IMAGE RECONSTRUCTION FROM ONE-BIT FOURIER PHASE: THEORY, SAMPLING, AND COHERENT IMAGE MODEL.

Abstract

The problem of recovering an image from its Fourier transform phase quantized to one bit, or, equivalently, from the zero crossings of the real part of the Fourier transform is dealt with. Theoretical results that set an algebraic condition under which real zero crossings uniquely specify a bandlimited image are presented. The authors also show through a large-scale set of experiments that sampling in the frequency domain presents a major obstacle to good reconstruction results, due to the information loss produced by the approximated knowledge of the zero-crossing locations. They 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, they can significantly reduce the effect of this information loss and improve the quality of image reconstruction.