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The Discrete Cosine Transform

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The Discrete Cosine Transform
The Discrete Cosine Transform
(DCT):
Theory and Application

1

Syed Ali Khayam
Department of Electrical & Computer Engineering
Michigan State University
March 10th 2003

1

This document is intended to be tutorial in nature. No prior knowledge of image processing concepts is assumed. Interested readers should follow the references for advanced material on DCT.

ECE 802 – 602: Information Theory and Coding
Seminar 1 – The Discrete Cosine Transform: Theory and Application

1. Introduction
Transform coding constitutes an integral component of contemporary image/video processing applications. Transform coding relies on the premise that pixels in an image exhibit a certain level of correlation with their neighboring pixels. Similarly in a video transmission system, adjacent pixels in consecutive frames2 show very high correlation. Consequently, these correlations can be exploited to predict the value of a pixel from its respective neighbors. A transformation is, therefore, defined to map this spatial (correlated) data into transformed
(uncorrelated) coefficients. Clearly, the transformation should utilize the fact that the information content of an individual pixel is relatively small i.e., to a large extent visual contribution of a pixel can be predicted using its neighbors.

A typical image/video transmission system is outlined in Figure 1. The objective of the source encoder is to exploit the redundancies in image data to provide compression. In other words, the source encoder reduces the entropy, which in our case means decrease in the average number of bits required to represent the image. On the contrary, the channel encoder adds redundancy to the output of the source encoder in order to enhance the reliability of the transmission. Clearly, both these high-level blocks have contradictory objectives and their interplay is an active research area ([1], [2], [3], [4], [5], [6], [7], [8]). However, discussion on joint source



References: Real Time Services on Packet Networks,” IEEE/ACM Transactions on Networking, 1993. Coding for Scalable Video Streaming over Wireless Channel," IEEE ISCAS’01, May, 2001, Sydney, Australia. [11] R. C. Gonzalez and P. Wintz, “Digital Image Processing,” Reading. MA: Addison-Wesley, 1977. Newyork: International Thomsan Publishing, 1993. 135-147, 1999. [15] R. J. Clark, “Transform Coding of Images,” New York: Academic Press, 1985. [16] A. K. Jain, “Fundamentals of Digital Image Processing,” New Jersey: Prentice Hall Inc., 1989. [22] M. Vetterli, “Fast 2-D Discrete Cosine Transform,” ICASSP '85, p. 1538.

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