Research On Signal Sampling And Sparse Representation For Wireless Sensor Networks Based On Compressed Sensing

With the gradual expansion of the scale of Wireless Sensor Networks(WSNs), energy issue has become one of the key problems need to be solved urgently. As a new sampling theory, Compressed Sensing(CS) can get accurate recovery of a signal under a lower sampling rate for lower energy consumption of WSNs. Standard CS theory consists of three parts, namely, the sparse representation of a signal, the design of a measurement matrix and the recovery of original signals. This paper mainly deals with the improvement for the sparse representation and the measurement part of the WSNs signals. The two specific contributions of this paper are as follows:(1) For commonly used random measurement matrix doesn't depend on the signal, it requires a large space to pre-store the measurement matrix. Furthermore, to generate a random matrix has high requirements for hardware,which will bring excessive hardware costs. Through in-depth study of the LEACH algorithm, this paper develops CS-LEACH scheme for signal sampling by combining the LEACH algorithm with the CS theory. According to this scheme, a measurement matrix based on nodes clustering is constructed. Experimental results show that CS-LEACH scheme effectively solves the problem that random matrix needs storage in advance and extends the lifetime of WSNs.(2) In order to get better sparse representation for WSNs, this paper studies three sparse representation algorithms, i.e., discrete cosine transformation(DCT), principle component analysis(PCA), and constructing over-complete dictionary by K-Means Singular Value Decomposition(K-SVD). As for DCT, the values of the original signals are ordered to analyze the effect of ordering. Experimental results show that the recovery accuracy of ordered-DCT is much better than the non-ordered. As for PCA, this paper introduces the process of getting the sparse representation of signals using principle component analysis, and analyses the performance of PCA basis on signal reconstruction. As for the dictionary constructed based on K-SVD, by improving the initial dictionary through combining K-SVD and discrete cosine transformation matrix, a new type dictionary which fits for the sparse representation of distributed WSNs signals is constructed. Experimental results show that K-SVD-DCT performs better in recovery accuracy and convergence stability than the traditional K-SVD dictionary under the CS framework.