Complex-Valued Wavelet Lifting and Applications

Jean Hamilton, Matthew A. Nunes, Marina I. Knight, Piotr Fryzlewicz

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Signals with irregular sampling structures arise naturally in many fields. In applications such as spectral decomposition and nonparametric regression, classical methods often assume a regular sampling pattern, thus cannot be applied without prior data processing. This work proposes new complex-valued analysis techniques based on the wavelet lifting scheme that removes “one coefficient at a time.” Our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal(s)’ characteristics. As our new lifting scheme produces complex-valued wavelet coefficients, it provides an alternative to the Fourier transform for irregular designs, allowing phase or directional information to be represented. We discuss applications in bivariate time series analysis, where the complex-valued lifting construction allows for coherence and phase quantification. We also demonstrate the potential of this flexible methodology over real-valued analysis in the nonparametric regression context. Supplementary materials for this article are available online.
Original languageEnglish
Pages (from-to)48-60
Number of pages13
JournalTechnometrics
Volume60
Issue number1
Early online date26 May 2017
DOIs
Publication statusPublished - 2 Jan 2018

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Lifting Scheme
Wavelets
Nonparametric Regression
Sampling
Time series analysis
Irregular Sampling
Fourier transforms
Spectral Decomposition
Time Series Analysis
Wavelet Coefficients
Decomposition
Quantification
Irregular
Fourier transform
Transform
Methodology
Alternatives
Coefficient
Demonstrate
Context

Cite this

Complex-Valued Wavelet Lifting and Applications. / Hamilton, Jean; Nunes, Matthew A.; Knight, Marina I.; Fryzlewicz, Piotr.

In: Technometrics, Vol. 60, No. 1, 02.01.2018, p. 48-60.

Research output: Contribution to journalArticle

Hamilton, J, Nunes, MA, Knight, MI & Fryzlewicz, P 2018, 'Complex-Valued Wavelet Lifting and Applications', Technometrics, vol. 60, no. 1, pp. 48-60. https://doi.org/10.1080/00401706.2017.1281846
Hamilton, Jean ; Nunes, Matthew A. ; Knight, Marina I. ; Fryzlewicz, Piotr. / Complex-Valued Wavelet Lifting and Applications. In: Technometrics. 2018 ; Vol. 60, No. 1. pp. 48-60.
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