PERFORMANCE ANALYSIS OF UNSYMMETRICAL TRIMMED MEDIAN AS DETECTOR ON IMAGE NOISES & ITS FPGA IMPLEMENTATION

International Journal of Information Sciences and Techniques (IJIST) Vol.2, No.3, May 2012
DOI : 10.5121/ijist.2012.2302 19
PERFORMANCE ANALYSIS OF UNSYMMETRICAL
TRIMMED MEDIAN AS DETECTOR ON IMAGE
NOISES & ITS FPGA IMPLEMENTATION
K.Vasanth1
and S.Karthik2
1
Department of Electrical & Electronic Engineering, Sathyabama University, Chennai,
Tamilnadu, India
vasanthecek@gmail.com
2
Project Associate, Cognizant Technology Solutions, Chennai, Tamilnadu, India
skarthick76@gmail.com
ABSTRACT
This Paper Analyze the performance of Unsymmetrical trimmed median, which is used as detector for the
detection of impulse noise, Gaussian noise and mixed noise is proposed. The proposed algorithm uses a
fixed 3x3 window for the increasing noise densities. The pixels in the current window are arranged in
sorting order using a improved snake like sorting algorithm with reduced comparator. The processed pixel
is checked for the occurrence of outliers, if the absolute difference between processed pixels is greater than
fixed threshold. Under high noise densities the processed pixel is also noisy hence the median is checked
using the above procedure. if found true then the pixel is considered as noisy hence the corrupted pixel is
replaced by the median of the current processing window. If median is also noisy then replace the
corrupted pixel with unsymmetrical trimmed median else if the pixel is termed uncorrupted and left
unaltered. The proposed algorithm (PA) is tested on varying detail images for various noises. The proposed
algorithm effectively removes the high density fixed value impulse noise, low density random valued
impulse noise, low density Gaussian noise and lower proportion of mixed noise. The proposed algorithm is
targeted on Xc3e5000-5fg900 FPGA using Xilinx 7.1 compiler version which requires less number of
slices, optimum speed and low power when compared to the other median finding architectures.
KEYWORDS
Snake like sorting, Trimmed filters, Impulse noise, Gaussian noise, field programmable gate array
1. INTRODUCTION
Images are often corrupted by noises due to poor image sensors or error in transmission medium.
The different types of noises that occur in images are additive random noise such as Gaussian
white noise and salt-and-pepper impulse noise, signal-dependent noise such as speckle [1]. In
order to restore the corrupted images, a suitable filter should be used. A good noise removal filter
would exactly restore the image by removing the noise distributions only. So to obtain the above
result, a suitable filtering algorithm must be stated to remove a noise distribution. In Practise, the
noise removal filter is designed to restore images well but there will be always some degree of
variation in the restored pixel values from the original image. If there is much deviation the
chosen algorithm is not suitable for the restoration In the above stated condition the restored
image might not be visually unacceptable if subjected to human inspection [2]. The poor photo

