The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition
The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition
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通过奇异值分解从任意位置的有限数量样本重建带限函数及其傅立叶变换
DOI：
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发表时间：
1992
影响因子：
5.4
通讯作者：
D. Wingham
中科院分区：
文献类型：
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作者：
D. Wingham
给出了在噪声存在的情况下，在任意位置的采样时刻已知的带限函数的稳定插值方法。奇异值分解用于提供一种级数展开，与抽样函数的方法相反，它允许在样本值中缺乏表示的最小范数空间中简单地识别向量。在存在噪声时，给出了米勒正则化、最小二乘估计和最大后验估计三种正则化重构方法。采用奇异值分解（SVD）方法对这些方法进行关联。给出了说明该技术的实例。>
A method for the stable interpolation of a bandlimited function known at sample instants with arbitrary locations in the presence of noise is given. Singular value decomposition is used to provide a series expansion that, in contrast to the method of sampling functions, permits simple identification of vectors in the minimum-norm space poorly represented in the sample values. Three methods, Miller regularization, least squares estimation, and maximum a posteriori estimation, are given for obtaining regularized reconstructions when noise is present. The singular value decomposition (SVD) method is used to interrelate these methods. Examples illustrating the technique are given. >