Research On Compressed Sensing Reconstruction Algorithm And Its Application In Wireless Sensor Networks

Compressed Sensing(CS) is a modern signal processing method, which can realize precise reconstruction of the signal with sparsity by simultaneous compression and sampling and improve the efficiency of signal processing as well as the resource utilization. One of the keys is its recovery algorithm. By combining with the theory of the Distributed Source Coding(DSC), CS can be applied to the reconstruction of the Wireless Sensor Networks(WSN) signals which utilizing both the inter-signal and the intra-signal correlations. The cost of communication and the energy consumption of the network are reduced by independent encoding and joint decoding,The thesis focuses on the reconstruction algorithm of CS and its applications in wireless sensor networks. The main contributions of this thesis are the following.First, a recovery algorithm combining generalized hard thresholding pursuit with semi-iterative idea is proposed, named Generalized Semi-Iterative Hard Thresholding Pursuit(GSHTP). In the algorithm, the seeking direction of objective function is modified with semi-iterative idea to achieve polynomial acceleration, the searching path can avoid zigzagging by using the liner combination of the n- th iteration result to gain the approximate solution. It is suitable for the case when there is no knowledge of the signal’s sparsity to realize the precise reconstruction of the signal. Numerical simulations show that the proposed algorithm can increase the performance of the reconstruction,such as the peak signal-to-noise ratio, the signal-to-noise ratio, and the matching rate. For a 256?256 Lena image with 0.5 compression ratio, the peak signal-to-noise ratio has improved0.9dB and the signal-to-noise ratio has improved 1dB, in comparison with the generalized hard thresholding pursuit algorithm. Meanwhile, the quality of the reconstruction in ghost imaging with the proposed recovery algorithm is superior to that with the generalized hard thresholding pursuit method.Second, in wireless sensor networks, the mixed support-set model can provide additional degrees of freedom for network frame since it has no constraint on the common signal components.A joint SHTP reconstruction algorithm by combining Semi-Iterative Hard Thresholding Pursuit algorithm with the mixed support-set model to solve the reconstruction problem of the signal groups in distributed compressed sensing is proposed. In the algorithm, a common support set is obtained by solving the common sparse signal part utilizing the inter-signal correlation, the individual signal part can be reconstructed using the intra-signal correlation with the commonsupport set. It is suitable for the joint reconstruction of signal groups in a wireless sensor networks setup where all the sensors transmit the sensing data to the centralized node. The simulation results show that, compared with the existed joint reconstruction algorithms, the joint SHTP algorithm could gain the maximum signal to reconstruction noise ratio and the minimum average support cardinality error. It is indicated that the proposed algorithm can achieve the precise reconstruction no matter the network setup is noisy or not.Third, a Side Information Semi-Iterative Hard Thresholding Pursuit(SI_SHTP) algorithm is proposed based on the side information. In the proposed algorithm, the signal from a sensor node is independently reconstructed firstly to gain the side information, the data of other sensor nodes can then be reconstructed by using the asymmetric distributed compressed sensing structure. Using the statistical correlation between the signals, the entire situation of the wireless sensor networks can be perceived with less measurement values. The achievable rate is derived by theoretical analysis when a joint measurement values received in the decoding side is less than the sum of values measured by each signal. Numerical simulations show that the SI_SHTP algorithm could gain the maximum reconstruction noise ratio and the minimum average relative distortion in comparison with the SHTP algorithm without the additional side information. Besides, the modified algorithm can save2% measurement times to SHTP without side information for the same reconstruction probability.