Quincunx Fundamental Refinable Functions in Arbitrary Dimensions

In this paper, we generalize the family of Deslauriers–Dubuc’s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the full-axis symmetry property. In dimension d = 2, we give the explicit form of such unique quincunx interpolatory masks, which implies the nonnegativity property of such a family of masks.