An improved algorithm for fractal estimation from noisy measurements

The authors first show that when the increments of sampled fractional Brownian motion (fBm), also known as discrete fractional Gaussian noise (DFGN), are set equal to the finest scale wavelet approximation coefficients and when the Haar basis is selected, the discrete wavelet transform (DWT) coefficients are weakly correlated and have a variance that is exponentially related to scale. The observation motivates a new fractal estimation algorithm, which is a variant of an algorithm introduced by Wornell and Oppenheim (IEEE Trans. vol.SP-40, no.3, p.611-23, March 1992) with the sampled fBm replaced by the increments of the sampled fBm. The performance of the new algorithm is compared with that of Wornell and Oppenheim´s algorithm in numerical simulation results.<>