Employing Quantile and Probability Plots for Comparing and Assessing Goodness of Fit for Stochastic Models of the DCT Coefficients of Lossy Compressed Images

The paper employs probability plots to perform goodness of fit tests for AC DCT coefficients of compressed images. Attention is paid to various probabilistic models of the DCT coefficients, conventional and rarely used. The Laplacian, generalized Gaussian and doubly Gamma distributions comprise the list. A variation of the method of moments, which involves the 2nd and 4th sample moments as well as Sheppard's corrections to estimate the shape and scale parameters of the distributions is used. Two types of images are considered, namely, texture-like images and those possessing vast regions of monotonicity. Special effort has been put into adjusting the apparatus of the probability plots to make them suitable for dealing with discrete data, in our case with the quantized DCT coefficients of lossy compressed images. As the source of the DCT coefficients, JPEG images are used. This does not lead us to a significant loss of generality: conclusions drawn in this paper remain applicable to a broad variety of formats of lossy compressed images.