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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 - The International Society for Optical Engineering
PublisherSPIE
Volume9449
ISBN (Print)9781628415650
DOIs
Publication statusPublished - 2015
EventInternational Conference on Photonics and Optical Engineering - Xian, Xi'an, United Kingdom
Duration: 13 Oct 201415 Oct 2014

Conference

ConferenceInternational Conference on Photonics and Optical Engineering
Abbreviated titleicPOE 2014
CountryUnited Kingdom
CityXi'an
Period13/10/1415/10/14

Keywords

  • optical vortex metrology
  • Riesz transform
  • speckles
  • stochastic process
  • vector correlations

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    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 - The International Society for Optical Engineering (Vol. 9449). [944904] SPIE. https://doi.org/10.1117/12.2081318