Construction of trivariate biorthogonal compactly supported wavelets

In this paper, first we introduce trivariate multiresolution analysis and trivariate biorthogonal wavelets. A sufficient condition on the existence of a pair of trivariate biorthogonal scaling functions is derived. Then, the pair of nonseparable or separable trivariate biorthogonal wavelets can be achieved from the pair of trivariate biorthogonal scaling functions.