A comparison of non-orthogonal and orthogonal fractal decoding [image coding applications]

The model coefficients for the case of the non-orthogonal basis in Jacquin´s mappings are contrast scaling and luminance offset. After orthogonalization, the model coefficients become range block mean and contrast scaling. These two fractal coding algorithms have the same encoding procedure except that luminance offset is replaced by range block mean, however, their decoding algorithms are different. In this paper, we prove that the orthogonal decoding algorithm converges faster than the non-orthogonal algorithm, while the two decoding algorithms produce the same iteration series if the initial image is the range-averaged image and the step size equals the side-length of the range block.