Communication Dans Un Congrès Année : 2007

Fractal Dimension Estimation: Empirical Mode Decomposition Versus Wavelets

Patrice Abry
Gabriel Rilling
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Patrick Flandrin
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Résumé

We address the problem of fractal dimension estimation of a discrete sample path. After recalling the multiplicity of possible definitions, we focus on the regularity dimension and on the regularization dimension, and report on the common ingredients that underlie these definitions: a scale transform of the signal, and a geometric or statistical measure on the scaled signal. Then, we propose to interchange wavelet transforms, ordinarily used as the scale transform, with empirical mode decomposition (EMD), a recently proposed signal-adaptive transform. The adaptivity of this latter yields estimation performance that overhauls usual wavelet-based techniques. To support our claim, we obtain comprehensive results from a Monte Carlo simulation on fractional Brownian motions.
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inria-00570565 , version 1 (04-02-2025)

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Paulo Gonçalves, Patrice Abry, Gabriel Rilling, Patrick Flandrin. Fractal Dimension Estimation: Empirical Mode Decomposition Versus Wavelets. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Apr 2007, Honolulu, Hawaii, United States. pp.III-1153-III-1156, ⟨10.1109/ICASSP.2007.366889⟩. ⟨inria-00570565⟩
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