Data Recovery of Sparse Sensors in Internet of Nano Things

The Internet of Nano Things (IoNT) is a nanonetwork comprised of numerous nano devices capable of data computation, storage, and actuation. IoNT has broad applications, including medicine and environmental protection. Monitoring specific molecular concentrations in the environment is necessary for practical tasks, such as disease monitoring and pollution tracking. However, sensors can only be sparsely arranged due to the limited space and high sensor costs. Consequently, it leads to the loss of monitoring data and seriously affects the performance of the IoNT. Therefore, it is indispensable to address the problem of how to effectively and accurately recover the missing data from the measurements of sparse sensors. To solve this problem, we propose a spatio-temporal constraint tensor completion (SCTC) algorithm based on CANDECOMP/PARAFAC (CP) decomposition. Specifically, we divide the entire environment into uniform grids and model the measurements of all grid positions over a period of time as a tensor. The sparse arrangement of sensors resulted in missing entire columns of data in the tensor, corresponding to the positions without sensors. Our objective is to recover these missing data utilizing the available measurements in the tensor. To effectively and accurately recover the missing data, the spatial and temporal constraint matrices are introduced to leverage the spatio-temporal correlations among the data. Due to the nonconvex optimization problem, CP decomposition is introduced to transform the problem of tensor recovery into solving multiple-factor matrices. The performances of the proposed SCTC algorithm are confirmed via simulation and experiment data.