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Complex-valued wavelet lifting and applications

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JournalTechnometrics
DateAccepted/In press - 8 Jan 2017
DateE-pub ahead of print - 17 Jan 2017
DatePublished (current) - 26 May 2017
Issue number1
Volume60
Number of pages13
Pages (from-to)48-60
Early online date17/01/17
Original languageEnglish

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.

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    Research areas

  • (Bivariate) time series, Coherence and phase, Lifting scheme, Nondecimated transform, Nonparametric regression, Wavelets

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