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. Index Terms-multifractal analysis, Bayesian estimation, wavelet leaders, multiplicative cascade processes, log-cumulants MOTIVATIONS, RELATED WORKS, CONTRIBUTIONS Multifractal analysis has become a standard tool for signal and image processing, focussing on the characterization of local regularity fluctuations and scale invariance properties. It has been successfully used in a variety of applications of very different natures, including biomedical (heart rate variability [1] [6] , to name but a few. A recently introduced powerful formalism for multifractal analysis relies on wavelet leaders LX (j, k) [13, 11, 16] , which are constructed from wavelet coefficients. It assumes that the time averages of the q−th powers of LX (j, k) at given analysis scales a = 2 j behave as power-laws over a wide range of scales a ∈ [am, aM ], i.e.,
Finally, a Bayesian estimation procedure for the parameter c 2 of multifractal time series has recently been proposed in REF .
Bayesian estimation for the multifractality parameter
2013 IEEE International Conference on Acoustics, Speech and Signal Processing
2013 IEEE International Conference on Acoustics, Speech and Signal Processing
Computer Science