Graph Signal Sampling Under Stochastic Priors
Graph Signal Sampling Under Stochastic Priors
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DOI：
10.1109/tsp.2023.3267990
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发表时间：
2022-06
影响因子：
5.4
通讯作者：
Junya Hara;Yuichi Tanaka;Yonina C. Eldar
中科院分区：
文献类型：
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作者：
Junya Hara;Yuichi Tanaka;Yonina C. Eldar
我们提出了随机图信号的广义抽样框架。随机图信号具有图广义平稳性（GWSS），它是标准时域信号广义平稳性的扩展。本文假设图信号满足GWSS条件，研究其采样和恢复过程。在广义采样中，在采样和重构算子之间插入校正滤波器以补偿非理想测量值。我们提出了一种校正滤波器的设计方法，以降低原始图信号和重构图信号之间的均方误差（MSE）。我们推导了两种情况下的校正滤波器：重构滤波器是任意选择的或预定义的。提出的框架允许任意采样方法，即在顶点或图频域采样。我们表明，如果在图频域中进行采样，则所得校正滤波器的图谱响应与WSS信号的广义采样相似。通过实验验证了该方法的有效性，并将其与现有方法进行了MSE比较。
We propose a generalized sampling framework for stochastic graph signals. Stochastic graph signals are characterized by graph wide sense stationarity (GWSS) which is an extension of wide sense stationarity (WSS) for standard time-domain signals. In this paper, graph signals are assumed to satisfy the GWSS conditions and we study their sampling as well as recovery procedures. In generalized sampling, a correction filter is inserted between the sampling and reconstruction operators to compensate for non-ideal measurements. We propose a design method for the correction filters to reduce the mean-squared error (MSE) between the original and reconstructed graph signals. We derive the correction filters for two cases: The reconstruction filter is arbitrarily chosen or predefined. The proposed framework allows for arbitrary sampling methods, i.e., sampling in the vertex or graph frequency domain. We show that the graph spectral response of the resulting correction filter parallels that for generalized sampling for WSS signals if sampling is performed in the graph frequency domain. The effectiveness of our approach is validated via experiments by comparing its MSE with existing approaches.