Fractal estimation using models on multiscale trees

TitleFractal estimation using models on multiscale trees
Publication TypeJournal Article
Year of Publication1996
AuthorsFieguth, P., and A. S. Willsky
JournalIEEE Transactions on Signal Processing
Pagination1297 - 1300
Keywords2-D random fields, Brownian motion, fractal estimation, fractal parameter, fractals, fractional Brownian motion, Hurst parameter, irregularly sampled data, likelihood function evaluation, maximum likelihood estimate, maximum likelihood estimation, multiresolution framework, nonstationary measurement noise, random noise, random processes, signal resolution, signal sampling, stochastic processes, trees (mathematics)

We estimate the Hurst parameter H of fractional Brownian motion (or, by extension, the fractal exponent phi; of stochastic processes having 1/f phi;-like spectra) by applying a multiresolution framework. This framework admits an efficient 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 with other proposed methods, and in contrast with 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