Scaling range automated selection for wavelet leader multifractal analysis

• Published in: Signal processing Vol. 105; pp. 243 - 257
• Main Authors: Leonarduzzi, Roberto F., Torres, María E., Abry, Patrice
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2014; Elsevier
• Subjects: Applied sciences; Automated scaling range selection; Bootstrap; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Multifractal analysis; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Telecommunications and information theory; Wavelet leaders; Bootstrap; Automated scaling range selection; Multifractal analysis; Wavelet leaders; Performance evaluation; Scale invariance; Monte Carlo method; Robust estimation; Multifractal system; Computational complexity; Multiresolution analysis; Bootstrapping; Heart rate; Fractal; Wavelet transformation; Database; Signal processing; Numerical simulation; Signal analysis; Power law
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2014.06.002

Scale invariance and multifractal analysis constitute paradigms nowadays widely used for real-world data characterization. In essence, they amount to assuming power law behaviors of well-chosen multiresolution quantities as functions of the analysis scale. The exponents of these power laws, the scaling exponents, are then measured and involved in classical signal processing tasks. Yet, the practical estimation of such exponents implies the selection of a range of scales where the power law behaviors hold, a difficult task with yet crucial impact on performance. In the present contribution, a nonparametric bootstrap based procedure is devised to achieve scaling range automated selection. It is shown to be effective and relevant in practice. Its performance, benefits and computational costs are assessed by means of Monte Carlo simulations. It is applied to synthetic multifractal processes and shown to yield robust and accurate estimation of multifractal parameters, despite various difficulties such as noise corruption or inter-subject variability. Finally, its potential is illustrated at work for the analysis of adult heart rate variability on a large database. •We propose an algorithm for the selection of scaling range in multifractal analysis.•The algorithm is non-parametric and based on bootstrap on the wavelet domain.•We illustrate its performance through extensive numerical simulations.•We also use it to analyze heart rate variability data.•We conclude that it provides close to optimal-MSE estimates of the scaling range.