A multistage representation of the Wiener filter based on orthogonal projections
A multistage representation of the Wiener filter based on orthogonal projections
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DOI：
10.1109/18.737524
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发表时间：
1998-11-01
影响因子：
2.5
通讯作者：
Scharf, LL
中科院分区：
文献类型：
--
作者：
Goldstein, JS;Reed, IS;Scharf, LL
从信息论的角度分析了平稳复高斯信号的维纳滤波器。对维纳滤波器的双端口分析导致了基于正交投影的分解，并产生了一种使用嵌套的标量维纳滤波器链来实现维纳滤波器的新的多阶段方法。维纳滤波器的这种新表示提供了对以前的、基相关的、降阶维纳滤波器进行信息理论分析的能力。这一分析表明，最近引入的交叉光谱度量是最优的，因为它最大限度地提高了观察过程和期望过程之间的相互信息。在此基础上开发了一种新的降阶维纳滤波器，该滤波器利用期望信号在正交的低维子空间上的连续投影来演化基。利用计算机对比分析模型对性能进行了评估，结果表明，低复杂度多级降秩维纳滤波器的性能优于更复杂的基于特征分解的方法。
The Wiener filter is analyzed for stationary complex Gaussian signals from an information-theoretic point of view. A dual-port analysis of the Wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the Wiener filter using a nested chain of scalar Wiener filters. This new representation of the Wiener filter provides the capability to perform an information-theoretic analysis of previous, basis-dependent, reduced-rank Wiener filters. This analysis demonstrates that the recently introduced cross-spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes. A new reduced-rank Wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal, lower dimensional subspaces. The performance is evaluated using a comparative computer analysis model and it is demonstrated that the low-complexity multistage reduced-rank Wiener filter is capable of outperforming the more complex eigendecomposition-based methods.