Research On Efficient Reconstruction Method Of Graph Signal

With the rapid development of information technology,massive,high-dimensional,irregular and other data characteristics have brought new challenges to information processing.Graph signal processing studies signals in irregular discrete domains,providing new ideas and important tools for information processing.Graph signal processing technology abstracts irregular discrete data into graph signals,and constructs a theoretical system similar to traditional signal processing.Sampling and reconstruction are important parts of signal processing.At present,the theoretical research on graph signal sampling and reconstruction is not perfect,and it is still in the initial stage of development.This thesis mainly studies the reconstruction of graph signals,including reconstruction algorithms with faster convergence speed,reconstruction methods for full-band graph signals,and sampling and reconstruction algorithms based on local aggregation.The main content and innovations of this thesis are as follows:1.Aiming at the slow convergence speed of existing graph signal reconstruction algorithms,an iterative reconstruction algorithm based on weighted propagation operator is proposed.The maximum degree segmentation method is used to divide the structure of the undirected weighted graph,and the cut-off frequency condition that satisfies the accurate reconstruction of the graph signal is analyzed and deduced;the weighted propagation operator is constructed,and the iterative reconstruction algorithm based on the weighted propagation operator is proposed.The simulation results show that the algorithm has faster reconstruction convergence speed and good noise resistance.Then,in view of the problem of signal value loss,the equivalence with random sampling is analyzed,and a local node set partition method based on the shortest path partition is proposed,and the iterative weighted propagation algorithm is used for reconstruction.Experimental simulation shows that under a low loss rate,accurate estimation of the lost signal value can be achieved.2.Aiming at the problems of large reconstruction error and unstable reconstruction performance when reconstructing the full-band graph signal with the least squares regression method,this thesis introduces the ridge regression and lasso regression methods.Analyze and compare the estimation performance of lasso regression and ridge regression,and apply lasso regression to the reconstruction of the full-band graph signal.The simulation results show that the reconstruction method based on lasso regression has smaller reconstruction errors and good reconstruction stability.Then,a descending selection method of the frequency domain component subset of the graph is proposed.Simulation experiments show that this method can retain more energy in the frequency domain of the graph,thereby achieving a smaller reconstruction error.3.The generalized sampling and reconstruction of graph signals are studied,and a local convergent sampling method based on local weights is proposed.The definition of local weights is given.Different selection methods of local weights are given in the noise-free scene and the noisy scene.The local weight is used to obtain the local aggregation signal value of the local node set.The difference between aggregation sampling and traditional selective sampling are analyzed,and the reconstruction algorithm based on local aggregation is proposed.The simulation results show that the sampling and reconstruction method based on local aggregation proposed in this thesis has faster reconstruction convergence speed and stronger noise resistance than selective sampling.