Final published version, 2.54 MB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -