Multivariate generalized sampling in shift-invariant spaces and its approximation properties

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:355

Article

Garcia, Antonio G.¹  Perez-Villalon, Gerardo² 

[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

[2] UPM, EUITT, Dept Matemat Aplicada, Madrid 28031, Spain

关键词: Shift-invariant spaces;    Dual frames;    Generalized sampling;    Approximation order;   

DOI  :  10.1016/j.jmaa.2009.01.057

来源: Elsevier

【 摘 要 】

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 Z(d). 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 Z(d). In this paper an L-2(R-d) 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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free