论文标题
统计图信号恢复使用变分贝叶
Statistical Graph Signal Recovery Using Variational Bayes
论文作者
论文摘要
本文研究了图的拓扑结构，研究了图信号恢复（GSR）的问题。在本文中，加权邻接矩阵的元素在统计上与正态分布相关，并且假定图形信号为高斯马尔可夫随机场（GMRF）。然后，通过以封闭形式计算后代，以贝叶斯方式通过变异贝叶斯（VB）算法解决了GSR的问题。事实证明，加权邻接矩阵的元素的后代具有新的分布，我们称其为广义化合物汇合了高温（GCCH）分布。此外，通过通过VB计算其后验来估计噪声的方差。合成和现实世界数据的仿真结果表明，在恢复图信号时，提出的贝叶斯算法比某些最新算法的优越性。
This paper investigates the problem of graph signal recovery (GSR) when the topology of the graph is not known in advance. In this paper, the elements of the weighted adjacency matrix is statistically related to normal distribution and the graph signal is assumed to be Gaussian Markov Random Field (GMRF). Then, the problem of GSR is solved by a Variational Bayes (VB) algorithm in a Bayesian manner by computing the posteriors in a closed form. The posteriors of the elements of weighted adjacency matrix are proved to have a new distribution which we call it generalized compound confluent hypergeometric (GCCH) distribution. Moreover, the variance of the noise is estimated by calculating its posterior via VB. The simulation results on synthetic and real-world data shows the superiority of the proposed Bayesian algorithm over some state-of-the-art algorithms in recovering the graph signal.
