In this paper, a high-dimensional statistical signal processing is revisited with the aim of introducing the concept of vector signal representation derived from the Riesz transforms, which are the natural extension and generalization of the one-dimensional Hilbert transform. Under the new concepts of vector correlations proposed recently, the statistical properties of the vector signal representation for random signal are presented and some applications to speckle metrology developed recently are reviewed to demonstrate the unique capability of Riesz transforms.

Date Published: 19 February 2015
PDF: 9 pages
Proc. SPIE 9449, The International Conference on Photonics and Optical Engineering (icPOE 2014), 944904 (19 February 2015); doi: 10.1117/12.2081318

Published in SPIE Proceedings Vol. 9449:
The International Conference on Photonics and Optical Engineering (icPOE 2014)
Ailing Tian; Anand Asundi; Weiguo Liu; Chunmin Zhang, Editor(s)