Fractal Estimation Using Models on Multiscale Trees [Correspondence] - Signal Processing, IEEE Transactions on

In this correspondence, we estimate the Hurst parameter H of fractional Brownian motion (or, by extension, the fractal exponent 9 of stochastic processes having 1/ f +‘-like spectra) by applying a recently introduced 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. Manuscript received February 3, 1995; rcvised November 28, 1995. This work was supported, in part, by the Office of Naval Research under Grant N00014-91 -J-1004, the Advanced Research Projects Agency under Grant F4962O-931-0604, by the Air Force Office of Scientific Research under Grant F49620-95-1-0083, and by an NSERC-67 fellowship of the Natural Sciences and Engineering Research Council of Canada. The associate editor coordinating the review of this paper and approving it for publication was Dr. Petar M. Djuric. The authors are with the Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 USA. Publisher Item Identifier S l053-587X(96)03060-7. Scale 2