Research Center of Smart Networks and Systems, School of Information Science and Technology, Fudan University, Shanghai 200433, China.
Center for Intelligent Medical Electronics, School of Information Science and Technology, Fudan University, Shanghai 200433, China.
Sensors (Basel). 2021 Feb 19;21(4):1460. doi: 10.3390/s21041460.
Graph signal sampling has been widely studied in recent years, but the accurate signal models required by most of the existing sampling methods are usually unavailable prior to any observations made in a practical environment. In this paper, a sequential sampling and estimation algorithm is proposed for approximately bandlimited graph signals, in the absence of prior knowledge concerning signal properties. We approach the problem from a Bayesian perspective in which we formulate the signal prior by a multivariate Gaussian distribution with unknown hyperparameters. To overcome the interconnected problems associated with the parameter estimation, in the proposed algorithm, hyperparameter estimation and sample selection are performed in an alternating way. At each step, the unknown hyperparameters are updated by an expectation maximization procedure based on historical observations, and then the next node in the sampling operation is chosen by uncertainty sampling with the latest hyperparameters. We prove that under some specific conditions, signal estimation in the proposed algorithm is consistent. Subsequent validation of the approach through simulations shows that the proposed procedure yields performances which are significantly better than existing state-of-the-art approaches notwithstanding the additional attribute of robustness in the presence of a broad range of signal attributes.
近年来，图信号采样受到了广泛的研究，但大多数现有采样方法所需的准确信号模型在实际环境中的任何观测之前通常是不可用的。在本文中，我们提出了一种用于近似带限图信号的顺序采样和估计算法，在没有关于信号特性的先验知识的情况下。我们从贝叶斯的角度来解决这个问题，其中我们用具有未知超参数的多元高斯分布来表示信号先验。为了克服与参数估计相关的互联问题，在提出的算法中，超参数估计和样本选择以交替的方式进行。在每一步中，基于历史观测更新未知超参数，然后根据最新的超参数通过不确定性采样选择下一个采样操作的节点。我们证明，在一些特定条件下，所提出的算法中的信号估计是一致的。通过仿真对该方法进行的后续验证表明，尽管在存在广泛信号属性的情况下具有稳健性的额外属性，但该方法的性能明显优于现有的最先进方法。
