Compressive Sensing based on local regional data in Wireless Sensor Networks

In order to save energy of sensors in the process of gathering data and transmitting information, Compressive Sensing (CS), as a novel and effective signal transform technology, has been used gradually in Wireless Sensor Networks (WSNs). In traditional usages of CS techniques in the previous literatures, the sparsities of the signals has to be known beforehand, which is much more importance for their recover results. However, it is difficult to realize precisely the structures of the signals actually in WSNs. Therefore, it is important to further exploit reasonable practicality availability in actual applications. In order to reduce energy of gathering and transmitting of sensors, this paper presents a model of optimized CS based on local regional data and design two corresponding algorithms, which could reconstruct the signals accurately and stably even if their sparsities could not be known in advance. Most important, our algorithms just need once extra transmission by sensors In the paper, we present two reasonable assumptions and then propose spatial-temporal correlation model for optimizing measure matrix of CS. Furthermore, two algorithms are designed in two kinds of situations that data satisfy random distribution or Gauss distribution, which is common in actual applications. According to experiments in the cases of both real data based on actual environments and two kinds of signals above based on simulation environments, our algorithm has been proved to be valuable for actual applications. Especially, when the amount of the sampling is only 15 with the dimension of the data is 256 and the sparsity is unknown, the relative error rate could be less than 6% in actual environments and 3.5% in simulation environments.