| There are a large number of graph-structured data in the real world,scholars represent these data as the signal of each vertex on the graph,and use the algebraic and spectral properties of the graph to study these data,which is called graph signal processing(GSP).Different from traditional signal processing,GSP technology considers information such as the position and topology of data in the graph structure.It is widely used in social network analysis,signal processing,machine learning and other fields.Due to the large scale of the network and information,the time-varying network topology,and the limitation of bandwidth and energy,the distributed GSP algorithm is more suitable for the processing of irregular domain data in large networks.An important aspect in GSP is graph signal recovery,that is,recovering all signal values from partial normal signal samples.This process is also commonly referred to as graph signal inpainting,inference or reconstruction.Therefore,this thesis mainly studies distributed graph signal recovery,and the research work is mainly divided into the following three points:(1)A distributed subspace projection graph signal recovery algorithm based on the graph filter with prior anomaly known(Disp GF)is proposed.Based on the assumption that the graph signal is band-limited and smooth,the graph signal recovery problem is transformed into a band-limited subspace optimization problem,and is solved by the gradient projection method.Considering the smoothness of the graph signal,regularization terms are utilized to constrain it.The gradient projection method can be divided into two steps: update process and projection process.For the projection operation,the graph filter matrix is used to replace the non-sparse projection matrix to realize distributed projection,which can approach the real projection matrix within the allowable error range through a small number of iterations.Compared with the previous method that approximates the real projection matrix by continuously iterating the matrix,the former can obtain the distributed projection matrix more quickly with the same error.In addition,compared with the previous graph signal recovery algorithm based on consensus estimation,the communication burden of each node is lower in iterations,and finally each node can directly obtain the estimated value.The convergence of the algorithm is theoretically analyzed,and the simulation results prove the feasibility of the proposed algorithm and the correctness of the theoretical results.(2)For the case that no prior anomaly information(anomalous nodes are unknown),an anomaly detection algorithm based on high-pass graph filter(GHPF)(AD algorithm)and an anomaly node localization algorithm based on smoothness(ANL algorithm)are proposed.In real-world environments,researchers cannot always assume that anomaly is known,that is,researcher cannot always pre-know which node is anomalous,and further judgment is required.In this thesis,the network environment is initially identified through AD algorithm,so that it can be pre-determined whether anomaly exist and reduce the subsequent computational complexity.However,the AD algorithm cannot locate the specific anomaly nodes,the thesis proposes ANL algorithm,and realizes the secure distributed recovery of the graph signal.The simulation results show that the proposed algorithm can detect anomaly nodes and realize graph signal recovery with no prior anomaly information.And the algorithm can achieve similar performance compared with the case where prior anomaly information is known.(3)A distributed dynamic bandwidth graph signal recovery(DG-ATC and DG-CTA)algorithm is proposed for the case where the bandwidth of graph signal is unknown.In this thesis,the assumption of the band-limited of the graph signal is relaxed,and the convex regularization term commonly used in compressed sensing is used to enhance the sparsity of the signal through the diffusion process on the network,so that the sparse structure of the signal to be recovered can be learned from the observed signal in real time,and the change of the sparsity can be tracked.The theoretical convergence of the proposed algorithm is analyzed.Simultaneously,the simulation results prove that the proposed algorithm can track and recover the dynamic bandwidth graph signal well.By studying graph signal recovery,the disturbed graph signal can be reconstructed,so that the relevant information in the signal can be analyzed and understood more accurately,and it can provide strong support for the development of related fields,such as computer vision,sensor networks,and biological networks. |
