Wavelet families of increasing order in arbitrary dimensions

We build discrete-time compactly supported biorthogonal wavelets and perfec t reconstruction filter banks for any lattice in any dimension with any num ber of primal and dual vanishing moments. The associated scaling functions are interpolating. Our construction relies on the lifting scheme and inheri ts all of its advantages: fast transform, in-place calculation, and integer -to-integer transforms. We show that two lifting steps suffice: predict and update. The predict step can be built using multivariate polynomial interp olation, while update is a multiple of the adjoint of predict. While we con centrate on the discrete-time case, some discussion of convergence and stab ility issues together with examples is given.