Journal of Software Engineering and Applications, 2013, 6, 106-110
doi:10.4236/jsea.2013.63b023 Published Online March 2013 (http://www.scirp.org/journal/jsea)
SVM-based Filter Using Evidence Theory and Neural
Network for Image Denosing
Tzu-Chao Lin
Department of Computer Science and Information Engineering, WuFeng University, Chiayi 62153, Taiwan.
Received 2013
ABSTRACT
This paper presen ts a novel decision-based fu zzy filter based on support vector machines and Dempster-Shafer evi-
dence theory for effectiv e noise suppression and detail preservation. The propo sed filter uses an SVM impulse detector
to judge whether an input p ixel is n oisy. Sour ces of ev idence are extracted, and then the fusion of evidence based on the
evidence theory provides a feature vector that is used as the input data of the proposed SVM impulse detector. A fuzzy
filtering mechanism, where the weights are constructed using a counter-propagation neural network, is employed. Ex-
perimental results shows that th e proposed filter has better p erformance in terms of noise suppression and de tail preser-
vation.
Keywords: Neural Network; Evidence Theory; Impulse Noise; Image Restoration
1. Introduction
Images are often contaminated by impulse noise during
image acquisition (i.e. sensor noise) or transmission (i.e.
channel noise) [1]. The median (MED) filter is com-
monly used for suppressing impulse noise due to its sim-
ple implementation and efficiency. However, the filter
causes smoothing, which blurs fine image details and
affects texture. A number of median-based filters have
been developed to suppress noise while preserving de-
tails. A simple revision of the MED filter is the cen-
ter-weighted median (CWM) filter, which gives more
emphasis to the center pixel in the filtering window [2].
The CWM filter improves detail preservation at the ex-
pense of lower noise suppression. To balance noise at-
tenuation and image detail preservation, Arakawa et al.
and Lin et al. proposed median-type filters based on
fuzzy inference rules [3-4]. The two filters use an adap-
tive scheme to set the weighted median value based on
fuzzy rules concerning the states of the input pixel.
The median filter and its variations are applied to all
pixels of an image irrespective of their level of corrup-
tion. These filters thus distort uncorrupted pixe ls, causing
useful information in the image to be lost. This problem
is alleviated by a decision-based filter, where the detec-
tion of corrupted pixels is carried out prior to filtering.
The switching median filter (SWM-I) is the most
straightforward decision-based filter [5]. Depending on
the threshold value, the noisy pixel value is replaced by
the output of the MED filter. Noise-free pixels are left
unchanged. However, a constant threshold value may not
provide satisfactory performance in all circumstances.
Thus, Pankaj and Banshidhar proposed the improved
adaptive impulse noise suppression filter based on an
artificial neural network [6]. Unfortunately, the strategy
may work well at a pre-assumed noise density level but
poorly at other noise density levels. Recently, Lin and Yu
proposed an adaptive two-pass median (ATM) filter and
Liu et al. proposed an SVM-EPR filter for image de-
noising based on support vector machines (SVMs) [7-8].
The ATM and SVM-EPR filters use SVMs to identify
whether an input pixel is noisy. SVM-based filters can
preserve image details while suppressing impulse noise,
but they sometimes leave noisy pixels undetected or
misdetect uncorr upt ed pixels as noisy.
To get rid of the above-mentioned drawbacks, this pa-
per proposes a novel decision-based fuzzy filter (DBFF)
based on Dempster-Shafer (D-S) evidence theory and
SVMs for effective noise suppression and detail preser-
vation. The proposed filter comprises an efficient SVM
impulse detector and a fuzzy filter. Evidence fusion and
SVMs are incorporated into the framework of the pro-
posed impulse detector. For noise cancellation, a fuzzy
filtering mechanism, where the weights are constructed
using a counter-propagation neural network (CNN), is
adopted. Experimental results confirm the effectiveness
of the proposed DBFF filter in terms of suppressing im-
pulse noise and perceived image qua lity.
The rest of this paper is organized as follows. The de-

