Fractal image compression is based on the self-similarity search of the image. The encoding processis computationally intensive. We present a fast fractal image encoding algorithm that is based on arefinement of the fractal code from an initial coarse level of a pyramid. Assuming that the distributionof the matching error is described by an independent, identically distributed (i.i.d.) Laplacian randomprocess, we derive the threshold sequence for the objective function in each pyramidal level. Thealgorithm is quasi-optimal in terms of minimizing the mean square error. Computational efficiencydepends on the depth of the pyramid and the search step size, and could be improved by up to twoorders of magnitude over the computational effort required for a full search of the original image.
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