Statistical Interpretation of the Importance of Phase Information in Signal and Image Reconstruction
Statistics & Analytical Sciences
In the Fourier representation of signals and images, phases have long been realized to be more important than magnitudes in the reconstruction. In this paper, a justification is presented from a statistical viewpoint. The main result shows that under random magnitudes, the DC component of the inverse Fourier transform converges to a positive value, while all the other components converge to zero. For random phases, such a result does not exist.
Ni, X., & Huo, X. (2007). Statistical interpretation of the importance of phase information in signal and image reconstruction. Statistics & Probability Letters, 77(4), 447-454. doi:10.1016/j.spl.2006.08.025