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

J. R. Wishart

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review


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 languageEnglish
Title of host publicationProceedings of COMPSTAT 2014
Subtitle of host publication21st International conference on computational statistcs
EditorsManfred Gilli, Gil Gonzalez-Rodriguez, Alicia Nieto-Reyes
Place of PublicationGeneva, Switzerland
PublisherInternational Statistical Institute
Number of pages9
ISBN (Print)9782839913478
Publication statusPublished - 2014
Externally publishedYes
EventInternational conference on computational statistcs (21st : 2014) - Geneva
Duration: 19 Aug 201422 Aug 2014


ConferenceInternational conference on computational statistcs (21st : 2014)


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


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