Sparsity-Based Online Missing Data Recovery Using Overcomplete Dictionary

Estimating missing sample values is an inherent problem in sensor network applications. In wireless sensor networks, due to power outage at a sensor node, hardware dysfunction, or bad environmental conditions, not all sensor samples can be successfully gathered at the sink. Additionally, in the context of data streams, some nodes may continually miss samples for a period of time. To address these issues, a sparsity-based online data recovery approach is proposed in this paper. First, we construct an overcomplete dictionary composed of past data frames and traditional fixed transform bases. Assuming the current frame can be sparsely represented using only a few elements of the dictionary, missing samples in each frame can be estimated by basis pursuit. If some delay is acceptable, the estimation of the current frame can be further improved by leveraging the observation from the next frames. Our method was tested on data from a real sensor network application, monitoring the temperatures of the disk drive racks at a data center. Simulations show that in terms of estimation accuracy and stability, the proposed approach outperforms existing average-based interpolation methods, and is more robust to burst missing along the time dimension.