The locally stationary dual-tree complex wavelet model

We here harmonise two significant contributions to the field of wavelet analysis in the past two decades, namely the locally stationary wavelet process and the family of dual-tree complex wavelets. By combining these two components, we furnish a statistical model that can simultaneously access benef...

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Bibliographic Details
Published in:Statistics and computing 2018-11, Vol.28 (6), p.1139-1154
Main Authors: Nelson, J. D. B., Gibberd, A. J., Nafornita, C., Kingsbury, N.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Covariance
Mathematics and Statistics
Probability and Statistics in Computer Science
Statistical models
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Wavelet analysis
Wavelet transforms
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Summary:We here harmonise two significant contributions to the field of wavelet analysis in the past two decades, namely the locally stationary wavelet process and the family of dual-tree complex wavelets. By combining these two components, we furnish a statistical model that can simultaneously access benefits from these two constructions. On the one hand, our model borrows the debiased spectrum and auto-covariance estimator from the locally stationary wavelet model. On the other hand, the enhanced directional selectivity is obtained from the dual-tree complex wavelets over the regular lattice. The resulting model allows for the description and identification of wavelet fields with significantly more directional fidelity than was previously possible. The corresponding estimation theory is established for the new model, and some stationarity detection experiments illustrate its practicality.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-017-9784-0