B. Hürtgen, T. Hain. On the convergence of fractal transforms. In Proceedings of ICASSP-1994 IEEE International Conference on Acoustics, Speech and Signal Processing, Volume 5, Pages 561-564, Adelaide, 1994.
This paper reports on investigations concerning the convergence of fractal transforms for signal modelling. Convergence is es-sential for the functionality of fractal based coding schemes. The coding process is described as non-linear transformation in the finite-dimensional vector space. Using spectral theory, a neces-sary and sufficient condition for the contractivity is derived from the eigenvalues of a special linear operator. In the same way some constraints for the choice of the encoding parameters are deduced which are less strict than those imposed so far. The pro-posed contractivity measure can be calculated directly from the transformation parameters during the encoding process. For com-plex encoding schemes the calculation of the eigenvalues may be infeasible. For those cases a contractivity criterion derived from the norm of the operator is suggested.
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@InProceedings{HuHa94,
Author = {Hürtgen, B. and Hain, T.},
Title = {On the convergence of fractal transforms},
BookTitle = {Proceedings of ICASSP-1994 IEEE International Conference on Acoustics, Speech and Signal Processing},
Volume = {5},
Pages = {561--564},
Address = {Adelaide},
Year = {1994}
}