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

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 proceeding › Conference 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 language	English
Title of host publication	Proceedings of SPIE - The International Society for Optical Engineering
Publisher	SPIE
Volume	9449
ISBN (Print)	9781628415650
DOIs	https://doi.org/10.1117/12.2081318
Publication status	Published - 2015
Event	International Conference on Photonics and Optical Engineering - Xian, Xi'an, United Kingdom Duration: 13 Oct 2014 → 15 Oct 2014

Conference

Conference	International Conference on Photonics and Optical Engineering
Abbreviated title	icPOE 2014
Country/Territory	United Kingdom
City	Xi'an
Period	13/10/14 → 15/10/14

Keywords

optical vortex metrology
Riesz transform
speckles
stochastic process
vector correlations

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10.1117/12.2081318

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@inproceedings{80594cdf23c846f88fb40b956ed3572b,

title = "Riesz transforms in statistical signal processing and their applications to speckle metrology: a review",

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..",

keywords = "optical vortex metrology, Riesz transform, speckles, stochastic process, vector correlations",

author = "Wei Wang and Shun Zhang and Ning Ma and Hanson, {Steen G.} and Mitsuo Takeda",

year = "2015",

doi = "10.1117/12.2081318",

language = "English",

isbn = "9781628415650",

volume = "9449",

booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",

publisher = "SPIE",

address = "United States",

note = "International Conference on Photonics and Optical Engineering, icPOE 2014 ; Conference date: 13-10-2014 Through 15-10-2014",

}

Wang, W, Zhang, S, Ma, N, Hanson, SG & 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, International Conference on Photonics and Optical Engineering, Xi'an, United Kingdom, 13/10/14. https://doi.org/10.1117/12.2081318

TY - GEN

T1 - Riesz transforms in statistical signal processing and their applications to speckle metrology

T2 - International Conference on Photonics and Optical Engineering

AU - Wang, Wei

AU - Zhang, Shun

AU - Ma, Ning

AU - Hanson, Steen G.

AU - Takeda, Mitsuo

PY - 2015

Y1 - 2015

N2 - 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..

AB - 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..

KW - optical vortex metrology

KW - Riesz transform

KW - speckles

KW - stochastic process

KW - vector correlations

U2 - 10.1117/12.2081318

DO - 10.1117/12.2081318

M3 - Conference contribution

AN - SCOPUS:84924388046

SN - 9781628415650

VL - 9449

BT - Proceedings of SPIE - The International Society for Optical Engineering

PB - SPIE

Y2 - 13 October 2014 through 15 October 2014

ER -

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

Abstract

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Keywords

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