Compressed sensing (CS) is a new technology for recovering sparse data from undersampled measurements. It shows great potential to reduce energy for sensor networks. First, a basic global superposition model is proposed to obtain the measurements of sensor data, where a sampling matrix is modeled as the channel impulse response (CIR) matrix while the sparsifying matrix is expressed as the distributed wavelet transform (DWT). However, both the sampling and sparsifying matrixes depend on the location of sensors, so this model is highly coherent. This violates the assumption of CS and easily produces high data recovery error. In this paper, in order to reduce the coherence, we propose to control the transmit power of some nodes with the help of t-average-mutual-coherence, and recovery quality are greatly improved. Finally, to make the approach more realistic and energy-efficient, the CIR superposition is restricted in local clusters. Two key parameters, the radius of power control region and the radius of local clusters, are optimized based on the coherence and resource consideration in sensor networks. Simulation results demonstrate that the proposed scheme provides a high recovery quality for networked data and verify that t-average-mutual-coherence is a good criterion for optimizing the performance of CS in our scenario.
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