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.
Bacchelli, B., Bozzini, M., Rossini, M. (2006). On the errors of multidimensional MRA based on non-separable scaling functions. INTERNATIONAL JOURNAL OF WAVELETS, MULTIRESOLUTION AND INFORMATION PROCESSING, 4(3), 475-488 [10.1142/S0219691306001397].
On the errors of multidimensional MRA based on non-separable scaling functions
BACCHELLI, BARBARA;BOZZINI, MARIA TUGOMIRA;ROSSINI, MILVIA FRANCESCA
2006
Abstract
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.
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