Image compression via adaptive self-quantization of wavelet subtrees

Fractal compression schemes do not t into the standard transform coder paradigm and have proven diicult 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 simpliies these schemes considerably. We show that fractal block coders are Haar wavelet subtree quan-tization 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 suuers from none of the convergence problems of fractal decoders.