| We introduce new anisotropic wavelet decompositions associated with the smoothness beta, beta = (beta1, ..., betad), beta 1, ..., betad > 0 of multi-dimensional data as measured in anisotropic Besov spaces Bbeta. We give the rate of compression of these wavelet decompositions of functions f ∈ Bbeta. Finally, we prove that, among a general class of anisotropic wavelet decompositions of a function f ∈ Bbeta the anisotropic wavelet decomposition associated with beta yields the optimal rate of compression of the wavelet decomposition of f. |
