Riesz transforms in statistical signal processing and their applications to speckle metrology: a review

Wei Wang; Shun Zhang; Ning Ma; Steen G. Hanson; Mitsuo Takeda

doi:10.1117/12.2081318

19 February 2015 Riesz transforms in statistical signal processing and their applications to speckle metrology: a review

Wei Wang, Shun Zhang, Ning Ma, Steen G. Hanson, Mitsuo Takeda

Author Affiliations +

Proceedings Volume 9449, The International Conference on Photonics and Optical Engineering (icPOE 2014); 944904 (2015) https://doi.org/10.1117/12.2081318
Event: The International Conference on Photonics and Optical Engineering and the Annual West China Photonics Conference (icPOE 2014), 2014, Xi'an, China

Abstract

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.

Citation Download Citation

Wei Wang, Shun Zhang, Ning Ma, Steen G. Hanson, and Mitsuo Takeda "Riesz transforms in statistical signal processing and their applications to speckle metrology: a review", Proc. SPIE 9449, The International Conference on Photonics and Optical Engineering (icPOE 2014), 944904 (19 February 2015); https://doi.org/10.1117/12.2081318

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