Sparse Measurement Matrix Design and RIP Prove Based on Compressive Sensing in WSN

The Compressive Sensing (CS) is an effective method on data collection, transmission and processing in wireless sensor networks. One of hot research points in CS is to design a kind of measurement matrix that satisfies Restricted Isometry Property (RIP). In this paper, a measurement matrix is designed depending on the analysis of sparsity in CS and the features of sensing nodes. The effort is to design sparse matrix with the least incurred computational cost and less storage space when it maintains quality of signal recovery. The design approach is based on the properties of combinations. And, an optimized proof method of RIP is proposed in this paper. The method can simplify the prove process. Finally, the rationality of the matrix and the effectiveness of the method are discussed through theoretical analysis and simulations.