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Sparsity-Based Spatial Interpolation in Wireless Sensor Networks

Guo D, Qu X, Huang L, Yao Y - Sensors (Basel) (2011)

Bottom Line: 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.

Affiliation: Department of Communication Engineering, Xiamen University, Xiamen 361005, China. guodi@xmu.edu.cn

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 l(1) norm minimization is proposed. It is shown that these missing samples can be reasonably recovered based on the 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.

A snapshot of mean monthly surface sunshine duration in June over global land areas, excluding Antarctica.
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f15-sensors-11-02385: A snapshot of mean monthly surface sunshine duration in June over global land areas, excluding Antarctica.

Mentions: To validate the performance of the sparsity-based missing data recovery in a sensor network, a mean monthly surface climate over global land areas, excluding Antarctica [2] is employed as the data set for simulation. The climatology data includes eight climate elements—precipitation, wet-day frequency, temperature, diurnal temperature range, relative humidity, sunshine duration, ground frost frequency and wind speed—and was interpolated from a data set covering the period from 1961 to 1990. The data are available through the International Water Management Institute World Water and Climate Atlas (http://www.iwmi.org) and the Climatic Research Unit (http://www.cru.uea.ac.uk). This data set consists of the monthly averaging surface sunshine duration in June over global land areas from 1961 to 1990. The final measurement points in the data set formed a regular grid of 10’ latitude/longitude over the region under study. We select a subset of 64 × 64 data that has no missing values, shown in Figure 15, as the original data without missing samples.

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Sparsity-Based Spatial Interpolation in Wireless Sensor Networks

Guo D, Qu X, Huang L, Yao Y - Sensors (Basel) (2011)

A snapshot of mean monthly surface sunshine duration in June over global land areas, excluding Antarctica.
© Copyright Policy
f15-sensors-11-02385: A snapshot of mean monthly surface sunshine duration in June over global land areas, excluding Antarctica.
Mentions: To validate the performance of the sparsity-based missing data recovery in a sensor network, a mean monthly surface climate over global land areas, excluding Antarctica [2] is employed as the data set for simulation. The climatology data includes eight climate elements—precipitation, wet-day frequency, temperature, diurnal temperature range, relative humidity, sunshine duration, ground frost frequency and wind speed—and was interpolated from a data set covering the period from 1961 to 1990. The data are available through the International Water Management Institute World Water and Climate Atlas (http://www.iwmi.org) and the Climatic Research Unit (http://www.cru.uea.ac.uk). This data set consists of the monthly averaging surface sunshine duration in June over global land areas from 1961 to 1990. The final measurement points in the data set formed a regular grid of 10’ latitude/longitude over the region under study. We select a subset of 64 × 64 data that has no missing values, shown in Figure 15, as the original data without missing samples.

Bottom Line: 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.

Affiliation: Department of Communication Engineering, Xiamen University, Xiamen 361005, China. guodi@xmu.edu.cn

ABSTRACT

Background: 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 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 Similar Images In: Results  - Collection
View Article: Pubmed Central -  PubMed
Show All Figures - Show MeSH
getmorefigures.php?pmc=3231630&rFormat=json&query=null&req=5