Sequential Compressed Sensing With Progressive Signal Reconstruction in Wireless Sensor Networks

This paper considers sequential compressed acquisition and progressive reconstruction of spatially and temporally correlated sensor data streams in wireless sensor networks (WSNs) via compressed sensing (CS). We develop a sequential framework based on sliding window processing, in which the sink can efficiently reconstruct the current sensors´ readings from a sequence of periodically delivered CS measurements by exploiting the joint compressibility via Kronecker sparsifying bases. Specifically, we derive a recursive CS recovery method which utilizes the estimates from the preceding decoding instants via a regularization and reweighted ℓ₁-minimization to improve the reconstruction accuracy of sensor data streams while reducing the necessary communications. As beneficial features, the method produces estimates for the current sensors´ readings without additional decoding delay, and, via adjusting the window size, it can dynamically trade-off between the CS recovery performance and decoding complexity. Numerical results show that our proposed method achieves higher reconstruction accuracy with a smaller number of required transmissions, and with lower decoding delay and complexity as compared to those of the state of the art CS methods.