. In the third part of this paper, we consider the 1-bit Fourier phase reconstruction problem when the original image is coherent, i.e., the image phase is random and highly uncorrelated. We show examples which demonstrate that the information loss produced by frequency sampling is not as severe as that in the classical problem. Motivated by digital phase-only holograms, we use a known random diffuser as the image phase and extend a well-known iterative reconstruction procedure 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 it-erations, unlike its noncoherent counterpart. © 1988 IEEE