Compressive Sensing Based Data Gathering And Reconstruction In Wireless Sensor Networks

The wireless sensor networks (WSNs) can sample a variety of informa-tion and transmit the information to the sink. The sink is a gateway which is used to communicate with Internet, satellite or mobile communication net-work. Compressive sensing can be used for compression and reconstruction between high-dimensional data and low-dimensional data, with the knowledge of matrix analysis, statistical probability theory, optimization and operational research. It has been applied in networks, communications, medical treatmen-t, and so on. This dissertation will study the compressive sensing based data gathering (CS-DG) algorithms and the reconstruction algorithms to reduce the energy consumption and the influence of the noise for WSNs. The main con-tributions of this dissertation are summarized as follows.(1) Cooperative Multiple Input Multiple Output-based Random Walk(CMIMO-RW) Algorithm. A dynamic CMIMO-RW algorithm is proposed to save energy. For each hop of each walk, we jointly optimize the number of transmitters and receivers as well as the set of the cooperative nodes, with the objective to minimize energy consumption of the cooperative multiple in-put multiple output (CMIMO) communication. Due to the high complexity,we then consider virtual multiple input single output (vMISO) and derive the approximate optimal number of the transmitters by exploiting the relationship with different transmission distances. Experimental results show that our pro-posed algorithm saves energy by 50% as compared to the traditional random walk algorithm.(2) Unbalanced Expander based CS-DG (UE-CSDG) algorithm. To re-duce the energy consumption in clustered WSNs, a UE-CSDG algorithm is pro-posed to leverage on the significant advantage of unbalanced expander graph in terms of the reconstruction accuracy. Theoretical analysis results show that the constructed sparse binary matrix is the adjacency matrix of an unbalanced expander graph when the parameters are appropriately chosen, i.e., the length of random walk and the probability of random sampling, the number of mea-surements and the number of clusters. Experimental results show that when the well-known hybrid energy-efficient distributed (HEED) clustering algorithm is used, our proposed algorithm can save energy by at least 27.8% for a network with 1000 sensors organized into 160 clusters.(3) Spatial-Temporal based CS-DG (ST-CSDG) algorithm. To reduce the energy consumption for WSNs adopting tree-based routing algorithms, an ST-CSDG algorithm is proposed by exploiting the spatial and temporal correlation of the sensory data and leveraging on the significant advantage of unbalanced expander graph in terms of the reconstruction accuracy. Our proposed algo-rithm works on a data set which consists of the sensory data of all the sensors sampled within a sensing period. The CS coding is performed on a few sensory data which are selected from the data set with random sampling and random walks. Simulation results show that our proposed algorithm has better perfor-mance than existing algorithms in terms of reconstruction accuracy and energy consumption.(4) Analysis and improvement of reconstruction algorithms of compres-sive sensing in noisy setting. When both the signal and the measurements are contaminated by the noises, the upper bounds of the reconstruction errors of l1-based algorithms and greedy algorithms are obtained based on the coherence of the measurement matrix. Experimental results show that the reconstruction errors are lower than the obtained upper bounds and the reconstruction errors of orthogonal matching pursuit algorithm are the lowest of all. To reduce the reconstruction errors, an autoregressive model based basis pursuit denoising(AM-BPDN) algorithm is proposed, which is an l1 minimization problem built by combining basis pursuit denoising algorithm and autoregressive model. The autoregressive model is built with the spatial correlation and its parameters are obtained with the historical data. Experimental results show that our proposed algorithm can reduce the reconstruction errors. When the random sampling based data gathering algorithm is used, the sampling rate and the signal to noise ratio are respectively set to be 0.4 and 20 dB, the reconstruction errors can be reduced by 18.8%.The above results can be summarized as reducing the energy consumption and the reconstruction errors in WSNs by the compressive sensing based data gathering algorithms and reconstruction algorithms. The energy consumption can be reduced by utilizing CMIMO, unbalanced expander graph and spatial and temporal correlation of the sensory data in the compressive sensing based data gathering algorithms. The reconstruction errors can be reduced by analyz-ing the upper bounds of reconstruction errors of reconstruction algorithms and with the AM-BPDN algorithm.