Image reconstruction using various discrete orthogonal polynomials in comparison with DCT

摘要

The energy compactness of various discrete orthogonal polynomials used as the basis functions in an image reconstruction kernel is being studied in this paper, specifically the discrete cosine transform (DCT), Tchebichef, Krawtchouk, Hahn and Poisson–Charlier. These polynomials were being tested with a variety of grayscale images, with and without block segmentation. As a result, we concluded that DCT is still the best among all for smooth images and Tchebichef is the best for rougher images. Krawtchouk would outperform Tchebichef sometimes; but Hahn and Poisson–Charlier performed badly overall. Moreover, the weighted form of Krawtchouk and Hahn might be slightly superior to their original form, but they create undesired blocking effects in block segmentation image reconstruction.