基于Jacobi ADMM的传感网分布式压缩感知数据重构算法

针对无线传感网中分布式数据收集及应用，采用分布式压缩感知理论中的JSM-1 (joint sparse model-1)模型，提出了一种基于Jacobi ADMM (alternating direction method of multipliers)的分布式压缩感知数据重构算法.该算法通过在簇头节点间交换公共信息以挖掘关联数据集的公共部分，并在各个簇头节点内部更新各自的独立部分，从而实现无线传感网中相关感知数据的分布式压缩重构.首先，将无线传感网中的数据收集问题抽象为一个分布式优化问题.然后，为了能够有效地解决分布式计算过程中产生的不收敛问题，在优化目标函数中引入了近似项，从而使得子优化问题具有严格凸性，并利用交替方向乘子法求解压缩感知数据的重构问题.最后，分别利用合成数据集和真实数据集进行验证.实验结果表明：与现有其他数据重构算法相比，基于Jacobi ADMM的分布式压缩感知数据重构算法具有更高的数据重构精度.

A Distributed Data Reconstruction Algorithm Based on Jacobi ADMM for Compressed Sensing in Sensor Networks

Considering the application scenario of decentralized data collection in wireless sensor networks (WSNs), a distributed data reconstruction algorithm based on Jacobi ADMM (alternating direction method of multipliers) for compressed sensing is proposed by adopting the JSM-1 (joint sparse model-1) model in the distributed compressed sensing (DCS) theory. Through exchanging the common information among cluster heads to determine the common components in the correlated sensed data and update the innovation components in each cluster head, the compressed sensed data in WSNs are reconstructed in a distributed way. The data collection operation in wireless sensor networks is firstly abstracted as a distributed optimization problem. In order to avoid non-convergence in the distributed data reconstruction process, a proximal component is then introduced into the aforementioned optimization problem with the goal of converting the sub-problem of the optimization objective function into its strictly convex form. After that, the ADMM method is utilized to solve the data reconstruction problem. Both the synthetic dataset and the real world datasets are used in the experiments to verify the performance of the proposed algorithm. Experimental results show that the proposed data reconstruction algorithm can provide higher data reconstruction accuracy than the state of the art data reconstruction algorithms.