Interpolatory biorthogonal multiwavelet transforms based on Hermite splines

We present new multiwavelet transforms for discrete signals. The transforms are implemented in two phases: 1. Pre (post)processing which transform the scalar signal into the vector one (and back). 2.Wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform. We present new pre(post)processing algorithms which do not degrade the approximation accuracy of the vector wavelet transforms. As a result we get fast biorthogonal algorithms to transform discrete-time signals which are exact on the sampled cubic polynomials. The bases for the transform are symmetric and have short support.