Quincunx fundamental refinable functions in arbitrary dimensions (Q2275130)

Summary: 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.