Nonideal sampling and interpolation from noisy observations in shift-invariant spaces
Nonideal sampling and interpolation from noisy observations in shift-invariant spaces
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DOI：
10.1109/tsp.2006.873365
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发表时间：
2006-07-01
影响因子：
5.4
通讯作者：
Unser, Michael
中科院分区：
文献类型：
--
作者：
Eldar, Yonina C.;Unser, Michael
信号的数字分析和处理固有地依赖于用于从损坏的离散时间样本序列重构连续时间信号的方法的存在。在本文中，这个问题的一般配方是开发，对待理想的，嘈杂的样本的插值问题，和反卷积的问题，在采样前的信号被过滤，在一个统一的方式。信号重构是在生成函数的整数移位所构成的移位不变子空间中进行的，其中展开系数是通过用数字校正滤波器处理噪声样本而获得的。提出了几种设计校正滤波器的替代方法，它们对信号和噪声的假设不同。经典的反卷积解决方案（最小二乘，吉洪诺夫，和维纳）是适应我们的特殊情况，并提出了新的方法，是最佳的极大极小意义上。解通常具有类似的结构，并且可以通过数字滤波简单有效地计算。给出了重建滤波器的一些具体示例，以及用于选择自由参数的简单指南（例如，正则化）的各种算法。
Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous-time signal from a sequence of corrupted discrete-time samples. In this paper, a general formulation of this problem is developed that treats the interpolation problem from ideal, noisy samples, and the deconvolution problem in which the signal is filtered prior to sampling, in a unified way. The signal reconstruction is performed in a shift-invariant subspace spanned by the integer shifts of a generating function, where the expansion coefficients are obtained by processing the noisy samples with a digital correction filter. Several alternative approaches to designing the correction filter are suggested, which differ in their assumptions on the signal and noise. The classical deconvolution solutions (least-squares, Tikhonov, and Wiener) are adapted to our particular situation, and new methods that are optimal in a minimax sense are also proposed. The solutions often have a similar structure and can be computed simply and efficiently by digital filtering. Some concrete examples of reconstruction filters are presented, as well as simple guidelines for selecting the free parameters (e.g., regularization) of the various algorithms.