Pseudo box splines

In this paper, we investigate a new family of refinable functions named pseudo box splines which generalize univariate pseudo-splines to the multivariate setting. The properties of pseudo box splines including stability and regularity are analyzed. Furthermore, we obtain a series of compactly supported C∞ refinable functions by applying nonstationary cascade algorithms to the masks of pseudo box splines. Using these functions, we construct compactly supported nonstationary C∞ tight wavelet frames in L2(Rs) with the spectral frame approximation order.