In this article, we propose and develop a spectral graph based vertex varying Wiener filtering framework in the joint vertex-frequency domain for denoising of graph signals defined on weighted, undirected and connected graphs. To this end, we first extend the Zadeh time-frequency filter concept to graph signals and obtain vertex-frequency transfer function of the proposed Wiener filter by transforming its vertex varying impulse response that minimizes the mean square error between original and recovered signals. To facilitate the derived Wiener filter, we present a detailed derivation of a recently proposed graph Rihaczek vertex-frequency signal distribution (GRD) so as to match the structure of the proposed graph Zadeh filter, based on a graph translation operator defined by generalized convolution with a delta signal. We express the filter transfer function in terms of this graph transform of the original, noiseless signal. The form of the obtained Wiener filter is, interestingly, different than those of time-frequency Wiener filters prevalent in the classical signal processing. We also investigate the invertibility of the employed GRD. Assuming that the original graph signal of interest can be viewed as deterministic, we propose two algorithms to implement the proposed vertex-frequency Wiener filter from a single realization of a noisy, input signal. We derive mean and variance of the GRD of the noisy signal, since they are required in one of these algorithms. We apply proposed Wiener filter algorithms to denoise a standard set of images and three irregularly structured graph signals, and demonstrate their competitiveness with compared high performance denoising methods.

中文翻译：

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基于频谱图的顶点频率维纳滤波，用于图像和图形信号降噪

在本文中，我们提出并开发了一种在联合顶点-频域中基于频谱图的基于顶点变化Wiener滤波框架的框架，用于对在加权图，无向图和连接图上定义的图信号进行去噪。为此，我们首先将Zadeh时频滤波器概念扩展到图形信号，并通过变换其顶点变化的脉冲响应来最小化原始信号和恢复信号之间的均方误差，从而获得所建议的Wiener滤波器的顶点频率传递函数。为了方便派生的维纳滤波器，我们基于广义卷积定义的图平移算子，给出了最近提出的图Rihaczek顶点频率信号分布（GRD）的详细推导，以匹配提出的图Zadeh滤波器的结构。增量信号。我们通过原始无噪声信号的图形变换来表达滤波器传递函数。有趣的是，所获得的维纳滤波器的形式不同于经典信号处理中普遍存在的时频维纳滤波器的形式。我们还研究了所用GRD的可逆性。假设感兴趣的原始图形信号可以被视为确定性的，我们提出了两种算法，从一个有噪声的输入信号的单一实现中实现提出的顶点频率维纳滤波器。由于这些算法之一需要它们，因此我们得出了噪声信号GRD的均值和方差。我们应用提议的维纳滤波器算法对一组标准的图像和三个不规则结构的图形信号进行去噪，