Finite resolution effects in p-leader multifractal analysis
For researchers using multifractal analysis in signal processing, this work addresses a critical practical bottleneck by providing a theoretically grounded correction for finite-resolution effects, improving estimation accuracy.
The paper identifies and corrects finite-resolution biases in p-leader multifractal analysis, proposing a universal closed-form correction that enables accurate estimation of scaling exponents. Numerical simulations across diverse multifractal processes and application to heart rate variability data validate the correction.
Multifractal analysis has become a standard signal processing tool,for which a promising new formulation, the p-leader multifractal formalism, has recently been proposed. It relies on novel multiscale quantities, the p-leaders, defined as local l^p norms of sets of wavelet coefficients located at infinitely many fine scales. Computing such infinite sums from actual finite-resolution data requires truncations to the finest available scale, which results in biased p-leaders and thus in inaccurate estimates of multifractal properties. A systematic study of such finite-resolution effects leads to conjecture an explicit and universal closed-form correction that permits an accurate estimation of scaling exponents. This conjecture is formulated from the theoretical study of a particular class of models for multifractal processes, the wavelet-based cascades. The relevance and generality of the proposed conjecture is assessed by numerical simulations conducted over a large variety of multifractal processes. Finally, the relevance of the proposed corrected estimators is demonstrated on the analysis of heart rate variability data.