Comparative Study of a Discrete Linear Basis for Image Data Compression

Transform imlige data compression consists of dividing the image into a number of nonoverlapping subimage regions and quantizing and coding the transform of the data from each subimage. KarbunenLoeve, Hadamard, and Fourier transforms are most commonly used in transform image compression. This paper presents a new discrete linear transform for image compression which we use in conjunction with ditferential pulse-code modulation on spatially adjacent transformed subimage samples. For a set of thirty-three 64 x 64 images of eleven ditferent categories, we compare the perfo~ of the discrete linear Manuscript received February 21, 1973; revised July 9, 1973. R. M. Haralick is with the Center for Research, Inc., and the Department of Electrical Engineering, University of Kansas, Lawrence, Kans. 66044. K. Shanmugam was with the Center for Research, Inc., and the Department of Electrical Engineering, University of Kansas, Lawrence, Kans. He is now with the Department of Electrical Engineering, Wichita State University, Wichita, Kans. 67218. transform compression technique with tbe Karhunen-Loeve and Hadamard transform techniques. Our measure of performance is the meansquared error between tbe original image and the reconstrncted image. We multiply the mean-squared error with a factor indicating the degree to which the error is spatially correlated. We find that for low compression rates, the Karhunen-Loeve outperforms both tbe Hadamard and the discrete linear basis ·method. However, for high compression rates, tbe performance of the discrete transform method is very close to that of the Karbunen-Loeve transform. The discrete linear transform method performs much better than the Hadamard transform method for all compression rates.