Performance bounds for fractal coding

This paper reports on investigations concerning the performance of fractal transforms. Emerging from the structural constraints of fractal coding schemes, lower bounds for the reconstruction error are given without regarding quantization noise. This implies finding an at least locally optimal transformation matrix. A full search approach is by definition optimal but also intractable for practical implementations. In order to simplify the calculation of some appropriate encoding parameter, the collage theorem and other fast but also suboptimal approaches are applied. For a memoryless Gaussian source and some real world images the optimal encoding parameters in view of the structural constraints are determined together with the minimal reachable distortion. This allows to quantify the performance of the suboptimal encoding procedures.