Name
Abstract | ||
|---|---|---|
Multifractal analysis has matured into a widely used signal and image processing tool. Due to the statistical nature of multifractal processes (strongly non-Gaussian and intricate dependence) the accurate estimation of multifractal parameters is very challenging in situations where the sample size is small (notably including a range of biomedical applications) and currently available estimators need to be improved. To overcome such limitations, the present contribution proposes a Bayesian estimation procedure for the multifractality (or intermittence) parameter. Its originality is threefold: First, the use of wavelet leaders, a recently introduced multiresolution quantity that has been shown to yield significant benefits for multifractal analysis; Second, the construction of a simple yet generic semi-parametric model for the marginals and covariance structure of wavelet leaders for the large class of multiplicative cascade based multifractal processes; Third, the construction of original Bayesian estimators associated with the model and the constraints imposed by multifractal theory. Performance are numerically assessed and illustrated for synthetic multifractal processes for a range of multifractal parameter values. The proposed procedure yields significantly improved estimation performance for small sample sizes. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/ICASSP.2013.6638929 | Acoustics, Speech and Signal Processing |
Keywords | Field | DocType |
Bayes methods,fractals,wavelet transforms,Bayesian estimation procedure,image processing tool,multifractal analysis,multifractality parameter,multiplicative cascade based multifractal process,multiresolution quantity,semiparametric model,signal processing tool,Bayesian estimation,log-cumulants,multifractal analysis,multiplicative cascade processes,wavelet leaders | Pattern recognition,Multiplicative cascade,Computer science,Artificial intelligence,Bayes estimator,Multifractal system,Wavelet transform,Covariance,Bayesian probability,Estimator,Wavelet | Conference |
ISSN | Citations | PageRank |
1520-6149 | 5 | 0.66 |
References | Authors | |
5 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Herwig Wendt | 1 | 170 | 33.82 |
| Nicolas Dobigeon | 2 | 2070 | 108.02 |
| Jean-Yves Tourneret | 3 | 835 | 64.32 |
| Patrice Abry | 4 | 567 | 63.81 |