Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces:: The Lp-theory
Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces:: The Lp-theory
复制标题
DOI：
10.1090/s0002-9939-98-04319-6
复制
发表时间：
1998-09-01
影响因子：
1
通讯作者：
Feichtinger, H
中科院分区：
文献类型：
--
作者：
Aldroubi, A;Feichtinger, H
我们证明了一个函数的精确重构可以由其样本S(x(I))在任何“足够稠密”的样本集{x(I)}(I Epsilon Lambda)上得到，只要已知S属于L-p(R-n)中的一大类样条型空间.此外，重建可以使用快速算法来实现。由于极限情况是带限函数空间，我们的结果推广了关于规则抽样的经典的Shannon-Whittaker抽样定理和关于非均匀抽样的Paley-Wiener定理。
We prove that the exact reconstruction of a function s from its samples s(x(i)) on any "sufficiently dense" sampling set {x(i)}(i epsilon Lambda) can be obtained, as long as s is known to belong to a large class of spline-like spaces in L-p(R-n). Moreover, the reconstruction can be implemented using fast algorithms. Since a limiting case is the space of bandlimited functions, our result generalizes the classical Shannon-Whittaker sampling theorem on regular sampling and the Paley-Wiener theorem on non-uniform sampling.