Image reconstruction from one-bit Fourier phase: Theory, sampling, and coherent image model

In this paper, we tackle the problem of recovering an image from its Fourier transform phase quantized to 1 bit, or, equivalently, from 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, however, through a large-scale set of experiments, that sampling in the frequency domain presents a major obstacle to good reconstruction resuits due to the information loss produced by the approximated knowledge of the zero crossing locations. We finally show that, by using a "coherent" image model in which the image is complex and the spatial-domain phase is random and highly uncorrelated, we can significantly reduce the effect of this information loss and improve the quality of image reconstruction.