Statistical Interpretation of the Importance of Phase Information in Signal and Image Reconstruction

Authors

Xuelei (Sherry) Ni, Kennesaw State UniversityFollow
Xiaoming Huo, Georgia Institute of Technology - Main Campus

Department

Statistics and Analytical Sciences

Document Type

Article

Publication Date

2-15-2007

Abstract

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.