A Scheme for Joint Signal Reconstruction in Wireless Multimedia Sensor Networks

The International Journal of Multimedia & Its Applications (IJMA) Vol.9, No.4/5/6, December 2017
A Scheme for Joint Signal Reconstruction in
Wireless Multimedia Sensor Networks
Javad Afshar Jahanshahi, Habibollah Danyali, and Mohammad Sadegh
Helfroush
Department of Electrical and Electronics Engineering, Shiraz University of
Technology,
Shiraz, Iran
Abstract. In context aware wireless multimedia sensor networks, scenarios are usually such that
signals of multiple distributed sensors contain a common sparse component and each individual
signal owns an innovation sparse component. So distributed compressive sensing based on joint
sparsity of a signal ensemble concept exploits both these intra- and inter- signal correlation struc-
tures and compress signals to the extent possible. This paper proposes an optimized reconstruction
scheme based on joint sparsity model which is derived from the distributed compressive sensing. In
this regard, based on distributed compressive sensing, a joint reconstruction scheme is proposed to
compress and reconstruct ensemble of signals even in large scale data transmission. Furthermore,
simulation results show the effectiveness of the proposed method in diverse compression ratios and
processing times in comparison with the joint sparsity model and individual compressive sensing
reconstruction methods.
Keywords: Wireless Multimedia Sensor Networks,Distributed Compressive Sensing, Joint Spar-
sity Model, Joint Reconstruction.
1 Introduction
As the field of telecommunication and new developed application advances, the need
of deploying distributed Wireless Sensor Networks (WSN) and Wireless Multimedia
Sensor Networks (WMSNs) which consist of many sensors for monitoring a specific
phenomenon in an area of interest both in time and space is increased. There are
three main challenges in WSN, i.e., network lifetime, computational ability and
bandwidth constraints [1, 2]. Assume that there are J sensors in the area which
are measuring a phenomenon in the spatio-temporal manner. A fusion center (FC)
receives all the measurements shown in (Fig. 1) and runs an algorithm to jointly
decode signal ensembles of the sensors and reconstruct the phenomenon at the
sensor sides. In such cases, when there is a significant correlation between the
signals of the sensors, the joint decoding based on the distributed source coding
(DSC) [3] could be used in the FC to decompress the transmitted signals of the
sensors. Using DSC methods, the compression rate can be higher and thus, data
can be transmitted with less power and bandwidth consumption. DSC concepts are
DOI: 10.5121/ijma.2017.9611. 121

also used to improve the wireless sensor networks’ performance in terms of data
reception accuracy and energy consumption efficiency [4].
In addition, compressive sensing (CS) provides a simultaneous sensing and com-
pression framework [5], enabling a potentially significant reduction in the sampling
and computation costs at a sensor with limited capabilities. The CS theory shows
that a signal with a sparse transform representation can be reconstructed from a
small set of incoherent random projections. CS scheme is exploited in many re-
search fields such as radar imaging [6], cognitive spectrum sensing [7, 8], channel
estimating [9] , error corrections [11], antenna array synthesis problems [10] and so
on. The CS technique as the data acquisition approach in a WMSN can significantly
reduce the energy consumed in the process of sampling and transmission through
the network, and also lower the wireless bandwidth required for communication.
In wireless sensor networks, sensors have limited computation capability and
energy resources without assistance of any established infrastructures, so many
studies in the literature are conducted considering these limitations for various ap-
plications [13]. Recently, the theory of distributed compressive sensing (DCS) [12]
have been used to exploit inter- and intra-signal correlations to propose new dis-
tributed source coding and compression algorithms for multi-signal ensembles based
on the CS theory. In a typical DCS setting and joint sparsity model (JSM) [12],
each sensor compresses its signal independently by projecting it onto an incoherent
basis and transmits the compressed information (actually sensed) to the FC. Under
the right conditions the FC can jointly reconstruct all the signals by knowing that
the measured signals of each sensor are individually sparse in some basis.
This present paper goes in the direction of proposing a framework for com-
pressing the signals of a WMSN and reducing the amount of the transmitted data
as much as possible. In the WMSN, the captured signals of each sensor should be
transmitted (direct or with a multi-hop architecture) to a central unit (FC) through
a wireless interface. In this paper, we address the problem of joint reconstruction
ensemble of signals for sensor nodes. The proposed model denoted as Enhanced
Common Method (ECM) basically can be used in WMSN’s services where an in-
trinsic shared part exists between the signals of the nodes that can be represented
sparsely in a dictionary or basis. It means that ECM is a context aware algorithm
and depends on the properties of the captured signals. Another aim of the ECM
framework is ability to robustly reconstruct the sensors’ signals if some disturbances
occur in the transmission procedure.
The rest of this paper is organized as follow; the system model and our approach
is described in Section 2 and 3, respectively. The corresponding experimental results
are presented and discussed in Section 4. Finally, the paper is concluded in Section
5.
122

