GG DCT COEFFICIENT MODELS

Abstract

It has been known that the distribution of the discrete cosine transform (DCT) coefficients of most natural images follow a Laplace distribution. However, recent work has shown that the Laplace distribution may not be a good fit for certain types of images and that the Gaussian distribution will be a realistic model in such cases. A model that contains both Laplace and Gaussian distributions as particular cases is the generalized Gaussian (GG) distribution. Assuming this generalized model, we derive a comprehensive collection of formulas for the distribution of the actual DCT coefficients. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. Finally, the superior performance of the derived distributions over the standard Gaussian and Laplace models is illustrated. It is expected that this work could serve as a useful reference and lead to improved modeling with respect to image analysis and image coding.