A complete parametrization of 2D nonseparable orthonormal wavelets

The problem of constructing compactly supported orthonormal multidimensional (k-D) nonseparable wavelets is considered. A complete solution to the problem of parametrizing all possible two-dimensional (2-D) wavelets having arbitrary degree of regularity is given. These results can be seen as a generalization of the Daubechies (1988) wavelets in two dimensions and go beyond those specific examples constructed by other workers in the field. Previous work on the multidimensional version of the problem does not provide a complete parametrization useful for generating all wavelets of interest