Decomposition of Surface Data into Fractal Signals Based on Mean Likelihood and Importance Sampling and Its Applications to Feature Extraction

摘要

This paper deals with the decomposition of surface data into several fractal signal based on the parameter estimation by the Mean Likelihood and Importance Sampling (IS) based on the Monte Carlo simulations. The method is applied to the feature extraction of surface data. Assuming the stochastic models for generating the surface, the likelihood function is defined by using wavelet coefficients and the parameter are estimated based on the mean likelihood by using the IS. The approximation of the wavelet coefficients is used for estimation as well as the statistics defined for the variances of wavelet coefficients, and the likelihood function is modified by the approximation. After completing the decomposition of underlying surface data into several fractal surface, the prediction method for the fractal signal is employed based on the scale expansion based on the self-similarity of fractal geometry. After discussing the effect of additive noise, the method is applied to the feature extraction of real distribution of surface data such as the cloud and earthquakes.