Complex-valued wavelet lifting and applications

Hamilton, Jean, Nunes, Matthew A., Knight, Marina I. and Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X (2018) Complex-valued wavelet lifting and applications. Technometrics, 60 (1). pp. 48-60. ISSN 0040-1706

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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.

Item Type:	Article
Official URL:	http://amstat.tandfonline.com/loi/utch20
Additional Information:	© 2017 The Authors
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	13 Jan 2017 14:52
Last Modified:	17 Oct 2024 17:12
Projects:	EP/L014246/1
Funders:	Engineering and Physical Sciences Research Council
URI:	http://eprints.lse.ac.uk/id/eprint/68859

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