Fractal image coding as generalized predictive coding

We point out that a prevalent form of fractal image coding can be viewed as a kind of generalized predictive coding. Several key issues in predictive coding are the prediction gain, the design of codebooks for predictors and prediction residuals, shaping of reconstruction errors, and codec complexity. Fractal coding can yield higher prediction gains than conventional predictive coding by its use of noncausal predictors and long-term predictors. However, noncausal prediction necessitates iterative decoding and long-term predictors require search over a large area, both of which increase codec complexity. Design of predictors and prediction codebooks for fractal coding has relied much on heuristics. Drawing on known results about predictive coding, we outline several directions for codec design, among which are short-term prediction and transform coding or vector quantization of prediction residuals. Shaping of reconstruction errors by noise-feedback or analysis-by-synthesis coding may also be beneficial