In this paper, a second-order Hermite basis of the space of C2quartic splines on the six-directional mesh is constructed and the refinable mask of the basis functions is derived. In addition, the extra parameters of this basis are modified to extend the Hermite interpolating property at the integer lattices by including Lagrange interpolation at the half integers as well. We also formulate a co...

In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite dimensional linear case, and then find the optimum compact support function that best approximates a given filter in the least square sense (l2 norm). The be...

This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are ra...

Univariate spline discrete quasi-interpolants (abbr. dQIs) are approximation operators using B-spline expansions with coefficients which are linear combinations of discrete values of the function to be approximated. When working with nonuniform partitions, the main challenge is to find dQIs which have both good approximation orders and bounded uniform norms independent of the given partition. N...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we consider the properties of monotonicity-preserving and global conservation preserving for ...

This paper presents new univariate linear non-uniform interpolatory subdivision constructions that yield high smoothness, C and C, and are based on least-degree spline interpolants. This approach is motivated by evidence, partly presented here, that constructions based on high-degree local interpolants fail to yield satisfactory shape, especially for sparse, non-uniform samples. While this impr...