Contourlet domain image modeling by using the alpha-stable family of distributions

It is known that the contourlet coefficients of images have non-Gaussian property and heavy tails. In view of this, an appropriate distribution to model the statistics of the contourlet coefficients would be the one having large peaks, and tails heavier than that of a Gaussian PDF, i.e., a heavy-tailed PDF. This paper proposes a new image modeling in the contourlet domain, where the magnitudes of the coefficients are modeled by a symmetric alpha-stable distribution which is best suited for modeling transform coefficients with a high non-Gaussian property and heavy tails. It is shown that the alpha-stable family of distributions provides a more accurate model to the contourlet subband coefficients than the formerly used distributions, namely, the generalized Gaussian and Laplacian distributions, both in terms of the subjective measure of the Kolmogorov-Smirnov distance and the objective measure of comparing the log-scale histograms.