Hybrid modeling of natural image in wavelet domain

Natural image is characterized by its highly kurtotic and heavy-tailed distribution in wavelet domain. These typical non-Gaussian statistics are commonly described by generalized Gaussian density (GGD) or α-stable distribution. However, each of the two models has its own deficiency to capture the variety and complexity of real world scenes. Considering the statistical properties of GGD and α-stable distributions respectively, in this paper we propose a hybrid statistical model of natural image´s wavelet coefficients which is better in describing the leptokurtosis and heavy tails simultaneously. Based on a linearly weighted fusion of GGD and α-stable functions, we derive the optimal parametric hybrid model, and measure the model accuracy using Kullback-Leibler divergence, which evaluates the similarity between two probability distributions. Experiment results and comparative studies demonstrate that the proposed hybrid model is closer to the true distribution of natural image´s wavelet coefficients than single GGD or α-stable modeling.