Signal representation in the combined phase-spatial space: Reconstruction and criteria for uniqueness

Motivated by the major roles of spectral phase in signal structure and by r ecent results on the importance of localized representation in images, we d evelop conditions for unique representation of a signal by a combination of its spectral (Fourier) phase and spatial samples. Methods for signal recon struction from various combinations of spatial and phase information are in troduced. It is concluded that most of the previous results in the area of phase-only representation and reconstruction are special cases of the gener al approach presented here.