Signal representation and reconstruction from partial information in the position-frequency space

Motivated by the human visual system, where both spectral phase and overlapping receptive fields play major roles, 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 the given combined information are introduced. It is concluded that most of the previous results in the area of Fourier phase-only representation and reconstruction are special cases of the general approach presented here