Multivariate and asymmetric generalized sampling in shift- invariant spaces with multidimensional

Abstract

We show the sampling theorems for multivariate , nonuniform average sampling , reconstruction in multiply generated , Riesz bases in Hilbert space related to sampling , dual frames in Hilbert space connected with generalized sampling , multivariate generalized sampling with approximation properties in shift-invariant spaces .We consider the average sampling in spline subspaces and in shift-invariant subspaces with symmetric averaging functions .We investigate the channeled sampling in translation and in shift-invariant spaces .We study approximating , by using very coarsely quantized data and sampling with recovery of multidimensional bandlimited functions . We discuss the sampling expansion and asymmetric multi-channel sampling in shift- invariant spaces.