Empirical mode decomposition synthesis of fractional processes in 1D- and 2D-space

Abstract

We report here on image texture analysis and on numerical simulation of fractional Brownian textures based on the newly emerged Empirical Mode Decomposition (EMD). EMD introduced by N.E. Huang et al. is a promising tool to non-stationary signal representation as a sum of zero-mean AM-FM components called Intrinsic Mode Functions (IMF). Recent works published by P. Flandrin et al. relate that, in the case of fractional Gaussian noise (fGn), EMD acts essentially as a dyadic filter bank that can be compared to wavelet decompositions. Moreover, in the context of fGn identification, P. Flandrin et al. show that variance progression across IMFs is related to Hurst exponent H through a scaling law. Starting with these recent results, we propose a new algorithm to generate fGn, and fractional Brownian motion (fBm) of Hurst exponent H from IMFs obtained from EMD of a White noise, i.e. ordinary Gaussian noise (fGn with H=1/2).