A Comparison of Discrete Orthogonal Basis Functions for Image Compression

In this report we analyse the image reconstruction accuracy when using different orthogonal basis functions as the kernel for a reversible image transform. In particular we examine the Discrete Cosine Transform(DCT), Discrete Tchebichef Transform(DTT), Haar Transform, and Walsh-Hadamard Transforms(WHT). We have found that the DCT provides the greatest energy compactness properties for continuous tone images(such as photographs). For images demonstrating rapid gradient variations the Haar Transform performs significantly better than any of the other transform we have analysed, although its performance on continuous tone images is substantially worse than either the DCT or DTT. The WHT performs poorly on either image type.