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

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