Research On Time-varying Signal Reconstruction Algorithm On Graph

With the rapid development of information science and technology,massive data will be produced every day.These data parts have irregular,high-dimensional features,which bring some new challenges to information processing.The signal on graph is an abstract representation of the data on the network,which can effectively characterize and process irregular,high-dimensional data.Therefore,it has attracted the attention of many researchers in recent years.The reconstruction of the graph signal is an important research field of the graph signal,which can recover the high-dimensional and irregular data.In the past,the time-varying characteristics of the signal were not taken into account in the study of the signal on the graph,but the analysis and processing of the static map signal was performed.However,in the real world,many graph signals have time-varying characteristics,which also poses a challenge to signal processing on graph.In this paper,for the problem that the time-varying signal is easy to generate signal missing or wrong,the difference total variation minimization reconstruction algorithm is proposed and in combination with the clustering theory to reconstruct the time-varying signal on graph.This article main research contents are as follows:First of all,this paper gives a detailed introduction to the current research background,current situation,significance and related theoretical basis.Next,this thesis study the time-varying signal reconstruction problem based on the smallest difference total variation.Specifically,we smooth the signal on graph based on the node difference operator on graph,and construct a time-varying graph signal reconstruction model based on the optimization theory,by using the gradient descent method to solve the unconstrained optimization problem corresponding to time-varying signal reconstruction,a time-varying signal on graph reconstruction algorithm with difference total variation is obtained.The simulation results of the proposed algorithm and the Tikhonov regularization method and the reconstruction algorithm of the total variation of the graph signal show that the proposed algorithm is better than the other two algorithms under the same experimental conditions.In addition,experimental simulations show that the algorithm can also be used for the reconstruction of directed time-varying signals on graph.Finally,in view of the topology graph signal often has the characteristics of community,clustering correlation algorithm is proposed to reconstruct the time-varying signal on graph.Through the relationship between nodes in the signal structure on the graph,nodes with similar properties are divided into the same community.In the undirected graph,the modularity and spectral clustering algorithms are used to re-divide the graph signals,and in the directed graph,the signal can be divided into communities by the motif method,and the clustered sub-network adopts the difference total variation algorithm for reconstruction processing.Because the clustering algorithm can eliminate the interference of the incoherent nodes in the reconstruction process of the graph signal,it has better reconstruction effect.The simulation results verify that the clustering method has a good effect in realizing the signal reconstruction on graph.