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Results and Conclusions

The most flat and regular nonseparable wavelets ever designed have been computed. We give for each flatness order the minimal size for achieving it, the number of remaining free degrees, a parametrization of the family of the minimal size filters for this flatness order, the optimization of the remaining free degrees and the analysis of the resulting filter banks in terms of regularity, frequency characteristics and performance in image compression.

The results of our study concerns four scientific communities :

Further work might include the study of other cascade forms for filter banks, or a proof that arbitrarily high flatness and regularity can be achieved in this filter bank family.


next up previous contents
Next: Bibliography Up: The filter bank design Previous: Computer algebra tools used