Measurements–Residuals Collaboration Sparse Reconstruction Under Missing Measurements in Wireless Sensor Networks for Mechanical Vibration Monitoring

Compressed sensing (CS) can substantially enhance the transmission efficiency of wireless sensor networks (WSNs). To tackle the difficulties of high transmission delay and reconstruction failure caused by compressible measurements loss, this article proposes a measurements–residuals collaboration sparse reconstruction (MCSR). First, the acquisition node performs embedded compressed sampling (ECS) to improve transmission efficiency. The measurements obtained from the ECS are transmitted wirelessly to the gateway node, and can be random lost owing to unstable communication link. In addition, sensing matrix adaptive matching is proposed to address the mismatch between the dimensions of the missing measurements and the dimensions of the sensing matrix resulting in a failure of the reconstruction, providing a basis for subsequent effective reconstruction. Moreover, learning dictionary-based split Bregman iteration (SBI-LD) sparse reconstruction algorithm is adopted to realize the initial signal reconstruction based on the effective measurements obtained from wireless transmission. Furthermore, based on the initial reconstruction signal, the learning dictionary-based residuals reconstruction algorithm is proposed to obtain the reconstructed signal of the measurement residuals. Finally, the experimental results demonstrate that the proposed algorithm achieves higher reconstruction accuracy, compared with other popular methods. This provides a solution of great significance for efficient and reliable mechanical vibration monitoring in WSN.