Data collection is a basic application of wireless sensor networks (WSNs). In practice, only a subset of sensor nodes is selected for data sensing and transmission due to the bandwidth constraint of the channel, energy constraint of the nodes, or malfunctions of the nodes. Data recovery from incomplete sensing data is vital to WSNs. Many works perform data recovery by utilizing the low-rank property of the spatio-temporal correlated data. However, these methods usually converge slowly to achieve satisfactory accuracy performance. In this paper, we propose an ADMM-ResNet framework based on residual networks (ResNets) for spatio-temporal correlated data recovery. The formulated optimization problem is solved by the alternating direction method of multipliers (ADMM) algorithm. The updates of auxiliary variable in the ADMM algorithm can be replaced by ResNets, and the ADMM algorithm is unrolled into a fixed-length neural network. The proposed ADMM-ResNet significantly reduces the number of iterations compared with traditional ADMM algorithm. We theoretically prove that the proposed ADMM-ResNet can globally converge to a fixed-point. Experimental results verify the theoretical convergence and demonstrate the effectiveness.

数据收集是无线传感器网络（WSN）的基本应用。实际上，由于信道的带宽约束，节点的能量约束或节点的故障，仅选择传感器节点的子集用于数据感测和传输。从不完整的传感数据中恢复数据对于WSN至关重要。许多作品都是利用时空相关数据的低秩属性来执行数据恢复的。但是，这些方法通常会缓慢收敛以达到令人满意的精度性能。在本文中，我们提出了一种基于残差网络（ResNets）的ADMM-ResNet框架，用于时空相关数据恢复。提出的优化问题通过乘数交替方向法（ADMM）算法解决。可以用ResNets替换ADMM算法中辅助变量的更新，并将ADMM算法展开到固定长度的神经网络中。与传统的ADMM算法相比，所提出的ADMM-ResNet大大减少了迭代次数。从理论上讲，我们证明了所提出的ADMM-ResNet可以全局收敛到一个定点。实验结果验证了理论收敛性并证明了其有效性。