Signal reconstruction from Fourier transform sign information

In this paper, we present new results on the reconstruction of signals from only the sign of the real part of the Fourier transform. Specifically, we develop new theoretical results which state conditions under which two-dimensional signals are uniquely specified to within a scale factor with this information and show that these conditions include a broad class of signals. Furthermore, we apply this result to the problem of reconstructing two-dimensional signals from their zero crossings. We also present two algorithms for reconstructing a signal from sign information in either the time or frequency domain.