Narrow Results

In this paper, we deal with two different problems. First, we provide the convergence rates of multiresolution approximations, with respect to the supremum norm, for the class of elliptic splines defined in Ref. 10, and in particular for polyharmonic splines. Secondly, we consider the problem of recovering a function from a sample of noisy data. To this end, we define a linear and smooth estimator obtained from a multiresolution process based on polyharmonic splines. We discuss its asymptotic properties and we prove that it converges to the unknown function almost surely.

This paper investigates the axis symmetry property of multivariate wavelets and proposes a general scheme for the construction of multiresolution analysis (MRA-based) wavelet systems with a generalized axis symmetry property according to the mix extension principle. The general formulas for the refinable masks with axis property with respect to the center are described. Using this basis, we are able to obtain the multivariate generalized symmetric wavelet systems.