Finite resolution effects in p-leader multifractal analysis

TL;DR

This paper investigates the finite-resolution bias in p-leader multifractal analysis, proposing a universal correction formula based on wavelet cascade models to improve the accuracy of multifractal property estimation.

Contribution

It introduces a universal correction for finite-resolution effects in p-leader multifractal analysis, validated through simulations and applied to heart rate variability data.

Findings

The correction improves the accuracy of scaling exponent estimates.

Numerical simulations confirm the correction's effectiveness across various multifractal processes.

Application to heart rate data demonstrates practical utility.

Abstract

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.