Fig. 1. A collection of sensors measure a phenomenon and send their measurements to the fusion
center. There exists some inter-relation between the signals and FC decodes them jointly.
2 System Model
Suppose that J sensors are distributed in the area and each of them capture a
signal xj ∈ RN (j ∈ 1, 2, ..., J). All J signals share a common component xc ∈ RN
such that xj = xc + xinnj where xinnj ∈ RN is the innovation part of each signal
xj. There is a dictionary D ∈ RN×K in which signals can be represented sparsely
(xj = Dαj) as a linear combination of the atoms (columns) of this dictionary.
Obviously, this dictionary has the ability to represent signals sparsely as Eq. (1)
which αc and αinnj s are belonged to space RK with diﬀerent sparsity levels.
xj = Dαj = D(αc + αinnj ),
xc = Dαc, αc 0 = kc,
xinnj = Dαinnj , αinnj 0
= kj, (1)
Each sensor compressed (actually sensed) its signal yj = Φjxj by using an
individual measurement matrix Φj ∈ Rwj×N . The samples of the sensed signal
yj ∈ Rwj of each sensor should be sent to and consequently detected in the fusion
center via a conventional digital communication transceiver module. Obviously, yj
is the combination of two parts: one is the common part ycj ∈ Rwj and another is
the innovation part yinnj ∈ Rwj , which can be expressed as:
ycj = Φjxc,
yinnj = Φjxinnj , (2)
Therefore, it is possible to write that
rj = rcj + rinnj , (3)
123

where rcj and rinnj are the received signals in the FC corresponding to the common
and innovation parts of the transmitted one.
Inspired from JSM models, we define the Common Method to recover and de-
compress the data as follows:
r = ΦΨα + n (4)
r =





r1
r2
...
rJ





, n =





n1
n2
...
nJ





, α =





αc
αinn1
...
αinnJ





(5)
Φ =





Φ1 0 · · · 0
0 Φ2 · · · 0
...
...
...
0 · · · 0 ΦJ





, Ψ =






D D 0 · · · 0
D 0 D · · ·
...
... ... 0
D 0 · · · 0 D






(6)
where r ∈ RW , n ∈ RW , α ∈ RK(J+1), Φ ∈ RW×NJ , Ψ ∈ RJN×K(J+1) and
W =
J
j=1
wj. In order to recover the desired signals, first ˆα = ˆαT
c ˆαT
inn1
· · · ˆαT
innJ
T
is computed by solving the optimization problem in Eq. (7).
ˆα = min
´α
´α 0 or 1 subject to r − ΦΨ ´α 2 ≤ (7)
Then ˆxj will be computed by
ˆxj = D( ˆαc + ˆαinnj ) (8)
where ˆαc and ˆαinnj s are located in the found ˆα vector.
3 The Proposed Enhanced Common Method
In order to recover the uncompressed signals xj more robustly, an enhanced com-
mon model (ECM ) is proposed which uses the shared common component xc based
on the JSM model [12] concepts and also can recover the data in the lower mea-
suring rate. However, firstly, we assume the common part αc to be known by the
fusion center. This phenomenon can be used in the receiver (FC) to enhance the
reconstruction performance and system’s efficiency. Hence, in order to enhance the
124

reconstruction performance, we remove the common part from the reconstruction
Eq. (7) as follows:
r = [ΦΨ]





