Image Filtering Using all Neighbor Directional Weighted Pixels: Optimization Using Particle Swarm Optimization

Signal & Image Processing : An International Journal (SIPIJ) Vol.2, No.4, December 2011
DOI : 10.5121/sipij.2011.2416 187
IMAGE FILTERING USING ALL NEIGHBOR
DIRECTIONAL WEIGHTED PIXELS: OPTIMIZATION
USING PARTICLE SWARM OPTIMIZATION
J. K. Mandal1
and Somnath Mukhopadhyay2
1
Department of Computer Engineering, University of Kalyani, Kalyani, West Bengal,
India
jkm.cse@gmail.com
1
Department of Computer Engineering, University of Kalyani, Kalyani, West Bengal,
India
som.cse@live.com
ABSTRACT
In this paper a novel approach for de noising images corrupted by random valued impulses has been
proposed. Noise suppression is done in two steps. The detection of noisy pixels is done using all neighbor
directional weighted pixels (ANDWP) in the 5 x 5 window. The filtering scheme is based on minimum
variance of the four directional pixels. In this approach, relatively recent category of stochastic global
optimization technique i.e., particle swarm optimization (PSO) has also been used for searching the
parameters of detection and filtering operators required for optimal performance. Results obtained shows
better de noising and preservation of fine details for highly corrupted images.
KEYWORDS
ADWNP, de noising, random valued impulse noise, miss and false, particle swarm optimization, swarm
intelligence, sensitivity and specificity
1. INTRODUCTION
Due to a number of non idealistic encountered in image sensors and communication channels
digital images are often corrupted by impulses during image acquisition or transmission. In most
of the image processing applications, the most important stage is to remove the impulses because
the subsequent tasks such as segmentation, feature extraction, object recognition, etc. are affected
by noises [1]. Various filtering methods have been suggested for the removal of impulses from
the digital images. Most of these methods are based on median filtering techniques, which use the
rank order information of the pixels in the filtering window. The standard median filter [1]
removes the noisy pixels by replacing test pixel with the median value of the pixels in the
window. This technique provides a standard noise removal performance but also removes thin
lines and dots, distorts edges and blurs image fine textures even at low noise ratios. The weighted
median filter [2], center weighted median filter [3] and adaptive center weighted median filter [4]
are modified median filters. They give extra weight to some pixels of the filtering window and
thus these filters achieve betterment to the standard median filter.

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The standard and weighted median filters are incapable of making distinction between the noisy
and noise less pixels of the noisy image. Hence these filters distort the noise free pixels of the
image. For such problems, switching median filter [5] has been proposed in which an impulse
detector has been introduced to classify the center pixel of the test window. If the center pixel is
detected as noisy then that pixel is replaced by standard median value of the test window.
Otherwise the window is not filtered. The performance of this method of filtering purely depends
on the performance of impulse detection algorithm but this method of filtering noisy image
performs considerably better to standard and weighted median filters. As a result, many impulse
detection methods along with switching median filters have been proposed [4] - [8]. Among
them, an iterative pixel-wise modification of MAD (median of the absolute deviations from the
median) filter [8] is a robust estimator of the variance used to efficiently separate noisy pixels
from the image details. The tri-state median filter [9] and multistate median filter [10] are
improved switching median filters those are made using a weighted median filter and an
appropriate number of center weighted median filters. These filters perform better than weighted
and center median filters at the cost of increased computational complexity. The progressive
switching median filter [11] is also a variant of switching median filter that recursively performs
the impulse detection and removal in two different stages. This filter performs better than many
other median filters but it has a very high computational cost due to its recursive nature. The
partition based median filter [12] is an adaptive median filter has been introduced to tackle both
impulse noise and Gaussian noise, which uses the LMS algorithm for optimization purpose. The
signal dependent rank ordered mean filter [13] is a switching mean filter that uses rank order
information for impulse detection and filter. This method is similar to the switching median filter
except that the median operation is replaced with a rank ordered mean operation. This filter
obtains better noise suppression quality than some state-of-the-art impulse noise removal
techniques for both gray and color images. To deal with random valued impulse noises in the
images, an advance median filter, directional weighted median filter [14] has been proposed. This
scheme uses a new impulse detection method and which is based on the differences between the
test pixel and its 16 neighborhood pixels aligned with four main directions in the 5 x 5 window.
The filtering scheme used here is a variant of median filter. It iterates the detection and filtering
algorithm a minimum of 8 to 10 times to give satisfactory results for the images having highly
random valued noises. Another switching median filter developed by Sa, Dash and Majhi, the
second order difference based impulse detection filter [15] takes all the neighborhood pixels in
the 3 x 3 window to detect and filter the random valued impulse noises in the image. This method
of removing impulses has a drawback that it does not work well for highly corrupted images but
good for very low rate of impulses in images. ANDWP [22] filter has varied the user parameters
in a particular range and searched them manually in the 3 dimensional space to optimize the
operator. Although it is a difficult task to determine the best parameter set to optimize the results
for the various images having different noise density. Hence in this paper we used a global
optimization technique, PSO to determine and optimize the restoration results.
In addition to the median and mean based filters discussed, a dozens of soft computing tools
based filters have also been proposed in this literature such as fuzzy filter [16], neuro fuzzy filter
[17]., etc. These filters perform relatively better in terms of noise removal and details
preservation compared to median and mean based filters. During noise suppression, a majority of
the above mentioned filters have more or less drawbacks of removing thin lines and edges and
thus blurring the fine textures in the images. Although these methods work fine for the images
corrupted with impulses with up to 30% noise level in the images. But when more percentage of
impulses presents in the images, these median and other filters don’t able to perform satisfactory
and they also can’t remove some black patches on the reconstructed image.
In this paper the scheme for removal of random valued impulse noise has been proposed which
uses all the neighborhood pixels for noise detection as well as for noise filtering in the 5 x 5

