Image Coding Using Orthogonal Basis Functions

The transform properties of several orthogonal basis functions are analysed in detail in this report, and their performance compared using a set of grayscale test images, containing both natural and artificial scenes. Well-defined image quality measures are used to determine the type of images that are most suitable for compression for a given basis function. The particular transforms that we have examined are the Discrete Cosine Transform, Discrete Tchebichef Transform, Walsh-Hadamard Transform and Haar Transforms. We have found that the Discrete Cosine Transform and Discrete Tchebichef Transform provide the greatest energy compactness for images containing natural scenes. For images with significant inter-pixel variations we have found that the Discrete Tchebichef Transform and Haar Transform provide the best performance. The Walsh-Hadamard Transform proved to be significantly less effective than either the Discrete Cosine or Discrete Tchebichef Transforms.