Finite-Resolution Effects in $p$ -Leader Multifractal Analysis Article - Juillet 2017

Roberto Leonarduzzi, Herwig Wendt, Patrice Abry, Stéphane Jaffard, Clothilde Melot

Roberto Leonarduzzi, Herwig Wendt, Patrice Abry, Stéphane Jaffard, Clothilde Melot, « Finite-Resolution Effects in $p$ -Leader Multifractal Analysis  », IEEE Transactions on Signal Processing, juillet 2017, pp. 3359 - 3368. ISSN 1053-587X

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.

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