Rights statement: 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
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Complex-valued wavelet lifting and applications
AU - Hamilton, Jean
AU - Nunes, Matthew Alan
AU - Knight, Marina
AU - Fryzlewicz, Piotr
N1 - 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
PY - 2018/2/22
Y1 - 2018/2/22
N2 - 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.
AB - 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.
KW - (Bivariate) time series
KW - Coherence and phase
KW - Lifting scheme
KW - Nondecimated transform
KW - Nonparametric regression
KW - Wavelets
U2 - 10.1080/00401706.2017.1281846
DO - 10.1080/00401706.2017.1281846
M3 - Journal article
VL - 60
SP - 48
EP - 60
JO - Technometrics
JF - Technometrics
SN - 0040-1706
IS - 1
ER -