Optimal selection of multi-dimensional biorthogonal wavelet bases

The selection is considered of scaling functions for optimal signal representation by multidimensional biorthogonal wavelet frames. Criterion for optimality is the minimization of the mean-square approximation error at each level of the decomposition. Conditions are given under which the approximation error of the decomposition approaches zero as the level increases. Optimal and suboptimal families of filters for the realization of the scaling functions are explicitly defined.<>