Sparsity-Based Spatial Interpolation in Wireless Sensor Networks

In wireless sensor networks, due to environmental limitations or bad wireless channel conditions, not all sensor samples can be successfully gathered at the sink. In this paper, we try to recover these missing samples without retransmission. The missing samples estimation problem is mathematically formulated as a 2-D spatial interpolation. Assuming the 2-D sensor data can be sparsely represented by a dictionary, a sparsity-based recovery approach by solving for l(1) norm minimization is proposed. It is shown that these missing samples can be reasonably recovered based on the null space property of the dictionary. This property also points out the way to choose an appropriate sparsifying dictionary to further reduce the recovery errors. The simulation results on synthetic and real data demonstrate that the proposed approach can recover the missing data reasonably well and that it outperforms the weighted average interpolation methods when the data change relatively fast or blocks of samples are lost. Besides, there exists a range of missing rates where the proposed approach is robust to missing block sizes.