αc
αinn1
...
αinnJ





+ n (9)
and it can be rewritten to Eq. (10) by using a combination of two distinct parts:
– Common part αc
– Innovation part αI = αinn1
T αinn2
T · · · αinnJ
T T
r = [A H]







αc
αinn1
...
αinnJ







+ n = Aαc + HαI + n (10)
If we define rinn = r − Aαc, the reconstruction formula is modified to find just
the innovation parts of the signals:
ˆαI = min
´αI
´αI 0 or 1 subject to rinn − H ´αI 2 ≤ (11)
Consequently, the signal of each sensor ˆxj is found by
ˆxj = D(αc + ˆαinnj ) (12)
where ˆαinnj s are located in the computed ˆαI vector. This modification is indicated
to bring faster solution and also better reconstruction accuracy. Moreover, in order
to improve the reconstruction accuracy and solution time of the recovery algorithm,
we removed the common components from the recovery algorithm.
4 Experimental Results
In order to show the ability of the proposed models some experimental results are
reported here. In the following experiments, five signals xj ∈ R400, j = {1, 2, ..., 5}
from J = 5 sensors are generated such that there is a shared common component
xc ∈ R400 between them and also each of them are sparse in a random dictionary
D ∈ R400×512 with different sparsity levels (maximum 50-sparse). Consequently,
the signals are sensed by five different measurement matrices Φj ∈ Rwj×400 with
125

Gaussian random set of projections. The sensed samples yj ∈ Rwj , j = {1, 2, ..., 5}
are then sent to the fusion center through a digital transceiver system. Binary phase
shift keying modulating (BPSK), 1/2 channel encoding, and DS-CDMA with 4-
chip’s length are the specifications of the used transceiver system. Simulations are
experimented for 100 frames with different xjs and the obtained mean results are
reported.
The CVX Matlab toolbox [16, 17] is used to solve the least square problem in
Eq. (11). The CVX is a programming package for specifying and solving convex
programs. Moreover, other sparse-based optimization problems in this paper are
solved using basis pursuit denoising (BPDN) relaxation method [14] which is more
robust than other conventional algorithms against the incomplete and inaccurate
samples. We also use the SparseLab [15] Matlab toolbox to run the BPDN algo-
rithm. SparseLab is a Matlab software package designed to find sparse solutions to
systems of linear equations, particularly under-determined systems.
45 50 55 60 65 70 75 80 85 90
10
−15
10
−10
10
−5
10
0
Number of measurments
NormalizedError
JSM reconstruction
proposed reconstruction algorithm
Fig. 2. Comparison between compression ability of the proposed models in a loss-less scenario.
Fig. 2 shows the reconstruction performance of all the proposed methods for
different sensing (wj) and compression rates evaluated by semi normalized mean
squared error (NMSE). The sensing rate and the compression rate can be computed
as
wj
400 and 1−
wj
400, respectively. The normalized mean squared error (NMSE) which
126

