Discrete tchebichef transform-A fast 4x4 algorithm and its application in image/video compression

Discrete Tchebichef transform (DTT), derived from a discrete class of the popular Chebyshev polynomials, is a novel orthogonal transform that has high energy compaction and de-correlation properties. Therefore, in this paper, DTT is examined and treated for transform coding applications. A framework is laid to derive an approximation-free integer representation of DTT to meet the current application requirements. A fast algorithm is further proposed for multiplier-free computation of DTT. The image compression performance of the 4-point DTT is found to be superior to that of the 4-point discrete cosine transform (DCT) and integer cosine transform (ICT), the integer approximation of DCT. It is shown that the fast DTT is easily derived, has low complexity, does not involve approximations and can be carried out within the same dynamic range. Hence, DTT can be used for image and data compression applications. Since the image compression performance and computational simplicity of DTT are found to be significantly better than that of ICT, the use of DTT in place of ICT for transform coding in the H.264/AVC looks promising.