Data-driven wavelet resolution choice in multichannel boxcar deconvolution with long memory

J. R. Wishart

Data-driven wavelet resolution choice in multichannel boxcar deconvolution with long memory

J. R. Wishart

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

Abstract

In wavelet deconvolution, the finest resolution level is a key parameter which needs to be chosen carefully. In this paper a data-driven method is presented that selects the finest resolution level using a blockwise thresholding method in the Fourier domain. In particular, we present a method that applies to the general multichannel model whereby a practitioner observes many box-car convolutions of a signal of interest (with possible different levels of box-car 'blur') with additive long memory noise. The box-car functions governing the blur are assumed to have Badly Approximable (BA) width. To the best of the author's knowledge, no automatic fine resolution selection method exists for the box-car wavelet deconvolution paradigm. We present a method that selects the optimal level that is adaptive to box-car width and noise levels and conduct a short numerical study to supplement the findings.

Original language	English
Title of host publication	Proceedings of COMPSTAT 2014
Subtitle of host publication	21st International conference on computational statistcs
Editors	Manfred Gilli, Gil Gonzalez-Rodriguez, Alicia Nieto-Reyes
Place of Publication	Geneva, Switzerland
Publisher	International Statistical Institute
Pages	299-307
Number of pages	9
ISBN (Print)	9782839913478
Publication status	Published - 2014
Externally published	Yes
Event	International conference on computational statistcs (21st : 2014) - Geneva Duration: 19 Aug 2014 → 22 Aug 2014

Conference

Conference	International conference on computational statistcs (21st : 2014)
City	Geneva
Period	19/08/14 → 22/08/14

Keywords

Box-car
Badly Approximable
Data-driven
fractional Brownian motion
Fourier analysis
Meyer Wavelet
Multichannel deconvolution
Wavelet Analysis

Access to Document

http://compstat2014.org/

Cite this

@inproceedings{11d72efb7c93435ebeb7c9f4a8f39b96,

title = "Data-driven wavelet resolution choice in multichannel boxcar deconvolution with long memory",

abstract = "In wavelet deconvolution, the finest resolution level is a key parameter which needs to be chosen carefully. In this paper a data-driven method is presented that selects the finest resolution level using a blockwise thresholding method in the Fourier domain. In particular, we present a method that applies to the general multichannel model whereby a practitioner observes many box-car convolutions of a signal of interest (with possible different levels of box-car 'blur') with additive long memory noise. The box-car functions governing the blur are assumed to have Badly Approximable (BA) width. To the best of the author's knowledge, no automatic fine resolution selection method exists for the box-car wavelet deconvolution paradigm. We present a method that selects the optimal level that is adaptive to box-car width and noise levels and conduct a short numerical study to supplement the findings.",

keywords = "Box-car, Badly Approximable, Data-driven, fractional Brownian motion, Fourier analysis, Meyer Wavelet, Multichannel deconvolution, Wavelet Analysis",

author = "Wishart, {J. R.}",

year = "2014",

language = "English",

isbn = "9782839913478",

pages = "299--307",

editor = "Manfred Gilli and Gil Gonzalez-Rodriguez and Alicia Nieto-Reyes",

booktitle = "Proceedings of COMPSTAT 2014",

publisher = "International Statistical Institute",

address = "Netherlands",

note = "International conference on computational statistcs (21st : 2014) ; Conference date: 19-08-2014 Through 22-08-2014",

}

Wishart, JR 2014, Data-driven wavelet resolution choice in multichannel boxcar deconvolution with long memory. in M Gilli, G Gonzalez-Rodriguez & A Nieto-Reyes (eds), Proceedings of COMPSTAT 2014: 21st International conference on computational statistcs. International Statistical Institute, Geneva, Switzerland, pp. 299-307, International conference on computational statistcs (21st : 2014), Geneva, 19/08/14. <http://compstat2014.org/>

Data-driven wavelet resolution choice in multichannel boxcar deconvolution with long memory. / Wishart, J. R.

Proceedings of COMPSTAT 2014: 21st International conference on computational statistcs. ed. / Manfred Gilli; Gil Gonzalez-Rodriguez; Alicia Nieto-Reyes. Geneva, Switzerland : International Statistical Institute, 2014. p. 299-307.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

TY - GEN

T1 - Data-driven wavelet resolution choice in multichannel boxcar deconvolution with long memory

AU - Wishart, J. R.

PY - 2014

Y1 - 2014

N2 - In wavelet deconvolution, the finest resolution level is a key parameter which needs to be chosen carefully. In this paper a data-driven method is presented that selects the finest resolution level using a blockwise thresholding method in the Fourier domain. In particular, we present a method that applies to the general multichannel model whereby a practitioner observes many box-car convolutions of a signal of interest (with possible different levels of box-car 'blur') with additive long memory noise. The box-car functions governing the blur are assumed to have Badly Approximable (BA) width. To the best of the author's knowledge, no automatic fine resolution selection method exists for the box-car wavelet deconvolution paradigm. We present a method that selects the optimal level that is adaptive to box-car width and noise levels and conduct a short numerical study to supplement the findings.

AB - In wavelet deconvolution, the finest resolution level is a key parameter which needs to be chosen carefully. In this paper a data-driven method is presented that selects the finest resolution level using a blockwise thresholding method in the Fourier domain. In particular, we present a method that applies to the general multichannel model whereby a practitioner observes many box-car convolutions of a signal of interest (with possible different levels of box-car 'blur') with additive long memory noise. The box-car functions governing the blur are assumed to have Badly Approximable (BA) width. To the best of the author's knowledge, no automatic fine resolution selection method exists for the box-car wavelet deconvolution paradigm. We present a method that selects the optimal level that is adaptive to box-car width and noise levels and conduct a short numerical study to supplement the findings.

KW - Box-car

KW - Badly Approximable

KW - Data-driven

KW - fractional Brownian motion

KW - Fourier analysis

KW - Meyer Wavelet

KW - Multichannel deconvolution

KW - Wavelet Analysis

M3 - Conference proceeding contribution

SN - 9782839913478

SP - 299

EP - 307

BT - Proceedings of COMPSTAT 2014

A2 - Gilli, Manfred

A2 - Gonzalez-Rodriguez, Gil

A2 - Nieto-Reyes, Alicia

PB - International Statistical Institute

CY - Geneva, Switzerland

T2 - International conference on computational statistcs (21st : 2014)

Y2 - 19 August 2014 through 22 August 2014

ER -

Data-driven wavelet resolution choice in multichannel boxcar deconvolution with long memory

Abstract

Conference

Keywords

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Cite this