Local Sampling and Reconstruction in Shift-Invariant Spaces and Their Applications in Spline Subspaces
Local Sampling and Reconstruction in Shift-Invariant Spaces and Their Applications in Spline Subspaces
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DOI：
10.1080/01630561003760128
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发表时间：
2010-04
影响因子：
1.2
通讯作者：
Jun Xian;Wenchang Sun
中科院分区：
文献类型：
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作者：
Jun Xian;Wenchang Sun
在信号处理的许多应用中，从样本的局部重构是最理想的性质之一。局部采样实际上是有用的，因为我们只需要考虑有界区间上的信号，计算机只能处理有限的样本。然而，局部采样和重建问题没有得到足够的重视。大多数已知的结果涉及全局采样和重建。关于样条子空间中的局部采样和重构问题，目前还没有什么结果。本文研究了一般移位不变空间和具有紧支撑生成元的多重生成移位不变空间中的局部采样和重构问题。然后给出了样条子空间和多重生成样条子空间中的几个应用。
The local reconstruction from samples is one of the most desirable properties for many applications in signal processing. Local sampling is practically useful since we need only to consider a signal on a bounded interval and computer can only process finite samples. However, the local sampling and reconstruction problem has not been given as much attention. Most of known results concern global sampling and reconstruction. There are only a few results about local sampling and reconstruction in spline subspaces. In this article, we study local sampling and reconstruction in general shift-invariant spaces and multiple generated shift-invariant spaces with compactly supported generators. Then we give several applications in spline subspaces and multiple generated spline subspaces.