论文标题
Wiener滤波器在图形和分布式多项式近似算法上
Wiener filters on graphs and distributed polynomial approximation algorithms
论文作者
论文摘要
在本文中，我们考虑Wiener滤波器从其观察值中重建确定性和（宽波段）固定的图形信号，这些观察值被随机噪声损坏，我们建议在网络上实现Wiener过滤器和逆滤波器，该网络对代理的网络进行了逆滤波器，在该网络中，配备有限的数据处理子系统，仅通过数据处理和计算数据处理，可用于临时数据处理，并促进一路交流。拟议的分布式多项式近似算法是一种基于雅各比多项式近似值和Chebyshev插值多项式近似值的指数收敛准牛顿方法，可用于分析功能。我们的数值模拟表明，维也纳（Wiener）过滤过程在脱氧（宽带）固定信号方面的性能要比tikhonov正则化方法更好，并且所提出的多项式近似算法比Chebyshev多项式近似近似算法和渐变型号的过滤量相关的多项式近似算法更快地收敛于Chebyshev多项式的过滤过程。图形移动。
In this paper, we consider Wiener filters to reconstruct deterministic and (wide-band) stationary graph signals from their observations corrupted by random noises, and we propose distributed algorithms to implement Wiener filters and inverse filters on networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. The proposed distributed polynomial approximation algorithm is an exponential convergent quasi-Newton method based on Jacobi polynomial approximation and Chebyshev interpolation polynomial approximation to analytic functions on a cube. Our numerical simulations show that Wiener filtering procedure performs better on denoising (wide-band) stationary signals than the Tikhonov regularization approach does, and that the proposed polynomial approximation algorithms converge faster than the Chebyshev polynomial approximation algorithm and gradient decent algorithm do in the implementation of an inverse filtering procedure associated with a polynomial filter of commutative graph shifts.