189
window. The method uses maximum possible information of the neighborhood in order to
improve the quality of the reconstructed image. The filtering operator is based on minimum
variance of the four directional pixels aligned in the 5 x 5 window. Three user parameters such as
number of iterations (I), threshold value (T) and decreasing rate (R) of threshold value in each
iteration are searched in a 3-Dimentional space to get global optimal solution using a stochastic
search strategy, particle swarm optimization (PSO) technique. The performance of the proposed
algorithm is experimented and compared with other methods under several noise densities and
different bench mark images. Experimental results show that the proposed algorithm performs
better noise suppressing quality and effective image fine details preservation.
Rest of the paper organization is as follows. Section 2 illustrates the impulse detection operator.
Section 3 explains the filtering strategy. The proposed particle swarm optimization based
technique is given in section 4.0. PSO based experiment results, comparisons and discussions are
given in Section 5.0. Section 6.0 presents concluding remarks.
2. IMPULSE DETECTOR
2.1. Random Valued Impulse Noise
The images corrupted by impulsive noises with probability p can be described as follows:
n (k) with probability p
X (k) =
f (k) with probability 1-p
Where n (k) denotes the image contaminated by impulse with noise ratio p, and f (k) means the
pixels are noise free. There are two types of the impulsive noises: fixed- and random-valued
impulses. In a gray-scale image, the fixed-valued impulse, known as salt and pepper noise, shows
up as either 0 or 255 with equal probability (i.e. p/2), while the random-valued impulse is
uniformly distributed over the range of[0, 255] at probability p.
2.2. Detection Rule
Fig. 1 Four Directional Weighted Pixels in the 5 x 5 window for impulse detection
In this scheme we have focused on the edges aligned with the four main directions along with
included the two end pixels in the 5 x 5 window in each direction shown in fig. 1. The impulse
detection algorithm is followed.

