Distributed Graph Signal Sampling And Reconstruction Method And Its Application

The Graph Signal Processing(GSP)method is suitable for network-based distributed information processing in the Wireless Sensor Networks(WSNs)application scenario,and can make up for the shortcomings of traditional signal processing methods in processing meshed high-dimensional data.The vertices of the graph represent sensor nodes in the network,and the edges represent the communication links between sensor nodes.The set of observations of all nodes in the network at a certain time is called the graph signal.The limited energy of WSN sensor nodes is one of the key factors restricting its development.Considering that in practical applications,the observation values of adjacent sensor nodes tend to be similar,and they exhibit low-frequency characteristics in the frequency domain of the graph signal.Using graph signal sampling and reconstruction methods,the graph signal can be reconstructed through the observation values of some nodes in the network,thus reduces network overhead.This thesis focuses on how to reduce the measurement overhead and communication overhead of distributed graph signal sampling and reconstruction methods.Combined with WSN-based air quality monitoring scenario simulation,the effectiveness of the proposed method is verified.Aiming at the problem of poor low-frequency characteristics of image signals in air quality monitoring scenarios,the paper constructs the feature graph topology and the communication graph topology of the network graph topology respectively.The feature graph topology reflects the features of the graph signal,and the communication graph topology determines the actual network communication links in the signal reconstruction algorithm.In order to make the graph signal have better low frequency characteristics in the feature graph topology,a feature graph topology construction method based on signal similarity is proposed.This method selects the set of neighbor nodes according to the signal difference between nodes and designs the weight coefficients between nodes,thereby obtaining a feature graph topology based on signal similarity.The communication graph topology can be constructed by the bridge node method mentioned below.The simulation results show that the feature graph construction method proposed in the thesis can reduce the number of frequency components and sampling nodes used in the graph signal reconstruction algorithm while ensuring the reconstruction performance,and reduce the communication and measurement overhead of the network.In order to reduce the communication overhead of the graph signal reconstruction method,the paper considers two aspects: improving the convergence rate and reducing the communication overhead in a single iteration.The Recursive-Least-Squares(RLS)graph signal reconstruction method has a faster convergence rate due to the use of the historical information of the graph signal.Based on the RLS graph signal reconstruction method,this paper proposes a distributed RLS graph signal reconstruction method based on bridge nodes to reduce the number of communication links in the communication graph topology.This method constrains the estimated value of the node in the network to be consistent with the estimated value of the bridge node by setting the bridge node,and optimizes the target optimization problem of the original RLS graph signal reconstruction method,so that ordinary nodes in the improved graph signal reconstruction algorithm do not need to exchange information.The simulation results show that the proposed distributed RLS graph signal reconstruction method based on bridge nodes can effectively reduce the communication overhead of the network.