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.