Transform Coding of Images Based on Fractal Functional Set.

Orthogonal fractal basis functional sets are proposed for the compression of images with long-tail power distributions. These functional sets are generated by the method of midpoint displacements from deterministic theory and are orthogonalized by the method of Schmidt. From computer simulations of transform data compression coding that uses a transform based on these functional sets and a nonuniform quantizer, the functional sets and a nonuniform quantizer, the functional sets proposed in this paper are shown to better preserve the self-similarity of fractal image data when compared to conventional methods that use the discrete cosine functional (DCF). Also, for standard images that possess local and approximate self-similarity fractal characteristics, although the measured SNR performance is lower, the proposed functional sets are preserve the fractal properties of the images. On the other hand, for standard images that do not possess these fractal properties, compression errors are apparent in blocks from both smooth and edge regions of the images. [ABSTRACT FROM AUTHOR]