Document Type
Thesis
Date of Award
Spring 5-31-2010
Degree Name
Master of Science in Electrical Engineering - (M.S.)
Department
Electrical and Computer Engineering
First Advisor
Yun Q. Shi
Second Advisor
Atam P. Dhawan
Third Advisor
Jie Hu
Abstract
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.
Recommended Citation
Narayanan, Gopal Thirumalai, "A study of probability distributions of DCT coefficients in JPEG compression" (2010). Theses. 61.
https://digitalcommons.njit.edu/theses/61