190
Step 1: The center pixel is classified as noisy by comparing the intensity value of that pixel with
the maximum and minimum intensity values of its neighborhood pixels. The method first finds
the maximum and minimum intensity values in the 5 x 5 window of the test pixel. If the test pixel
does not lie within the intensity range spread of its neighbors it is detected as impulses. Otherwise
it is assumed that it may not be impulses and passed to next level detection rule. Let yi,j is the test
pixel and Wmin and Wmax be the maximum and minimum intensity values respectively within the
test window around yi,j. Thus the detection of noisy pixel is given as
j
i
y , = Noisy pixel: Wmin ≥ yi,j ≥ Wmax
Undetected: Wmin < yi,j < Wmax (1)
Step 2: Let Sk (k=1 to 4) denotes a set of seven pixels aligned in kth
direction, origin at (0, 0), i.e,
S1= {(-1,-2), (-2,-2), (-1,-1), (0, 0), (1, 1), (2, 2), (1, 2)}
S2= {(1,-2), (0,-2), (0,-1), (0, 0), (0, 1), (0, 2), (-1, 2)}
S3= {(2,-1), (2,-2), (1,-1), (0, 0), (-1, 1), (-2, 2), (-2, 1)}
S4= {(-2,-1), (-2, 0), (-1, 0), (0, 0), (1, 0), (2, 0), (2, 1)}.
Then let 0
k
S = Sk (0, 0), ∀ k from 1 to 4.
Step 3: In 5 x 5 window centered at (i, j), in each direction, define )
(
,
k
j
i
d the sum of all absolute
differences of intensity values between yi+s,j+t and yi,j with (s, t)∈ 0
k
S (k= 1 to 4), given in eq. 2.
Step 4: In each direction, weigh the absolute differences between two closest pixels from the
center pixel with a large ωm, weigh the absolute differences between two corner pixels from the
center pixel with ωn and weigh the absolute differences between two far pixels from the center
pixel with a small ωo, before calculate the sum. Assign ωm=2,ωn = 1 and ωo= 0.5.
Thus we have, )
(
,
k
j
i
d = )
4
1
|,
|
(
0
)
,
(
,
,
, <=
<=
−
∑
∈
+
+ k
y
y
k
s
t
s
j
i
t
j
s
i
t
s
ω (2)
ωm: ( s, t) ∈Ω3
Where ω s, t = ωo: (s, t) ∈Ω2
(3)
ωn: otherwise
Where Ω3
= {(s, t):-1 ≤s, t≤ 1}, and (4)
Ω2
= {(s, t): (s, t) = ± {(-1, -2), (1, -2), (2, -1), (-2, -1)}} (5)
Step 5: )
(
,
k
j
i
d is termed as direction index. Find the minimum of these four direction indices, which
is used for impulse detection, denoted as
ri, j = min{ )
(
,
k
j
i
d : 1≤ k≤ 4 } (6)
There may be three cases for value of ri,j .
1. ri,j is small when the center pixel is on a noise free flat region.

191
2. ri,j is small when the center pixel is on the edge.
3. ri,j is large when the center pixel is a noisy pixel.
Step 6: So from the above analysis, classify the center pixel by introducing a threshold T.
Define the complete impulse detection rule as
j
i
y , is a Noisy pixel: Wmin ≥ yi,j ≥ Wmax
Noise free pixel: ri,j ≤ T and Wmin < yi,j < Wmax (7)
3. IMPULSE DETECTOR
In the proposed technique a novel scheme has been introduced which is based on minimum
variance of all the four directional pixels. The followings are the procedure to restore a noisy
pixel yi, j using its neighbourhood pixels.
Step 1: Calculate the standard deviation,
)
(
,
k
j
i
σ of all yi+s, j+t with (s, t) ∈ 0
k
S , k=1 to 4
Step 2: Find the minimum of
)
(
,
k
j
i
σ : k=1 to 4, as
j
i
l , =
k
min
{ )
(
,
k
j
i
σ : k=1 to 4} (8)
Step 3: Select the set of pixels in the j
i
l , direction as S. And replace the middle pixel by a
variable x to form S = {a, b, c, x, d, e, f}. (9)
Step 4: Formulate a quadratic equation f(x) by calculating the variance (σ 2
) of the above set,
given in eq. 10. So
2
2
2
2
2
2
2
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
mean
f
mean
e
mean
d
mean
x
mean
c
mean
b
mean
a
x
f
−
+
−
+
−
+
−
+
−
+
−
+
−
=
(10)
7
/
)
( f
e
d
x
c
b
a
mean
where +
+
+
+
+
+
= (11)
Step 5: Compute first order derivative (f’
(x)) and second order derivative (f’’
(x)) of f(x).
Step 6: By the principle of maxima/minima on a quadratic equation and where a, b, c, d, e and f
are positive integer constants, the value of f’’(x) is always positive for any value of x, where x
∈[0,255]. So solve the equation f’(x) =0, and get an x, where x ∈ [0,255] for which f(x) is
minimum.
Step 7: Replace ij
y by x.
The methods of detection and filtering of noisy pixels discussed work with three important user
parameters. These are number of iterations (I), threshold value (T) and decreasing rate (R) of
threshold value in each iteration. These parameters I, T and R are estimated to get optimum
restoration results by a population based randomized search technique. Using this technique, the
detection and filtering algorithm does not require any parameter to be supplied by the user for any
level of noise density in the image.

