Quincunx fundamental refinable functions and Quincunx biorthogonal wavelets
Mathematics of Computation
Effortless critical representation of laplacian pyramid
IEEE Transactions on Signal Processing
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We analyze the approximation and smoothness properties of fundamental and refinable functions that arise from interpolatory subdivision schemes in multidimensional spaces. In particular, we provide a general construction of bivariate interpolatory refinement masks such that the corresponding fundamental and refinable functions attain the optimal approximation order and smoothness order. In addition, these interpolatory refinement masks are minimally supported and enjoy full symmetry. Several examples are explicitly computed.