Citation: He, J.; Li, Y.; Zhang, X.; Li, J.
Missing and Corrupted Data
Recovery in Wireless Sensor
Networks Based on Weighted Robust
Principal Component Analysis.
Sensors 2022, 22, 1992. https://
doi.org/10.3390/s22051992
Academic Editors: Alvaro
Araujo Pinto and Hacene Fouchal
Received: 6 January 2022
Accepted: 1 March 2022
Published: 3 March 2022
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Article
Missing and Corrupted Data Recovery in Wireless Sensor Networks
Based on Weighted Robust Principal Component Analysis
Jingfei He * , Yunpei Li , Xiaoyue Zhang and Jianwei Li
Tianjin Key Laboratory of Electronic Materials and Devices, School of Electronics and Information Engineering,
Hebei University of Technology, Tianjin 300401, China; liyunpei_hebut@163.com (Y.L.);
zxy_zhangxiaoyue@163.com (X.Z.); ljw__0917@163.com (J.L.)
* Correspondence: hejingfei@hebut.edu.cn
Abstract:
Although wireless sensor networks (WSNs) have been widely used, the existence of data
loss and corruption caused by poor network conditions, sensor bandwidth, and node failure during
transmission greatly affects the credibility of monitoring data. To solve this problem, this paper
proposes a weighted robust principal component analysis method to recover the corrupted and
missing data in WSNs. By decomposing the original data into a low-rank normal data matrix and a
sparse abnormal matrix, the proposed method can identify the abnormal data and avoid the influence
of corruption on the reconstruction of normal data. In addition, the low-rankness is constrained
by weighted nuclear norm minimization instead of the nuclear norm minimization to preserve the
major data components and ensure credible reconstruction data. An alternating direction method of
multipliers algorithm is further developed to solve the resultant optimization problem. Experimental
results demonstrate that the proposed method outperforms many state-of-the-art methods in terms
of recovery accuracy in real WSNs.
Keywords:
wireless sensor networks; missing and corrupted data recovery; weighted nuclear norm;
robust principal component analysis
1. Introduction
Wireless sensor networks (WSNs) contain a group of spatially distributed sensor nodes
that are capable of communicating wirelessly and collecting data from the surrounding
environments [
1
,
2
]. Recently, WSNs have been widely applied in different domains, such as
environmental monitoring [
3
], military management [
4
], and health care [
5
]. Typically, the
main task of WSNs is to collect sensing data from all sensor nodes to a certain sink and then
perform further analysis based on the monitoring data, and the collected data are usually
composed of readings sensed by multiple nodes in consecutive time slots. However, due
to the poor environments and energy constraints in WSNs, data loss and corruption are
inevitable in practical applications. Therefore, it is important to reconstruct the real data
from partially collected data with corruption.
Recently, various reconstruction methods have been proposed for data recovery
in WSNs. Based on data interpolation techniques, a K nearest neighbor (KNN)-based
method [
6
] was proposed to simply utilize the values of the nearest neighbors to estimate
the missing values. The Delaunay triangulation (DT) [
7
] utilizes the vertices as their global
errors to reconstruct virtual triangles for data interpolation. Based on compressed sensing
(CS) [
8
], the distributed compressed sensing (DCS) method [
9
,
10
] was proposed to exploit
the sparsity of the data under various transform domains.
Since many signals in various applications are always distributed into two-dimensional
data (i.e., matrix form) and exhibit second-order sparsity (i.e., the low-rankness), matrix
completion (MC) [
11
] has emerged as a novel technology and has been applied to many
fields, such as image inpainting [
12
], magnetic resonance imaging [
13
], and recommen-
dation systems [
14
]. The matrix completion aims at recovering the missing entries of a
Sensors 2022, 22, 1992. https://doi.org/10.3390/s22051992 https://www.mdpi.com/journal/sensors