192
4. PSO BASED OPTIMIZATION
In this paper, a biologically-inspired evolutionary computation (EC) techniques motivated by a
social analogy has been incorporated. Particle swarm optimization (PSO) is a population based
stochastic optimization technique developed by Dr. Eberhart and Dr. Kennedy in 1995 [18],
inspired by social swarming behaviour of bird flocking, fish schooling or even in human social
behaviour, from which the swarm intelligence (SI) paradigm has been developed [19]. The main
strength of PSO is its fast convergence and easy implementation. The system is initialized with a
population of random solutions and searches for optima by updating generations. In PSO, the
potential solutions, called particles, fly through the problem space by following the current
optimum particles. The search is continued either for fixed number of iterations or till some
criteria of optimum solutions based on fitness value is met. Each particle keeps track of its
coordinates in the problem space which are associated with the best solution (fitness) it has
achieved so far. This value is called pBest. Another "best" value that is tracked by the particle
swarm optimizer is the best value, obtained so far by any particle in all the population as its
topological neighbours, the best value is a global best and is called gBest. The particle swarm
optimization concept consists of, at each time step, changing the velocity of (accelerating) each
particle toward its pBest and gBest locations. Acceleration is weighted by a random term, with
separate random numbers being generated for acceleration toward pBest and gBest locations. The
problem formulation based on PSO model in the supervised way has been resented in next
subsection.
4.1. Performance Metric
As the maximum value of PSNR to be estimated using eq. 12, same equation is used as fitness
function f for the particles in PSO based optimization technique.
f= PSNR (I1, I2) = 10 * log10 ( )
.
2
2
1
*
1
2
))
,
(
)
,
(
(
255
∑ −
n
m
N
M
n
m
I
n
m
I
(12)
where M and N are the dimensions of the input images respectively. I1 and I2 are the
original and enhanced images respectively.
The detection of noisy pixels depends upon a threshold value T, which is decreased by a rate R
and the finite numbers of iterations are required to obtain the optimum fitness value depending
upon the parameter R and I respectively. The problem under consideration is to find the particles
having the best fitness value (i.e., maximum PSNR) and that has been implemented in supervised
way using the algorithm given in section 4.2.
4.2. PSO based optimization algorithm
Step 1: Three dimensional search space represented through the attributes I, T and R as
parameters and initialized 3 to 6, 300 to1000 and 0.6 to 0.95 respectively. Particles are initialized
randomly at xp in a fixed size of swarm. Here ‘p’ represents particle number in a swarm. Swarm
size is considered here of 6 to 10 particles. At the initial position xp, fitness values fp are evaluated
for individual particle using eq. 12.
Step 2: The updated positions xp (i+1) of the particles are evaluated on calculating the velocities
of each particle vp (i+1) in the search space using eq. 13 and 14.
vp (i+1) = h(i)vp(i)+Ψp*rp*(xpbp(i) –xpn(i) ) + Ψg*rg *((xgbp(i) –xp(i)) (13)

