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The locally stationary dual-tree complex wavelet model

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The locally stationary dual-tree complex wavelet model. / Nelson, James; Gibberd, Alex; Nafornita, Corina et al.
In: Statistics and Computing, Vol. 28, No. 6, 11.2018, p. 1139-1154.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Nelson, J, Gibberd, A, Nafornita, C & Kingsbury, N 2018, 'The locally stationary dual-tree complex wavelet model', Statistics and Computing, vol. 28, no. 6, pp. 1139-1154. https://doi.org/10.1007/s11222-017-9784-0

APA

Nelson, J., Gibberd, A., Nafornita, C., & Kingsbury, N. (2018). The locally stationary dual-tree complex wavelet model. Statistics and Computing, 28(6), 1139-1154. https://doi.org/10.1007/s11222-017-9784-0

Vancouver

Nelson J, Gibberd A, Nafornita C, Kingsbury N. The locally stationary dual-tree complex wavelet model. Statistics and Computing. 2018 Nov;28(6):1139-1154. Epub 2017 Oct 26. doi: 10.1007/s11222-017-9784-0

Author

Nelson, James ; Gibberd, Alex ; Nafornita, Corina et al. / The locally stationary dual-tree complex wavelet model. In: Statistics and Computing. 2018 ; Vol. 28, No. 6. pp. 1139-1154.

Bibtex

@article{aa578ff3e8b541a99c7487b180b24f54,
title = "The locally stationary dual-tree complex wavelet model",
abstract = "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.",
keywords = "Locally stationary wavelet, Random fields, Dual-tree complex wavelets, Stationarity detection",
author = "James Nelson and Alex Gibberd and Corina Nafornita and Nick Kingsbury",
year = "2018",
month = nov,
doi = "10.1007/s11222-017-9784-0",
language = "English",
volume = "28",
pages = "1139--1154",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer Netherlands",
number = "6",

}

RIS

TY - JOUR

T1 - The locally stationary dual-tree complex wavelet model

AU - Nelson, James

AU - Gibberd, Alex

AU - Nafornita, Corina

AU - Kingsbury, Nick

PY - 2018/11

Y1 - 2018/11

N2 - 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.

AB - 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.

KW - Locally stationary wavelet

KW - Random fields

KW - Dual-tree complex wavelets

KW - Stationarity detection

U2 - 10.1007/s11222-017-9784-0

DO - 10.1007/s11222-017-9784-0

M3 - Journal article

VL - 28

SP - 1139

EP - 1154

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 6

ER -