Energy-Efficient Compressive State Recovery From Sparsely Noisy Measurements

The compressive sensing theory has been intensively inspired to develop new methods and applications. Energy conservation for every node and overall energy consumption in the network is one of the main design issues in such networks. In large-scale sensor networks, information is relatively sparse compared with the number of nodes. In such networks, the state recovery problem can be recast as a sparse signal recovery problem in the discrete spatial domain to be solved with a small number of linear measurements as an underdetermined linear system by an
l
₁
-norm minimization program. A series of signal processing methods is applied to recover the current state of sensory data, e.g., temperature, pressure, force, flow, humidity, position, or motion, from noisy measurements. We propose an energy-efficient state recovery method for sensor networks; then, the proposed method is employed to recover an air quality signal in an air-quality-monitoring system. The signal contains the air quality indexes for all monitoring sites in the system. To have a sparse representation of the signal, it is first transformed to frequency domain and then recovered and reconstructed from a small portion of coefficients. Different random matrices driven from Bernoulli and Gaussian distributions are investigated to find an energy-efficient sensing scheme for signal reconstruction. The results reveal more than 60% saving in power consumption with only 10% reconstruction and recovery error. The proposed method prolongs network lifetime with noticeable saving in deployment and maintenance cost, particularly in large-scale sensor networks with slowly varying phenomena.