193
xp(i+1) = xp(i) + vp(i+1) (14)
variables and constants of the above equations are initialized as follows:
1. Ψp and Ψg are the positive learning factors respectively. Usually Ψp equals to Ψg and
ranges from [0, 4]. Present implementation considered Ψp and Ψg >1.
2. rp and rg random numbers in [0, 1], generated in every iteration separately. They are the
real constants used to maintain the diversity of the populations.
3. i is the iteration number initialized to 1 and IMAX is the desired maximum number of
generations. In the experimentation, it is set to [10- 20].
4. h(i) are the inertia factors, which has positive real random values in less than 1. This
value is kept fixed for individual iteration.
5. xp(i) and vp(i) are position and velocity of the pth
particle at ith
iteration, respectively.
Initial positions of particles are randomly initialized and initial velocities are initialized to
zero as discussed earlier.
6. fpB(i) and fgB(i) are the pBest (personal best fitness value of a particle) value and gBest
(global best fitness value of particles) values at ith
iteration, respectively. Initially fpB(i)
are the values of fp which is calculated in step 1 and the best value among the initialized
fp(i) is the global best initialized value which is assigned to all particles as fpB(i).
7. xpB(i) and xgB(i) are the personal best positions and the global best position of pth particle
at ith
iteration, respectively. These values are initialized by assigning location of particle
where fpB(i) and fgB(i) have been obtained respectively, in step 6.
Step 3: The velocities and positions of particles are updated using eqns. 13 and 14 respectively.
These velocities and positions are calculated using three components; current velocity of each
particle, distance between its current position and its pBest position of each particle and distance
between its current position and gBest position of the entire swarm particle.
Step 4: To keep the new positions in the search boundary, it is set to [vMin, vMax]. If new positions
of particles are found beyond the boundaries of search space then they are restricted to the
boundary values of the search space. The boundary values of I, T and R is discussed in step 1.
Step 5: The fp(i+1) calculated in step 4 is compared with its previous fpB(i). If fp(i+1) is better
than previous fpB(i) then fpB(i+1) is updated by fp(i+1), otherwise old fpB(i) is retained as a current
fpB(i+1). Similarly xpB(i+1) is also updated according to this updated fitness fpB(i+1).
Step 6: Best value among the all current fpB(i+1) calculated in step 5 is considered as new
fgB(i+1). If new value of fgB(i+1) is better than previous fgB(i) then values of fgB(i) is updated by
new fgB(i+1), otherwise old fgB(i) is retained as new fgB(i+1). Similarly, xgB(i+1) is also updated
according to this updated fitness fgB(i+1).
Step 7: Steps 3 to 6 is repeated until an adequate fitness is reached or a desired maximum number
of iterations are met, but for present implementation the interval [10, 20] is taken as steps for
iteration.
5. SIMULATIONS
The proposed impulse detection, filtering and optimization using particle swarm optimization
techniques discussed in previous section is implemented and the performance of the proposed
algorithm is simulated on various bench mark images like Boats, Bridge, Lena and Baboon
corrupted by various noise ratios. All test images have the dimensions of 512 x 512 and 8-bit gray
levels. The proposed filter is experimented to see how well it can remove the random valued
impulses and enhance the image restoration performance for signal processing. These extensive

