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Sensors 2011, 11(3), 2385-2407; doi:10.3390/s110302385

Sparsity-Based Spatial Interpolation in Wireless Sensor Networks

Department of Communication Engineering, Xiamen University, Xiamen 361005, China
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Author to whom correspondence should be addressed.
Received: 8 November 2010 / Revised: 26 December 2010 / Accepted: 9 February 2011 / Published: 25 February 2011
(This article belongs to the Section Physical Sensors)

Abstract

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 l1 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. View Full-Text
Keywords: data interpolation; sparsity; wireless sensor network data interpolation; sparsity; wireless sensor network
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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Guo, D.; Qu, X.; Huang, L.; Yao, Y. Sparsity-Based Spatial Interpolation in Wireless Sensor Networks. Sensors 2011, 11, 2385-2407.

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