Comparison of Generalized Gaussian and Cauchy distributions in modeling of dyadic rearranged 2D DCT coefficients

The dyadic rearrangement of block two-dimensional Discrete Cosine Transform (2D DCT) coefficients when used with zero tree quantizers show comparable performance with that of discrete wavelet transform based methods for image compression applications. Recently we have shown that Generalized Gaussian distribution better models the statistics of subband rearranged 2D DCT coefficients compared to Gaussian, Laplacian and Gamma distributions. This paper presents results of distribution tests that indicate that for most of the natural images Cauchy distribution models the subband coefficients more accurately than Generalized Gaussian distribution. The knowledge of the suitable distribution helps in design of optimal quantizers that may lead to minimum distortion and hence achieve optimal coding efficiency.