194
experiments have been conducted to evaluate and compare the performance of the proposed PSO
based optimization filter with a number of existing impulse removal techniques. The proposed
algorithm have been executed on the machine configuration as ACPI uni-processor with Intel®
Pentium® E2180 @ 2.00 Ghz CPU and 2.98 Gbyte RAM with MATLAB
8a environment.
5.1. Results and Comparisons
To compare the restoration results of proposed operator with various existing operators each of
Lena, Boat and Bridge images corrupted with 40%, 50% and 60% noise densities respectively are
taken into account. Using the proposed algorithm on these nine images restoration results are
obtained and average PSNR values obtained are given in table 1, table 2 and table 3 respectively.
It is seen from these tables that the performance of the ACWM [4] is the worst of all in all the
cases. The MSM [10] is considerably better than the ACWM [4] in all the cases but worse than
the others. The performances of the SD-ROM [13] and PWMAD [8] are very close to each other
in all the three types restoration cases. The performances of the DWM [14] operator shows that
this filter works better than any existing filter in restoring 40% or more corrupted images. The
ANDWP [22] operator also gives excellent restoration results. But the proposed filter obtained
very good results (average PSNR) for all the images taken in de noising highly corrupted images.
Fig. 2 shows the restoration images in enlarged form to show the preservation of fine details
using various filters. For this purpose Baboon is taken as test image corrupted by 25% random
value impulse noise. It is observed from this figure that the performance of the SMF [1] and
MSM [10] are very close to each other. Some noise patches are easily visible in the output images
of these two filters. The output images of the SD-ROM [13], FF [16], and PSM [11] are almost
indistinguishable from each other and they are significantly better than those of the SMF [1] and
MSM [10]. SD-ROM [13], FF [16], and PSM [11] filters show very good noise removal
performance but considerably blur the fine details of the image. It is seen that the proposed
operator yields much better detail in terms of preservation.
Restoration results in output images by different filters along with the proposed filter on 60%
corrupted Lena image is given in Fig. 3. We can see from this figure that the output image by
MSMF [10] cantains maximum black pathes and performs worst. SD-ROM [13] and PWMAD
[8] performs better than MSM [10] but not so well as these have also noise in the reconstructed
images respectively. On the contrary DWM filter[14] performs good as it preserves the fine
details but can not remove all the patches on the enhanced image. From these restoration results
we can see that the proposed operator performs quite well. It has removed almost all the noisy
pixels with preservation of image details.
Table 4 shows the performances of the proposed operator in comparison to other filters. The noise
densities used here from 20% to 60% with 10% increments. It is seen from this table, the
performances of the SMF [1] operator is very poor when the PSM [11] is much better than that in
restoring only 20% noise density but for other noise densities it is better but not so good. The
ACWM [4], MSM [10], SD-ROM [13] and Iterative median [20] perform very similar way. SD-
ROM [13] performs optimally among them in restoring only 50% and 60% noise densities. The
PWMAD [8] is better than second order filter [15] in all cases except the 60 % case. The DWM
[14] operator performs best than any existing filter in all cases. The ANDWP [22] operator also
performs excellently with restoration results. But the proposed filter performs significantly better
than any existing filter in restoring 40% or more corrupted images.

195
Table 1
Average PSNR (dB) values for 40% noise density
Lena Boat Bridge Average
ACWM[4] 28.79 26.17 23.23 26.06
MSM[10] 29.26 25.56 23.55 26.12
SD-ROM[13] 29.85 26.45 23.8 26.7
PWMAD[8] 31.41 26.56 23.83 27.26
DWM Filter[14] 32.62 27.03 24.09 27.91
ANDWP[22] 32.65 29.23 26.38 29.42
Proposed 32.88 29.33 26.57 29.59
Table 2
ACWM[4] 25.19 23.92 21.32 23.47
MSM[10] 26.11 24.27 22.03 24.13
SD-ROM[13] 26.8 24.83 22.42 24.68
PWMAD[8] 28.5 24.85 22.2 25.18
DWM Filter[14] 30.26 25.75 23.04 26.35
ANDWP[22] 30.50 28.72 25.51 28.24
Proposed 30.91 28.92 25.62 28.48
Table 3
ACWM[4] 21.19 21.37 19.17 20.57
MSM[10] 22.14 22.21 20.07 21.47
SD-ROM[13] 23.41 22.59 20.66 22.22
PWMAD[8] 24.3 22.32 20.83 22.48
DWM Filter[14] 26.74 24.01 21.56 24.10
ANDWP[22] 28.29 26.95 23.42 26.22
Proposed 28.53 26.96 23.76 26.41

196
Fig.2 (a) SMF [1] (b) FF [16] (c) MSM [10] (d) SD-ROM [13] (e) PSMF [11] (f) Proposed.
Fig.3 (a) Original (b) 60 % Noisy (c) SD-ROM [13] (d) MSM [10] (e) PWMAD [8]
(f) DWM [14] (g) Proposed.
(a) (b) (c)
(d) (e) (f)

