ON SYNTHESIZING DISCRETE FRACTIONAL BROWNIAN-MOTION WITH APPLICATIONSTO IMAGE-PROCESSING

This paper evaluates the following four methods for synthesizing discr ete fractional Brownian motion (dfBm): sampled fBm, displaced interpol ation, spectral synthesis, and Karhunen-Loeve-like wavelet expansion w ith respect to the following questions: Does the candidate dfBm have t he correct second-order statistics? Does the candidate dfBm have the c orrect fractal dimension? To estimate the fractal dimension we apply s pectral linear regression, multiresolution energy analysis, and maximu m likelihood estimation, Running an estimation routine on synthesized data raises the final question: How do the assumptions of the estimati on method interact with the assumptions of the synthesis method to pro duce the results of the various trials? Our main conclusions relative to these questions are: (1) Sampled fBm is the only one of the four me thods which has the correct second-order statistics, but only spectral synthesis produces a stationary signal, (2) The fractal dimension of signals produced by sampled fBm, displaced interpolation, and spectral synthesis can be estimated with reasonable accuracy, On the other han d, the wavelet signals are only slightly sensitive to the input values of H. (3) Analysis routines which make assumptions not made by the sy nthesis routine generally yield poor estimates of H, whereas a match o f assumptions generally produces good estimates. (C) 1996 Academic Pre ss,Inc.