Multivariate generalized sampling in shift-invariant spaces and its approximation properties |
| |
Authors: | Antonio G. Garcí a,Gerardo Pé rez-Villaló n |
| |
Affiliation: | a Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés-Madrid, Spain b Departamento de Matemática Aplicada, E.U.I.T.T., U.P.M., Carret. Valencia km. 7, 28031 Madrid, Spain |
| |
Abstract: | Nowadays the topic of sampling in a shift-invariant space is having a significant impact: it avoids most of the problems associated with classical Shannon's theory. Under appropriate hypotheses, any multivariate function in a shift-invariant space can be recovered from its samples at Zd. However, in many common situations the available data are samples of some convolution operators acting on the function itself: this leads to the problem of multivariate generalized sampling in shift-invariant spaces. This extra information on the functions in the shift-invariant space will allow to sample in an appropriate sub-lattice of Zd. In this paper an L2(Rd) theory involving the frame theory is exhibited. Sampling formulas which are frame expansions for the shift-invariant space are obtained. In the case of overcomplete frame formulas, the search of reconstruction functions with prescribed good properties is allowed. Finally, approximation schemes using these generalized sampling formulas are included. |
| |
Keywords: | Shift-invariant spaces Dual frames Generalized sampling Approximation order |
本文献已被 ScienceDirect 等数据库收录! |
|