Statistical evaluation of fractal coding schemes

This paper reports on investigations concerning the convergence of the reconstruction process in fractal coding schemes from a statistical point of view. For a rather general family of “fractal operators” a necessary and sufficient condition for the convergence based on the spectral radius of the fractal operator is provided. Emerging from this condition the probability density function (pdf) of the magnitude of the eigenvalues is formulated which enables to determine a probabilistic measure for the convergence of the reconstruction process. Since the pdf considerably depends on the structure of the operators, various coding schemes can be analyzed with respect to their convergence properties in a statistical sense. The presented results indicate that certain types of operators are less suited for applications in the field of fractal coding compared to others.