Abstract
Fractal compression schemes do not fit into the standard transform coder paradigm and have proven difficult to analyze. The theory of iterated function systems motivates a broad class of fractal schemes but does not give much guidance for their implementation. We introduce a wavelet-based framework for analyzing fractal block coders which simplifies these schemes considerably. We show that fractal block coders are Haar wavelet subtree quantization schemes, and we thereby place fractal schemes in the context of conventional transform coders. We derive a wavelet-based analog of fractal compression, the self-quantization of subtrees (SQS) scheme. SQS compression outperforms the best fractal schemes in the literature by roughly 1 dB in PSNR across a broad range of compression ratios and has performance comparable to some of the best conventional wavelet schemes. We describe a fast SQS decoding scheme which suffers from none of the convergence problems of fractal decoders.
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