A mathematical analysis of the DCT coefficient distributions for images

Over the past two decades, there have been various studies on the distribut ions of the DCT coefficients for images. However, they have concentrated on ly on fitting the empirical data from some standard pictures with a variety of well-known statistical distributions, and then comparing their goodness -of-fit. The Laplacian distribution is the dominant choice balancing simpli city of the model and fidelity to the empirical data. Yet, to the best of o ur knowledge, there has been no mathematical justification as to what gives rise to this distribution. In this paper, we offer a rigorous mathematical analysis using a doubly stochastic model of the images, which not only pro vides the theoretical explanations necessary, but also leads to insights ab out various other observations from the literature. This model also allows us to investigate how certain changes in the image statistics could affect the DCT coefficient distributions.