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electronic detectors which results in thermal noise which is modelled as additive zero mean
Gaussian noise corrupts the images [3]. Impulse noise is caused by transmission in a noisy
channel. Basically there are two common types of impulse noise are the salt-and-pepper noise and
the random-valued noise. For images corrupted by salt-and pepper noise, the noisy pixels can take
only the peak and the valley values while in the case of random-valued noise; they can take any
random value in the dynamic range [3]. A conventional method to remove noise from image data
is to use a spatial filter. Spatial filters broadly classified into non-linear and linear filters. Many
non-linear filters fall into the category of order statistic neighbourhood operators. This means that
the local neighbours are ordered in ascending order and this list is processed to give an estimate
of the underlying image brightness. The simplest order statistic operator is the median [3], where
the central value in the ordered list is used for the new value of the brightness. The median is
good at reducing impulse noise However, A mean or average filter is the optimal linear filter for
Gaussian noise removal which tends to blur sharp edges, destroy lines and other fine image
details. Median filter often blur the image for larger window size and insufficient noise
suppression for small window sizes [4]. Adaptive Median Filter (AMF) blurs the image at
high noise densities but fairs well at low and medium noise densities [5].
In Threshold decomposition filter (TDF) the pixels are decomposed based on various
threshold levels and subjected to Boolean operation. This eliminated the need for
complex sorting technique. This decomposition algorithm requires large threshold levels
for operation and fails at higher noise densities. The above mentioned Median and its
variant filters operate uniformly over the entire image results in the modification of
uncorrupted pixel. Ideally the filtering should be applied only to corrupted pixels while
leaving uncorrupted pixels intact. Therefore, a noise-detection process should
discriminate between uncorrupted pixel and the corrupted pixel prior to applying
nonlinear filtering is highly desirable. To elude the drawback of the above filters
switched median filters were introduced. These filters work on the basis of impulse
detection and correction. One of the popular switched median filter is Progressive
Switched Median filter (PSMF). In this filter the decision is based on fixed threshold
value and hence a procuring a strong decision is difficult. Hence at increasing noise
densities the switched filters do not consider any of the local detail of the image and
hence edges are not preserved properly [6]-[7].
The DPF filter removes noise at medium noise densities but fails to eliminate salt and
pepper noise at high noise densities [8]. Decision based filter [9] identifies the processed
pixel as noisy, if the pixel value is either 0 or 255; else it is considered as not noisy.
Under High noisy environment the DBA filter replaces the noisy pixel with
neighbourhood pixel. Due to repeated replacement of neighbourhood pixel results in
streaks in restored image. To avoid streaks in images an improved DBA (DBUTMF)
[10] is proposed with replacement of median of unsymmetrical trimmed output, but
under high noise densities all the pixel inside the current would take all 0’s or all 255’s or
combination of both 0 and 255. Replacement of trimmed median did not fair well for
above case. Hence Modified decision based un-symmetric trimmed median filter
(MDBUTMF) [11] is proposed. The above cause is eliminated by replacing the mean of
the current window. When the noise densities scale greater than 80% the Smudging of
edges occurs. All the Estimation based Threshold algorithms and conventional
algorithms fairs well for low and medium density impulse noise but fails at high noise
densities also these algorithms do not preserve edges. Hence a suitable algorithm that

21
detects, eliminates impulse noise and preserves edges for high noise densities is
proposed. This paper is organized as follows. Section II describes noise model. Section
III gives a overview of related work on Image De-noising using proposed algorithm and
its hardware implementation. Section IV deals with Exhaustive Experimental Results and
Discussions and finally Concluding Remarks are given in Section V.
2. NOISE MODEL
Let the true image x belong to a proper function space S(Ω) on Ω = [0; 1]2
, and the observed
digital image y be a vector in Rmxm indexed by A ={1,2,..m} X {1,2,.m}.The image degradation
can be modeled as y = N(Hx), where H : S(Ω) Rmxm is a linear operator representing blurring,
and N : Rmxm Rmxm models the noise. Usually, y = n
Hx σ
+ where σn Є Rmxm is an
additive zero-mean Gaussian noise with standard deviation σ= 0 . Outliers are modeled as
impulse noise. Then a realist model for our data is
y’ = g
K
x
H σ
+
.
. (1)
y = )
'
( y
N (2)
Where N represents the impulse noise and K refers to speckle noise as given in equation 1 2.
The noise model for salt pepper noise is given below . If [0; 255] denote the dynamic range of
y’, i.e., 0 = y’ij = 255 for all (i,j), then they are denoted by Salt-and-pepper noise: the gray
level of y at pixel location (i j) is illustrated in the equation 3.
yij = 0 with probability p;
y’ij with probability 1 - p - q;
255 with probability q; (3)
Where s = p + q denotes the salt-and-pepper noise level [12].
3. PROPOSED ALGORITHM
3.1. Snake like improved shear sorting
Over the years sorting algorithm is a basic operation behind all the median filters. All the existing
sorting algorithms require more comparators. In this paper a new snake like improved shear
sorting algorithm is proposed for ordering the entire array of processed pixels as shown in figure
1.