we define for our experiments is as follows:
NMSE =
1
JN
J
j=1
N
n=1
(
xj(n)
xj 2
−
xj(n)
xj 2
)
2
(13)
where J and N are the number of sensors and signals’ samples, respectively. Note
that, the defined semi normalized mean squared error calculates the mean (with
respect to the number of sensors) of the sum of all differences between the actual
and reconstructed samples of each sensor’s signal. It means that, the averaging
process is only performed with respect to J and N which can cause the computed
semi normalized mean squared error to be larger than 1. It can be inferred from
Fig. 2 that using the Enhanced Common Model, as compared to the JSM model,
causes signals to be reconstructed more efficiently and in a lower sensing rate. This
fact is based on that, removing the known common part from the reconstruction
formula and reducing the length of the desired sparse vector makes the finding of
the sparse vector to be more accurate. Moreover, Fig. 2 concludes and shows the
accuracy of signal reconstruction for different sensing rates by using the proposed
method and the state of the art JSM model. However, the performance shown in
Fig. 2 is achieved when the sensed samples yj ∈ Rwj , j = {1, 2, ..., 5} are sent to
the fusion center through a lossless system without any symbol errors. In fact, Fig.
2 was just reported to show the compression ability of the proposed methods.
In order to find a sense about the reconstruction performance of the semi nor-
malized mean squared error and sparsity property of the αjs, Figures 3 and 4 are
presented. Fig. 3 illustrates a frame of the signal of a sensor xj and its reconstructed
version ˆxj by using the ECM algorithm and JSM reconstruction method. The re-
construction accuracy is compared between the two methods in Fig. 3. Moreover,
corresponding to the signal shown in the Fig. 3 the original related sparse vectors
αjs and their computed versions ˆαjs by FC are shown in Fig. 4.
5 Conclusion
In this paper, an enhanced common framework is proposed to compress the cap-
tured signals of the sensors which should be transmitted to FC. the proposed ECM
basically can be used in WMSN services where an intrinsic shared part exists be-
tween the sensors’ captured signals and also the signals can be sparsely represented
in a dictionary or basis. This makes ECM to be a context aware method and use-
ful in many applications. Because of compressing the signals of the sensors and
therefore, lower transmitted data, ECM can be used in lower bandwidth usage.
Furthermore, since compressive sensing sampling method is used to compress the
signals of the sensors, using ECM brings lower computational cost and therefore,
greater lifetime in the sensor side.
127

100 120 140 160 180 200 220 240 260 280 300
−0.15
−0.1
−0.05
0
0.05
0.1 recovered signal
original signal
(a) Reconstructed with JSM reconstruction method
100 120 140 160 180 200 220 240 260 280 300
−0.15
−0.1
−0.05
0
0.05
0.1 recovered signal
original signal
(b) Reconstructed with ECM algorithm
Fig. 3. A frame of the signal of a sensor xj and its reconstructed versions ˆxj by FC.
128

100 120 140 160 180 200 220 240 260 280 300
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
ˆαj
αj
(a) Reconstructed with JSM reconstruction method
100 120 140 160 180 200 220 240 260 280 300
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
ˆαj
αj
(b) Reconstructed with ECM algorithm
Fig. 4. Sparse vectors αj and their reconstructed versions ˆαj corresponding to the signal of the
Fig. 3.
129

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Authors
Javad Afshar Jahanshahi received his B.Sc. and M.Sc. Degrees both in Electri-
cal Engineering from the University of the Sistan Baluchestan and Shahid Beheshti
University, in 2006 and 2010, respectively. Now, he is pursuing Ph.D. program at the
Department of Telecommunication Engineering, Shiraz University of Technology.
His main research interests are in wireless communications and image processing.
Habibollah Danyali received the B.Sc. and M.Sc. degrees in Electrical Engineer-
ing respectively from the Isfahan University of Technology, Isfahan, Iran, in 1991
and the Tarbiat Modarres University, Tehran, Iran, in 1993. From 1994 to 2000
he was with the Department of Electrical Engineering, University of Kurdistan,
Sanandaj, Iran, as a lecturer. In 2004 he received his Ph.D. degree in Computer
Engineering from the University of Wollongong, Australia. After ﬁnishing his PhD
he continued his academic work with University of Kurdistan as an assistant pro-
fessor. As of September 2009, he is with the Department of Telecommunication
Engineering, Shiraz University of Technology, Shiraz, Iran. His research interests
include data hiding, scalable image and video coding, medical image processing and
biometrics.
Mohammad Sadegh Helfroush received the B.Sc. and M.Sc. degrees in Elec-
trical engineering from Shiraz University of Shiraz and Sharif University of Tech-
nology, Tehran in 1993 and 1995, respectively. He performed his Ph.D. degree in
Electrical Engineering from Tarbiat Modarres University, Tehran, Iran. Actually
he is working as associate professor in department of Electrical and Electronics
Engineering, Shiraz University of Technology, Shiraz, Iran.
131

A Scheme for Joint Signal Reconstruction in Wireless Multimedia Sensor Networks

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