Parametrizations for Daubechies wavelets

Two parametrizations are presented for the Daubechies wavelets. The first one is based on the correspondence between the set of multiresolution analysis with compact support orthonormal basis and the group ${\mathrm{SU}}_{\mathit{I}}$(2,openC[z,${\mathit{z}}^{\mathrm{-}1}$]) developed by Pollen. In the second parametrization, emphasis is put on the regularity condition of the Daubechies wavelets and a solitonic cellular automaton algorithm is introduced to solve the orthonormality conditions characterizing the Daubechies wavelets.