A WAVELET-BASED ANALYSIS OF FRACTAL IMAGE COMPRESSION

Why does fractal image compression work? What is the implicit image mo del underlying fractal block coding? How can we characterize the types of images for which fractal block coders will work well? These are th e central issues we address. We introduce a new wavelet-based framewor k for analyzing block-based fractal compression schemes. Within this f ramework we are able to draw upon insights from the well-established t ransform coder paradigm in order to address the issue of why fractal b lock coders work, We show that fractal block coders of the form introd uced by Jacquin [1] are Haar wavelet subtree quantization schemes, We examine a generalization of the schemes to smooth wavelets with additi onal vanishing moments. The performance of our generalized coder is co mparable to the best results in the literature for a Jacquin-style cod ing scheme. Our wavelet framework gives new insight into the convergen ce properties of fractal block coders, and it leads us to develop an u nconditionally convergent scheme with a fast decoding algorithm. Our e xperiments with this new algorithm indicate that fractal coders derive much of their effectiveness from their ability to efficiently represe nt wavelet zerotrees. Finally, our framework reveals some of the funda mental limitations of current fractal compression schemes.