SVM-based Filter Using Evidence Theory and Neural Network for Image Denosing
107
sign of the proposed DBFF filter is presented in Section
II. In Section III, experimental results are provided to
demonstrate the performance of the proposed scheme.
Finally, the conclusion is given in Section IV.
2. The Decision-Based Fuzzy Filter
2.1. The Structure of the DBFF Filter
Let ()
x
k represent the input gray level of the image at
location k with coordinates 12 (, ).kk The observed filter
window {}wk is defined in terms of the image coordi-
nates symmetrically surrounding the current pixel ().
x
k
The filter window with size 21
M
n (n is a non-
negative integer) can be given by:
{}{():1,2,, ,1,,},
f
wkx kfnnM  (1)
where the input pixel 1 () ()
n
x
kxk

 is the central pixel.
The proposed DBFF filter consists of an SVM impulse
detector and a filtering mechanism, as shown in Figure 1.
In the noise-filtering process, if the input pixel ()
x
k is
identified as noisy, then the output of the fuzzy filtering
replaces the pixel. Otherwise, the pixel is kept unchanged.
The fuzzy filtering is performed based on a CNN weight
controller to remove any noisy pixels.
2.2. The SVM Impulse Detector
The proposed decision-making approach consists of two
steps: evidence extraction and fusion, and training of the
SVM impulse detector. To apply D-S evidence theory to
the SVM impulse detector, the frame of discernment in-
cludes two elements: noisy (N) and noise-free (F). The
hypotheses to be considered in the D-S formulation are:
,

singleton hypothesis N, singleton hypothesis F, and
compound hypothesis NF (we denote {}NF as NF ).
To extract the sources of evidence, we take into ac-
count the local features in the filter window {}wk. The
following nine feature extraction variables can be defined
to obtain the nine independent sources of evidence, re-
spectively.
Definition 1 :
() (){},dkxk MEDwk (2)
where
M
ED represents the median operation.
SVM
impulse
de tecto
r
)(ky
Evidence
extraction
and fusion
Switch
CNN
weight
controlle
r
Fuzzy
filter
)(kx
Figure 1. The detailed block diagram of the DBFF filter.
Definition 2 :
12
()() ()()
() ,
2
cc
x
kxkxkxk
ek   (3)
where
12
()() ()() ()(),
1,1,1,2.
cci
x
kxkxkxkxkxk
iMin cc

 
Notably, 1()
c
x
k and 2()
c
x
k of the filter window
{}wk are selected as the pixel values closest to that of
()
x
k [4].
Definition 3: The evidence ()
i
ck associated with the
local contrast at location k in the filter window {}wk is
defined by:
1
() ()
() ,
() ()
i
iM
i
i
xk xk
ck
x
kxk



 (4)
where ()
x
k is the mean gray level in the filter window
{}wk with size M. ()ck (or 1())
n
ck
 is the associated
feature variable [4].
Definition 4 :
12
()() ()()
() ,
2
cc
ck ckck ck
fk   (5)
where
12
()()()()() (),
1,1, 1,2.
cci
ck ckckckck ck
iMin cc

 
Notably, 1()
c
ck and 2()
c
ck of the filter window {}wk
are selected as the variable values closest to that of ()ck
[4].
Definition 5 :
3
() ()(),
g
kxkjk (6)
where
31111
3
(){(),,(), (),(), (),,()}
nnnn M
times
jkMEDxkxkx kx kx kxk


 
Definition 6 :
() ()(),
avg
hkxk w k (7)
where 1, 1
1
() ()
1
M
avg i
iin
wk xk
M



 is the mean gray
level excluding ()
x
k in the filter window {}wk .
Definition 7 :
4
1
() ,
4
i
il
nk   (8)
where i
li

th smallest {}
i
o [9]. Excluding (),
x
k
for each pixel (){},
i
x
kwk

i o is defined as the abso-
lute difference in intensity between ()
x
k and ();
i
x
k
i.e., () ().
ii
oxkxk Then, i o values are sorted in
increasing order into the s equence {}.
i
o
Definition 8 :

