Compressed Sensing of Wireless Sensor Networks Data with Missed Measurements

In Wireless sensor networks (WSNs), missed measurements may be caused by the sensor malfunction and interruption of communication between sensor nodes. The feasibility of exact recovery of WSNs data with missed measurements is analyzed in the framework of compressed sensing. A new incomplete measurement model was developed and the data reconstruction algorithm was proposed. The required number of the missing measurements and the sparsity condition of network data are found for exact compressed sensing of WSNs data. Theoretical derivation shows that a WSNs data of length N with no more than M/(log(N/M)+1) nonzero coefficients can be exactly recovered with M Gaussian measurements, provided that fraction of the missed measurements is less than a quarter of the Restricted isometry property (RIP) constant squared. Simulation results validate the theoretical results.