A study of probability distributions of DCT coefficients in JPEG compression

The Discrete Cosine Transform (DCT) used in JPEG compression has shown excellent energy compaction properties that rival that of the ideal Karhunen-Loève Transform. Lossy compression in JPEG is achieved by distorting 8x8 block DCT coefficients through quantization. It has been shown in literature that DC block DCT coefficients are Gaussian probability distributed and AC block DCT coefficients are Generalized Normal probability distributed.In this investigation, three probability density models for individual modes of non- quantized AC block DCT coefficients are evaluated and are used as basis for the derivation of probability distributions for quantized block DCT coefficients. The suitability of each of the three derived models is evaluated using the Kolmogorov-Smirnov and χ2 goodness-of-fit tests, and the moments of the best-fit model are derived. The best-fit model is applied to detect the presence and extent of JPEG compression history in bitmap images. A model for all quantized AC block DCT coefficients is derived using mixtures of individual quantized block DCT modes, and the model hence developed is used to validate the Generalized Benford's Law for leading digit distributions of quantized AC block DCT coefficients.