Complex-valued wavelet lifting and applications

Hamilton, Jean and Nunes, Matthew Alan and Knight, Marina and Fryzlewicz, Piotr (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: Journal Article
Journal or Publication Title: Technometrics
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Technometrics on 17/01/2017, available online: http://www.tandfonline.com/10.1080/00401706.2017.1281846
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 83876
Deposited By: ep_importer_pure
Deposited On: 10 Jan 2017 11:16
Refereed?: Yes
Published?: Published
Last Modified: 26 Feb 2020 03:34
URI: https://eprints.lancs.ac.uk/id/eprint/83876

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