Title :
A mathematical analysis of the DCT coefficient distributions for images
Author :
Lam, Edmund Y. ; Goodman, Joseph W.
Author_Institution :
Dept. of Electr. Eng., Stanford Univ., CA, USA
fDate :
10/1/2000 12:00:00 AM
Abstract :
Over the past two decades, there have been various studies on the distributions of the DCT coefficients for images. However, they have concentrated only 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 simplicity of the model and fidelity to the empirical data. Yet, to the best of our knowledge, there has been no mathematical justification as to what gives rise to this distribution. We offer a rigorous mathematical analysis using a doubly stochastic model of the images, which not only provides the theoretical explanations necessary, but also leads to insights about 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
Keywords :
Gaussian distribution; discrete cosine transforms; image coding; mathematical analysis; stochastic processes; transform coding; DCT coefficient distributions; Gaussian distribution; Laplacian distribution; central limit theorem; doubly stochastic model; empirical data; image coding; image statistics; mathematical analysis; standard pictures; statistical distributions; Discrete cosine transforms; Gaussian distribution; Histograms; Image coding; Laplace equations; Mathematical analysis; Mathematical model; Statistical distributions; Stochastic processes; Testing;
Journal_Title :
Image Processing, IEEE Transactions on