Approximation orders for natural splines in arbitrary dimensions

Approximation Orders for Natural Splines in Arbitrary

Pseudo-splines, Wavelets and Framelets

The first type of pseudo-splines were introduced by [Daubechies, Han, Ron and Shen, 2003] (DHRS) to construct tight framelets with desired approximation orders via the unitary extension principle of [Ron and Shen, 1997]. In the spirit of the first type of pseudo-splines, we introduce here a new type (the second type) of pseudo-splines to construct symmetric or antisymmetric tight framelets with...

Symmetric box-splines on root lattices

Root lattices are efficient sampling lattices for reconstructing isotropic signals in arbitrary dimensions, due to their highly symmetric structure. One root lattice, the Cartesian grid, is almost exclusively used since it matches the coordinate grid; but it is less efficient than other root lattices. Box-splines, on the other hand, generalize tensor-product B-splines by allowing non-Cartesian ...

CLASSIFICATION OF REFINABLE SPLINES IN Rd

A refinable spline in R is a compactly supported refinable function whose support can be decomposed into simplices such that the function is a polynomial on each simplex. The best known refinable splines in R are the box splines. Refinable splines play a key role in many applications, such as numerical computation, approximation theory and computer aided geometric design. Such functions have be...

HB - splines : a Blend of Hermite splines and B - splinesLaurent Grisoni

HB-splines: a Blend of Hermite splines and B-splines Laurent Grisoni Carole Blanc Christophe Schlick LaBRI [grisonijblancjschlick]@labri.u-bordeaux.fr Abstract This paper proposes to study a spline model, called HB-splines, that is in fact a B-spline representation of Hermite splines, combined with some restriction on the di erential values at segment boundaries. Although this model does not ap...