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New results for fractal/wavelet image compression

In this research, we perform a multiresolution analysis of the mappings used in fractal image compression. We derive the transform-domain structure of the mappings and demonstrate a close connection between fractal image compression and wavelet transform coding using the Haar basis. We show that under certain conditions, the mappings correspond to a hierarchy of affine mappings between the subbands of the transformed image. Our analysis provides new insights into the mechanism underlying fractal image compression, leads to a non-iterative transform-domain decoding algorithm, and suggests a transform-domain encoding method with extensions to wavelets other than the Haar transform. As a result, we also propose a novel transform-domain encoding scheme whereby the image is hierarchically encoded starting with a coarse approximation and detail is added through a casual sequence of affine mappings between the subbands. This new approach is not only theoretically elegant, but also useful for embedded representation, i.e. images can be decoded to an intermediate resolution.