Fractal Estimation using Models on Multiscale Trees

In this paper we estimate the fractal dimension of stochastic processes with 1/f-like spectra by applying a recently-introduced multiresolution framework. This framework admits an effi-cient likelihood function evaluation, allowing us to compute the maximum likelihood estimate of this fractal parameter with relative ease. In addition to yielding results that compare well to other proposed methods. and in contrast to other approaches, our method is directly applicable, with at most very simple modification, in a variety of other contexts including fractal estimation given irregularly sampled data or nonstationary measurement noise and the estimation of fractal parameters for 2-D random fields.