22
Figure 1 illustration of the proposed sorting methodology
Let D be an m x n matrix which is mapped with linear integer sequence W. Sorting the sequence
W is then equivalent to sorting the elements of D in some Pre determined indexing scheme. The
proposed Snake like modified algorithm consists of two basic operations row sorting, column
sorting and semi diagonal sorting. The algorithm of the proposed snake like improved shear
sorting algorithm is as follows.
Step1: The considered 2D processing window as shown in figure 1.a
Step2: Sort the 1th
and 3rd
rows of the 2D array in ascending order and 2nd
row in descending
order independently .The sorted sequence is fed to step3 as shown in figure1.b.
Step3: Sort the three columns of the 2D array in ascending order .The sorted sequence is fed to
step4 as shown in figure 1.c.
Step4: Repeat step 2 and 3 once again as shown in figure1.d and e.
Step5: Now Sort the upper semi diagonal of the semi sorted 2D array in ascending order as
shown in figure1.e.
Step6: Sort the Lower semi diagonal sorted array in ascending order as shown in figure1.f.
Resulting array is sorted in a snake like order. The procedure is repeated for the other windows of
the image [13].
3.2. Proposed Algorithm
The brief illustration of the proposed algorithm is as follows.
Step 1: Choose 2-D window of size 3x3. The processed pixel in current window is assumed as
pxy.
Step 2: sort the 2D window data in ascending order using snake like modified shear sorting which
is given by S. now Convert sorted 2D array into 1D array. Smed is the median of the sorted array
Step 3: Unsymmetrical trimmed median filter
Initialize two counters, forward counter (F) and reverse counter (L) with 1 and 9 respectively.
When a 0 or 255 are encountered inside the Sorted array (S), F is incremented by 1 or L is
decremented by 1 respectively. The resulting array will be holding non noisy pixels of the current

23
window. The median of this array is termed as UTMED (unsymmetrical trimmed median) [10].
Step 4: Salt and pepper noise Detection
Case (1): If the absolute difference between the processed pixel and unsymmetrical trimmed
median filter (UTMED) is greater than the fixed threshold (T) then pixel is considered as noisy.
As illustrated in equation 3
If │P(x,y)-UTMED│ T (3)
Case (2): If the case 1 is true find the absolute difference between the median of and
unsymmetrical trimmed median filter (UTMED). Check the difference is greater than the fixed
threshold (T1) then median is considered as noisy as illustrated in equation 4.Case 2 is done for
high noise densities where the computed median is also noisy.
If │Smed-UTMED│ T1 (4)
Step 4: Salt and pepper noise Correction logic
If the case1 │P(x, y)-UTMED│ T is true then check for the second case2 │Smed-UTMED│
T1. if both the condition are true then processed pixel and computed median is noisy. Hence
replace the corrupted pixel with median of Unsymmetrical trimmed median. If condition 1 is true
and condition 2 is false then corrupted pixel is replaced with the median of the sorted array. If
both case 1 and case 2 fails then the pixel is termed as non noisy. The pixel is left unaltered [13].
3.3 Methodology of proposed work
The bigger matrix refers to image and values enclosed inside a rectangle is considered to be the
current processing window. The element encircled refers to processed pixel. The above discussed
methodology is illustrated as below.
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255
255
255
255
0
255
124
187
0
0
123
25
255
0
0
255
155
205
177
94
255
0
255
0
0
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255
255
255
255
0
255
124
187
0
0
123
25
155
0
0
255
155
205
177
94
255
0
255
0
0
Corrupted image segment Restored image segment
Case (a): Initialize forward counter F=1 and reverse counter L=9. Convert the 2D array into 1D
array and sort the converted array. F and L counter moves in forward and reverse directions
respectively. When a 0 is detected F is incremented by 1 and when a 255 is detected L is
decremented by 1.
Unsorted array: 177 0 0 205 255 187 155 25 124
Sorted array Sxy 0 0 25 124 155 177 187 205 255
Here the median Smed value is 155. The case (1) is illustrated as follows. Now check for the
presence of 0 or 255 in the sorted array. Every time a 0 is detected F is incremented by 1 and if
255 is detected L is decremented by1. In the above example there is two 0 and one 255. Hence F
is incremented by two times and L is decremented by one time. Now finally F is holding 3 and L
is holding 8. Now the variable DET is assigned with the median of the rank ordered
unsymmetrical trimmed output i.e. corrupted pixel is replaced by median

24
(25,124,155,177,187,205) = 166. i.e, DET=166. Now perform first step detection │255-166│
40. This condition is true. The Second condition is checked │155-166│ 20 and the second
condition is false. Hence the pixel is considered as noisy and median is considered as non noisy.
The corrupted pixel is replaced by median of sorted array ie., output =155.