SVM-based Filter Using Evidence Theory and Neural Network for Image Denosing
108
5
() ()(),
s
kxkjk (9)
where
51 111
5
( ){( ),,( ),( ),( ),( ),,( )}
nn n nM
times
jkMEDxkxkx kx kx kxk



Definition 9 :
/2 1/2
() ()
() (),
2
MM
rkrk
tk xk  (10)
where 121 (),(),,()
M
rk rkrk

 are the elements of the
filter window {}wk (excluding ()
x
k itself) arranged
in ascending order such that12
() ()rk rk 1().
M
rk



How to extract sources of evidence and properly ini-
tialize the mass function induced by each source of evi-
dence are key points in the application of D-S evidence
theory. Thus, these nine feature variables can be sources
of evidence. The strategy for obtaining the mass function
values of ,,NFand NF of each source of evidence is
as follows [9]:
() ,
()2 / 3(1()),
()1/3(1 ()),
z
zz
zz
mN z
mF mN
mNF mN






(11)
where z denotes one the nine variables (),(),(),dk ek ck
(),(), (), (),(),().
f
kgkhknksktk The three mass functions
() ()
,
dk ek
mm and ()ck m can be combined to obtain the
combined mass function l
m according to Dempster’s
combination rule. The three mass functions () ()
,
f
kgk
mm,
and ()hk
m can be combined to obtain the combined
mass function .
p
m The three mass functions () ,
nk
m
()
s
k
m, and ()tk m can be combined to obtain the com-
bined mass function .
o
m Finally, the evidence vector is
given by:
)}.(),(),({}{ NmNmNmkE opl  (12)
After obtaining the evidence vector, {}Ek is used as
the input data set for the SVM impulse detector. This
evidence information is also used in the filtering stage.
To obtain an optimal separating hyperplane for classi-
fying the pixels into noisy and noise-free classes in the
SVM impulse detector, we extract evidence vector
{}Ek in a training image. That is, the optimal separating
hyperplane can be obtained through a training process by
using a set of supervised class labels (0 or 1) for the
training noisy image [11]. After training, the nonlinearly
inseparable discrimination function is obtained to sepa-
rate the training data into the noisy or noise-free class.
2.3. The Noise Filtering
1) The fuzzy filtering
The noise filtering of the DBFF filter is shown in Fig-
ure 1. We incorporate fuzzy filtering into the DBFF filter.
The output value ()yk of the fuzzy filter at the proc-
essed pixel ()
x
k is obtained as follows:
}.{)()())(1()( kMEDwkkxkky





(13)
To judge whether impulse noise exists at pixel (),
x
k
the membership function ()k

should take a continu-
ous value from 0 to 1 according the fuzzy rules. There-
fore, how to decide the value of the membership function
is the main issue for the fuzzy filter. In this work, a novel
neural-based learning approach is proposed to solve this
problem.
2) The CNN learning algorithm
To design (),k

the weight controller based on
counter-propagation neural network (CNN) shown in
Figure 1 is proposed. The fr amework of th e CNN weight
controller architecture is shown in Figure 2. The CNN
weight controller is composed of a three-layer neural
network. The competitive layer which has Q nodes is a
simple net for determining the nearest competitive ex-
emplar. The operation and the learning of the network
use the counter-propagation algorithm [10]. A synaptic
prototype weight
j
w that has the same dimension as the
input data {}Ek is associated with each neuron j in
the competitive layer, as shown in Figure 2.
Each node in the competitive layer competes (winner
takes all) based on the given inputs. The CNN uses the
Manhattan distance to calculate the similarity between
the input and the weight vector. Manhattan distance
j
U
is the difference between the input data {}Ek and the
weight of the j-th node in the competitive layer.
.,,2,1,}{ 1QjwkEUjj  (14)
When all
j
U are determined, the competitive layer
nodes begin to compete. The node with the smallest
j
U
value wins. Suppose that the q-th node is the winner. The
output
j
i of the j-th node in the competitive layer is:
.
,0
,1





qj
qj
ij (15)

j
b
j
w
)(k

Input layer
Competitive layer
Output layer
Q
)(Nml
)(Nmp
)(Nmo
Figure 2. The architecture of CNN weight controller.

