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

Wei Wang, Shun Zhang, Ning Ma, Steen Grüner Hanson, Mitsuo Takeda

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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.
Original languageEnglish
Title of host publicationProceedings of SPIE
Number of pages9
Volume9449
PublisherSPIE - International Society for Optical Engineering
Publication date2015
Article number944904
DOIs
Publication statusPublished - 2015
EventInternational Conference on Photonics and Optical Engineering - Xi'an, China
Duration: 13 Oct 201415 Oct 2014

Conference

ConferenceInternational Conference on Photonics and Optical Engineering
CountryChina
CityXi'an
Period13/10/201415/10/2014
SeriesProceedings of SPIE, the International Society for Optical Engineering
Volume9449
ISSN0277-786X

Bibliographical note

Copyright 2015 Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic electronic or print reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Cite this

Wang, W., Zhang, S., Ma, N., Hanson, S. G., & Takeda, M. (2015). Riesz transforms in statistical signal processing and their applications to speckle metrology: a review. In Proceedings of SPIE (Vol. 9449). [944904] SPIE - International Society for Optical Engineering. Proceedings of SPIE, the International Society for Optical Engineering, Vol.. 9449 https://doi.org/10.1117/12.2081318