Research On Reconstruction Algorithm Of Time-varying Graph Signal

In recent years,massive data has been generated in the fields of social relations network,electric energy network,transportation networks,sensor networks,etc.These data defined on the irregular graph domain have complex non-Euclidean characteristics.The massive,high-dimensional and irregular structure characteristics of these data bring new challenges to data processing.Graph signal processing is a new tool for processing high-dimensional non-Euclidean data.However,in a large number of practical applications,noise pollution and data loss often appear in data acquisition tasks.In addition,part of the information will be lost in data sampling for saving energy or for convenient data transmission.Moreover,graph signals often change with time.Therefore,how to reconstruct time-varying graph signals from noisy or missing time-varying graph signal observations to obtain real data is a question worth studying.Based on this problem,the main research contents of this article are as follows:First of all,this paper introduces the research background,research status,research significance and related theoretical basis of the time-varying graph signal reconstruction algorithm in detail.Next,this paper proposes a time-varying graph signal reconstruction algorithm using joint smoothness.In this algorithm,based on the two characteristics that the time-varying graph signal is smooth in the graph domain and the time domain and the time difference graph signal is smoother in the graph domain than the signal itself,a convex optimization model is established.The closed solution of the optimization problem is also given.Further,in order to reduce the computational complexity,in this paper,the conjugate gradient method is used to solve the optimization problem,and the iterative solution is the reconstructed time-varying graph signal.Experimental results on two real data sets show that the proposed algorithm has a smaller reconstruction error than the latest batch reconstruction of time-varying graph signals and joint variation minimization reconstruction algorithm.Further,in this paper,considering that the variation metric matrix of the time difference graph signal on the graph is sparse,on the basis of the joint smoothness prior information,this paper introduces the sparsity of the variation metric matrix of the time difference graph signal on the graph.A new time-varying signal reconstruction optimization model is established,and the optimization problem is solved by the alternating direction method of multipliers to obtain the reconstructed time-varying graph signal.The experimental results on two real data sets show that compared with the latest batch reconstruction of time-varying graph signals,joint variation minimization reconstruction algorithm and time-varying graph signal reconstruction algorithm based on joint smoothness proposed in this paper,time-varying graph signal reconstruction algorithm based on sparsity has certain advantages.