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.
翻译:在本文中,我们考虑维纳过滤器,以重建确定性和(宽带)固定图形信号,这些信号来自其观测结果,被随机噪音腐蚀,我们提出分布式算法,以在网络上实施维纳过滤器和反过滤器,在这些网络上,代理器配备了数据处理子子系统,用于有限的数据储存和计算能力,并有一个单点通信子系统,仅用于与其相邻的代理器直接数据交换。拟议的分布式多边近似算法是一种指数趋同准纽顿法,其依据是Jacobi 多元诺米约近似和Chebyshev 间推近多边近近光法和切伯谢夫间推近多位接近法与立方体分析功能。我们的数字模拟显示,维纳过滤程序在除去(宽带)固定信号方面比Tikhonov 常规方法表现得更好,而且拟议的多点近比Chebyshev 多边近比法和梯度正值算法更快地结合,在实施与多位图转换的多端过滤法相关的反过滤程序时,以反过滤程序为基础。