Discrete Tchebichef transform and its application to image / video compression

The discrete Tchebichef transform (DTT) is a novel polynomial-based orthogonal transform. It exhibits interesting properties, such as high energy compaction, optimal decorrelation and direct orthogonality, and hence is expected to produce good transform coding results. Advances in the areas of image and video coding have generated a growing interest in discrete transforms. The demand for high quality with a limited use of computational resources and improved cost benefits has lead to experimentation with novel transform coding methods. One such experiment is undertaken in this thesis with the DTT. We propose the integer Tchebichef transform (ITT) for 4x4 and 8x8 DTTs. Using the proposed ITT, we also design fast multiplier-free algorithms for 4-point and 8-point DTTs that are superior to the existing algorithms. We perform image compression using 4 {604} 4 and 8 {604} 8 DTT. In order to analyze the performance of DTT, we compare the image compression results of DTT, discrete cosine transform (DCT) and integer cosine transform (ICT). Image quality measures that span both the subjective and objective evaluation techniques are computed for the compressed images and the results analyzed taking into account the statistical properties of the images for a better understanding of the behavioral trends. Substantial improvement is observed in the quality of DTT-compressed images. The appealing characteristics of DTT motivate us to take a step further to evaluate the computational benefits of ITT over ICT, which is currently being used in the H.264/AVC standard. The merits of DTT as demonstrated in this thesis are its simplicity, good image compression potential and computational efficiency, further enhanced by its low precision requirement