197
Table 4
PSNR (dB) values obtained against different noise densities on Lena image
Filter Name 20% 30% 40% 50% 60%
SMF[1] 30.37 30 27.64 24.28 21.58
PSM[11] 35.09 30.85 28.92 26.12 22.06
ACWM[4] 36.07 32.59 28.79 25.19 21.19
MSM[10] 35.44 31.67 29.26 26.11 22.14
SD-ROM[13] 35.72 30.77 29.85 26.80 23.41
Iterative Median [20] 36.90 31.76 30.25 24.76 22.96
Second Order[15] 34.35 32.53 30.90 28.22 24.84
PWMAD[8] 36.50 33.44 31.41 28.50 24.30
DWM Filter[14] 37.15 34.87 32.62 30.26 26.74
ANDWP[22] 34.42 33.01 32.65 30.50 28.29
Proposed 34.53 33.12 32.88 30.91 28.53
5.2. Comparison of Sensitivity and Specificity
The miss and false are two measures of performance of noise detection. The miss counts the
actual numbers of noisy pixels those are not counted. The false parameter measures the numbers
of noise free pixels which are identified as noisy pixels. A theoretical optimal result can achieve
zero miss and zero false values. Using the proposed PSO based noise removal algorithm, the miss
and false values on 40%, 50% and 60% noisy Lena images are given in table 5. We can see from
table 5 that SD-ROM [13] and ACWM [4] filter performs excellent for identifying false values
but it performs very poor for identifying noisy pixels and these undetected noisy pixels become
the noticeable patches on the reconstructed image. The ANDWP [22] operator also gives
excellent miss and false results. From table 5 it is also seen that the proposed algorithm can
identify the noisy pixels as well as it can ignore the noise free pixels correctly with a remarkable
difference compared to all other existing filters. It gives optimum miss and false values among all
filters taken into account for the experiment.
Two other statistical measurement tools of performance are also used to measure the performance
of proposed algorithm. These are sensitivity (Sen#) and specificity (Spc#). Sensitivity measures the
proportion of positives which are correctly identified as such. Specificity measures the proportion
of negatives which are correctly identified. 100% sensitivity and 100% specificity are the optimal
results.
It is seen from table 6 that the sensitivity and specificity for different conventional filters along
with the proposed for 40%, 50% and 60% corrupted Lena images, proposed algorithm obtain very
good results in terms of sensitivity and specificity.

198
Table 5
Comparison of miss and false results for “Lena” image
Filter
40% 50% 60%
miss false miss false miss False
SD-ROM[13] 22842 411 32566 998 45365 2651
MSM[10] 16582 7258 20857 10288 26169 15778
ACWM[4] 16052 1759 23683 2895 32712 7644
PWMAD[8] 11817 9928 14490 15003 17760 19577
DWM[14] 9512 7761 9514 11373 12676 12351
ANDWP[22] 7852 6018 8260 7512 8812 9304
Proposed 7602 5836 8066 7452 8565 9158
Table 6
Comparison of sensitivity and specificity results for “Lena” image for different noise
densities
Filter
40% 50% 60%
Sen#
%
Spc#
%
Sen# % Spc# % Sen# %
Spc#
%
SDROM[13] 78 99 72 99 71 98
MSM[10] 84 97 84 92 83 89
ACWM[4] 84 98 81 97 79 95
PWMAD[8] 88 90 88 88 88 87
DWM[14] 90 92 92 91 91 92
ANDWP[22] 93 94 94 94 94 94
Proposed 93 93 93 93 94 94
6. CONCLUSIONS
In this paper, a novel approach has been presented for filtering high random valued impulse noise
from digital images. In this approach tuning parameters of noise detection and filtering operator
has been optimized in supervised way using PSO based optimization technique. The main
advantage of the proposed operator over most other operators is that it efficiently removes

199
impulse noise from digital images while successfully preserving thin lines, edges and fine details
in the enhanced image.
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Authors:
Jyotsna Kumar Mandal, M. Tech.(Computer Science, University of
Calcutta),Ph.D.(Engg., Jadavpur University) in the field of Data Compression and
Error Correction Techniques, Professor in Computer Science and Engineering,
University of Kalyani, India. Life Member of Computer Society of India since 1992
and life member of cryptology Research Society of India. Dean Faculty of
Engineering, Technology & Management, working in the field of Network Security,
Steganography, Remote Sensing & GIS Application, Image Processing. 25 years of
teaching and research experiences. Eight Scholars awarded Ph.D. and 8 are pursuing.
Total number of publications 189.
Somnath Mukhopadhyay did his graduation in Bachelor of Computer Application
form the University of Burdwan in 2004 and MCA in 2008 from the same university.
He did his M.Tech (CSE) in 2011 from the University of Kalyani. Currently he is
engaged in teaching profession with three years of experience. Broad area of his
research interest includes Signal and Image Processing, Bioinformatics and Pattern
Recognition. He has 7 publications in international conference proceedings and
journals.

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