How I came up with the discrete cosine transform

Abstract

During the late sixties and early seventies, there was a great deal of research activity related to digital orthogonal transforms and their use for image data compression. As such, there were a large number of transforms being introduced with claims of better performance relative to others transforms. Such comparisons were typically made on a qualitative basis, by viewing a set of “standard” images that had been subjected to data compression using transform coding techniques. At the same time, a number of researchers were doing some excellent work on making comparisons on a quantitative basis. In particular, researchers at the University of Southern California’s Image Processing Institute (Bill Pratt, Harry Andrews, Ali Habibi, and others) and the University of California at Los Angeles (Judea Pearl) played a key role. In this regard, the variance criterion and the rate distortion criterion were developed and used extensively as performance measures for evaluating image data compression. In addition, the Karhunen-Loeve transform (KLT) evolved as the optimal transform for comparison purposes. With this as background, I can now address the DCT issue. What intrigued me was that the KLT was indeed the optimal transform on the basis of the meansquare-error criterion and the first-order Markov process model, and yet there was no efficient algorithm available to compute it. As such, the focus of my research was to determine whether it would be possible to come up with a good approximation to the KLT that could be computed efficiently. An approach that I thought might be worth looking into was Chebyshev interpolation, a neat discussion of which was available in a text book (Computer Evaluation of Mathematical Functions, by C. T. Fike, Prentice-Hall, 1968, Sections 7.4 and 7.5). This was in early 1972, and I wrote a proposal to the National Science Foundation (NSF)