TY - GEN
T1 - A Bayesian approach for the joint estimation of the multifractality parameter and integral scale based on the Whittle approximation
AU - Combrexelle, S.
AU - Wendt, H.
AU - Abry, P.
AU - Dobigeon, N.
AU - McLaughlin, S.
AU - Tourneret, J. Y.
PY - 2015/8/4
Y1 - 2015/8/4
N2 - Multifractal analysis is a powerful tool used in signal processing. Multifractal models are essentially characterized by two parameters, the multifractality parameter c2 and the integral scale A (the time scale beyond which multifractal properties vanish). Yet, most applications concentrate on estimating c2 while the estimation of A is in general overlooked, despite the fact that A potentially conveys important information. Joint estimation of c2 and A is challenging due to the statistical nature of multifractal processes (i.e. the strong dependence and non-Gaussian nature), and has barely been considered. The present contribution addresses these limitations and proposes a Bayesian procedure for the joint estimation of (c2, A). Its originality resides, first, in the construction of a generic multivariate model for the statistics of wavelet leaders for multifractal multiplicative cascade processes, and second, in the use of a suitable Whittle approximation for the likelihood associated with the model. The resulting model enables Bayesian estimators for (c2, A) to also be computed for large sample size. Performance is assessed numerically for synthetic multifractal processes and illustrated for wind-tunnel turbulence data. The proposed procedure significantly improves estimation of c2 and yields, for the first time, reliable estimates for A.
AB - Multifractal analysis is a powerful tool used in signal processing. Multifractal models are essentially characterized by two parameters, the multifractality parameter c2 and the integral scale A (the time scale beyond which multifractal properties vanish). Yet, most applications concentrate on estimating c2 while the estimation of A is in general overlooked, despite the fact that A potentially conveys important information. Joint estimation of c2 and A is challenging due to the statistical nature of multifractal processes (i.e. the strong dependence and non-Gaussian nature), and has barely been considered. The present contribution addresses these limitations and proposes a Bayesian procedure for the joint estimation of (c2, A). Its originality resides, first, in the construction of a generic multivariate model for the statistics of wavelet leaders for multifractal multiplicative cascade processes, and second, in the use of a suitable Whittle approximation for the likelihood associated with the model. The resulting model enables Bayesian estimators for (c2, A) to also be computed for large sample size. Performance is assessed numerically for synthetic multifractal processes and illustrated for wind-tunnel turbulence data. The proposed procedure significantly improves estimation of c2 and yields, for the first time, reliable estimates for A.
KW - Bayesian Estimation
KW - Integral Scale
KW - Multifractal Analysis
KW - Wavelet Leaders
KW - Whittle Likelihood
UR - http://www.scopus.com/inward/record.url?scp=84946048596&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2015.7178699
DO - 10.1109/ICASSP.2015.7178699
M3 - Conference contribution
AN - SCOPUS:84946048596
SN - 9781467369978
VL - 2015-August
T3 - Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
SP - 3886
EP - 3890
BT - Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on
PB - IEEE
T2 - 40th IEEE International Conference on Acoustics, Speech and Signal Processing 2015
Y2 - 19 April 2015 through 24 April 2015
ER -