Statistical interpretation of the importance of phase information in signal and image reconstruction

Ni, Xuelei (Sherry) and Xiaoming Huo

Statistics & Probability Letters, 2007, vol. 77, issue 4, 447-454

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.

Keywords: Reconstruction; Fourier; transform; Importance; of; phases (search for similar items in EconPapers)
Date: 2007
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