基于重加权图拉普拉斯正则化的时变图信号重构算法

A time-varying graph signal reconstruction algorithm based on reweighted graph Laplacian regularization

针对实际观测到的时变信号由于噪声污染、机器故障等引起数据缺失,从而导致后续数据处理结果不准确的问题,提出了一种基于重加权图拉普拉斯正则化(ReweightedGLR)的时变图信号重构算法。首先,该算法根据数据的空间距离信息构建图模型;其次,根据图模型中时变图信号的空间域平滑特性将时变图信号重构问题归结为一个无约束优化问题;最后,利用重加权迭代算法求解该优化问题。该方法随时间变化对边权重进行调整,动态更新图拉普拉斯矩阵,以此刻画数据随时间变化时的内在关联性,充分利用了时变图信号的时间-空间关联性。仿真结果表明,所提出的算法与基于时变图信号空间域图平滑性的重构算法相比,进一步挖掘了时变图信号的时间关联性,降低了重构误差,提高了重构性能。

A time-varying signal reconstruction method based on Reweighted Graph Laplacian Regularization(Reweighted GLR)is proposed to solve the problem that the observed time-varying signals are missing due to noise pollution and machine malfunction,which leads to inaccurate results of the subsequent data processing.algorithm.Firstly,the algorithm constructs a graph model based on the spatial distance information of the data.Secondly,the time-varying graph signal reconstruction problem is summarized as an unconstrained optimization problem based on the spatial domain smoothing property of the time-varying graph signal in the graph model.Finally,the optimization problem is solved by using a reweighted iterative algorithm,which adjusts the edge weights as time changes and dynamically updates the graph Laplacian matrix,such that the inherent correlation of the data as it changes over time is portrayed and the time-space correlation of the time-varying graph signal is fully exploited.Simulation results show that the pro-posed algorithm further exploits the temporal correlation of time-varying graph signals,reducing reconstruction errors and improv-ing reconstruction performance compared with reconstruction algorithms based on the smoothness of the spatial domain graph of time-varying graph signals.