Parameter Estimation Of Fractal Signal And Its Application

The fractal image compression coding, which has highly attracted the attention of thewhole academe, is the representative application of 1/ f-Type Fractal Signal. It has brokenthrough the theoretical boundary of the traditional entropy compression coding. Obviously, inview of the fact that the noise existence is of universality, the most important task should be toestimate the parameter of the fractal stochastic process embedded in noise from an observedsample path.In 1992, Wornell and Oppenheim first obtained the maximum Likelihood (ML) estimatorof the 1/f -type fractal parameter β ,σ2and σ w2 in noise, however ML iterative algorithm is ofextremely complexity and receives the influence of the range of the spectrum exponentγ( γ ∈(0,1)). Moreover this algorithm is not suit for the excellent model of fractal signal, i.e.the fractional Brownian motions (FBM).Using wavelets analysis, this paper has utilized many kinds of ways to imitate the reliableprocess of FBM successfully and presented a new estimator of the parameter β ,σ2and σ w2 ofFBM in noise theoretically and deeply.In addition, it has simulated a great number of experimental datum in the new way from theprocess of FBM that comes into being through the imitation. Compared with the classical MLmethod in detail, it is proved that the new way has three advantages: i) it is more effective andpractical, ii) the distribution of noise is not restricted within Gauss Distribution. iii) the range ofestimate parameter is wider( γ ∈(0,3)). It is unmatchable with the classic arithmetic of theparameter estimator of 1 /f fractal process in noise.This paper shows the practical application values of the representative fractal signalsthrough the MATLAB programming. Then the general applications of fractal theory nowadaysare being discussed. Although the fractal block-coding by automatically searching, which wasproposed by A.E. Jacqain, could have the whole coding done automatically, the computing timespent on the block-coding needs a great deal. The novel method combining the fixed-reseaumethod with the quarter-gray-gradation-arranging-and-classifying method, which is adopted inthis paper, has reduced the searching time greatly and simplified the computation complexity. Asa result of the realization of the fractal coding in wavelet domain, the compression ratio may beenhanced, as well as the image loss of the detail parts may be reduced. Furthermore, the codingtime may be decreased considerably. This paper, therefore, has made all efforts to attempt toindicate that the effect can overmatch the DCT-coding and the fractal coding in spatial domain.