SVM-based Filter Using Evidence Theory and Neural Network for Image Denosing
109
The nodes in the competitive layer compete for the
input vector to be classified. The node with the largest
similarity is the winner; it sends signal 1 to the output
node
j
i.
Each training vector is presented to the input layer.
The nodes in the competitive layer compete for the input
vector to be classified. The CNN network determines the
winning node for the training vector in the competitive
layer. Then, weight vector ,
q
w from the winner (q-th
node) in the competitive layer to the input layer, is up-
dated using the following learning rule.
)),(}{()()1( twkEtwtw qqq 

(16)
where

denotes the learning rate. Notably, the weight
vectors to the loser nodes stay unchanged.
In the second learning stage, only the weight con-
nected to the winner is updated. The weight
j
b from the
winner node in the competitive layer (the j-th node) to
the node in the output layer is updated as follows.
()()( ( ){}),(1)0
(1) 0, (1)0
jj
jj
btetxk MEDwkbt
bt bt
  








(17)
where ()et is the difference between the desired output
and physical output, and

is the learning rate. There-
fore, weight
j
b serv es as th e weigh t ()k

of the fuzzy
filter.
3. Experimental Results
The optimal separating hyperplane was obtained using
training image ‘Couple’ corrupted by 20% impulse noise
in the training process. The tested images were outside
the training set to test the generalization capability. Ta-
ble 1 shows the accuracy comparison of the SVM im-
pulse detector (for ATM [7], ASVC [11], and DBFF) for
some images corrupted by 20% impulse noise. The pro-
posed DBFF impulse detector has the highest classifica-
tion accuracy.
The image ‘Couple’ corrupted by 20% impulse noise
was used as the training image in the CNN weight con-
troller. The CNN converged after 25 training epochs. The
effectiveness of the proposed DBFF filter was assessed
by comparing its results with those of existing filters.
Figure 3 shows the restoration result comparison on the
TABLE I. ACCURACY COMPARISON OF THE SVM DETECTO
R
FOR SOME IMAG ES CORR UP TED BY 20% IM PU LSE NO ISE.
Fi lter Image
Lena Boats Cameraman Goldhill Lake
ATM 0.9731 0.9731 0.9315 0.9674 0.9623
ASVC 0.9767 0.9728 0.9555 0.9698 0.9641
DBFF 0.9843 0.9807 0.9605 0.9796 0.9715
(a) (b)
(c) (d)
Figure 3. Subjective visual quality of re stored image ‘Lake’
(a) original image, (b) corrupted image by 20% impulse
noise and filtered by (c) ATM filter, and (d) DBFF filter.
image ‘Lake’ corrupted by 20% impulse noise among
MED, ATM and DBFF. Apparently, the DBFF filter is
capable of producing better subjective visual quality re-
stored image by offering more noise suppression and
detail preservation.
4. Conclusion
An impulse detector based on SVMs was proposed to
judge whether an input pixel is noisy. Sources of evi-
dence are extracted, and then the fusion of evidence
based on D-S evidence theory provides a feature vector
that is used as the input data of the proposed SVM im-
pulse detector. A fuzzy filtering mechanism, where the
weights are constructed using a counter-propagation
neural network, is employed. Experimental results show
that the proposed DBFF filter achieves much better per-
formance than those of existing decision-based filters in
terms of noise suppression and detail preservatio n.
5. Acknowledgment
The author is grateful to the National Science Council of
the Taiwan, for their support of this research under grant
NSC-101-221-E274-010-.
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