基于概率稀疏随机矩阵的压缩数据收集方法

测量矩阵设计是应用压缩感知理论解决实际问题的关键。该文针对无线传感器网络压缩数据收集问题设计了一种概率稀疏随机矩阵。该矩阵可在减少参与投影值计算节点个数的同时，让参与投影值计算的节点分布集中化，从而降低数据收集的通信能耗。在此基础上，为提高网络数据重构精度，又提出一种适用于概率稀疏随机矩阵优化的测量矩阵优化算法。仿真实验结果表明，与稀疏随机矩阵和稀疏Toeplitz测量矩阵相比，采用优化的概率稀疏随机矩阵作为压缩数据收集的测量矩阵可显著降低通信能耗，且重构误差更小。

Compressive Data Gathering Method Based on Probabilistic Sparse Random Matrices

Designing measurement matrix is one of the key points of applying Compressed Sensing (CS) to solve practical issue. In this paper, a kind of probabilistic sparse random matrix is designed for compressive data gathering in Wireless Sensor Networks (WSNs). Besides cutting the number of projection calculating nodes, the probabilistic sparse random matrices also make their location centralized, which leads a further reduction of communication overhead. Then, an optimization method for probabilistic sparse random matrices is also proposed to enhance the accuracy of network data reconstruction. Compared with the existing data gathering method using sparse random matrices and sparse Toeplitz matrices, the proposed method can reduce significantly not only the energy consumption, but also the reconstruction error.