Fractal Dimension Estimation: Empirical Mode Decomposition Versuswavelets

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.