Recovering Piecewise Smooth Functions from Nonuniform Fourier Measurements
Recovering Piecewise Smooth Functions from Nonuniform Fourier Measurements
复制标题
从非均匀傅立叶测量中恢复分段平滑函数
DOI：
10.1007/978-3-319-19800-2_8
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Hansen
中科院分区：
文献类型：
--
作者：
B. Adcock;M. Gataric;A. Hansen
在这篇文章中，我们考虑了从分段光滑函数的傅里叶变换的非均匀样本中重构出高精度的问题。我们使用非均匀广义抽样(NUGS)的框架来做到这一点，为了确保高精度，我们使用了由样条或(分段)多项式组成的重建空间。分析了重构空间的维数与非均匀样本带宽的关系，证明了对于固定次数的样条和分段多项式，它是线性的；对于变次数分段多项式，它是二次的。
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and piecewise polynomials of fixed degree, and quadratic for piecewise polynomials of varying degree.