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255
255
255
255
0
255
255
255
0
0
255
0
185
0
0
125
0
0
177
94
255
0
255
0
0
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255
255
255
255
0
255
255
255
0
0
255
155
185
0
0
125
0
0
177
94
255
0
255
0
0
Corrupted image segment Restored image segment
Case (b): Initialize forward counter F=1 and reverse counter L=9. Convert the 2D array into 1D
array and sort the converted array. When a 0 is detected F is incremented by 1 and when a 255 is
detected L is decremented by 1.
Unsorted array: 0 185 255 0 0 255 125 255 255
Sorted array Sxy 0 0 0 125 185 255 255 255
Here the median Smed value is 185. The case (2) is illustrated as follows. Now check for the
presence of 0 or 255 in the sorted array. Every time a 0 is detected F is incremented by 1 and if
255 is detected L is decremented by1. In the above example there is three 0 and three 255. Hence
F is incremented by three times and L is decremented by three times. Now finally F is holding 4
and L is holding 6. Now the variable DET is assigned with the median of the rank ordered
unsymmetrical trimmed output i.e. corrupted pixel is replaced by median (125,185) = 155. i.e.,
DET=155. Now perform first step detection │0-155│ 40. This condition is true. The Second
condition is checked │185-155│ 20 and the second condition is true. Hence the processed pixel
and the computed median is considered as noisy. Hence the corrupted pixel is replaced with
Unsymmetrical trimmed median ie 155 output=155.
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255
255
255
255
0
255
124
255
122
0
123
255
255
103
0
255
255
255
119
104
255
0
255
0
0
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255
255
255
255
0
255
124
255
122
0
123
255
255
103
0
255
255
255
119
104
255
0
255
0
0
Corrupted image Segment Restored image Segment
Case (3): Initialize F=1 and L=9. After sorting the current window in ascending order, the
counters propagate in the 1D array resulting in holding count=6, F=4 and L=6. DET will hold
median (103, 104, 119) ie, DET=104. Now perform impulse detection │119-104│ 40. This
condition is false and hence processed pixel is considered as non noisy hence left unaltered [13].

25
3.4 FPGA implementation of the proposed Algorithm
Figure 2 Proposed Sequential Architecture
The proposed algorithm is implemented for the FPGA device Xc3e5000-5fg900 using
VHDL The proposed sequential architecture consists of various snake like sorting, FSMD
scheduler, Decision maker unit as shown in figure 2.
3.4.1 Snake like sorting:
We propose a parallel architecture for the proposed algorithm which uses 3x3 spatial windows for
processing. The Proposed architecture is illustrated in figure 3. The Basic Processing element of
the proposed architecture uses a three cell sorter. The function of the three cell sorter is order the
data and produce outputs in maximum, middle and minimum values. The three pixel elements of
the first, second and third rows are sent inside the three parallel three cell sorter as part of
arranging first and third row in ascending and the second one is descending. This results in
minimum1, minimum2, minimum3, middle1, middle2, middle3, maximum1, maximum2,
maximum3. In the second phase minimum 1, maximum2 and minimum3 is fed to the first of
three cell sorters, middle1, middle2, middle3 is given to second three cell sorters. The
maximum1, minimum2 and maximum3 are fed to the third three cell sorter. This result in column
sorting thereby the sorted signals are given as minimum4, minimum4, minimum4 middle5,
middle5, middle5, maximum4, maximum5, maximum6. For the second row sorting
minimum4,5,6 is fed into first three cell sorter, middle 4,5,6,maximum 4,5,6 into second and third
level of three cell sorters respectively. The output signals of this stage are marked as minimum7,
minimum8, minimum9 middle7, middle8, middle9, maximum7, maximum8, maximum9. The
second column sorting is facilitated by minimum 7, maximum8 and minimum9 is fed to the first
of three cell sorters, middle7, middle8, middle9 is given to second three cell sorters. The
maximum7, minimum8 and maximum9 are fed to the third three cell sorter. The resultant signal
is denoted as minimum10, minimum11, minimum12 middle10, middle11, middle12,
maximum10, maximum11, maximum12. Now to facilitate the semi diagonal sorting
minimum11,median11,maximum11 are given to the first of last stage three cell sorters and
middle10,maximum10,maximum11is given to second of the last three cell sorter. The output is
marked as min1, min2, min3 and max1, max2, max3 from the last stage sorters respectively.

26
Minimum10 is the minimum value of the array, max1, 2, 3 refers to the second, third, fourth
minimum of an array. Middle 11 is marked as the median of the array. max1, 2, 3 gives the
maximum values after median in the array. Maximum 12 is maximum value of the array. The
order specifies the rank ordering of the array [14].
Figure 3: Parallel architecture for the proposed Snake like sorting algorithm
3.4.2 FSMD Scheduler Unit
The proposed FSMD scheduler unit consists of 8 states. The states are named as idle, Dat1, index,
Decision, Out_even, Out_odd, final process, output final. When the system reset is inactive the
control of the program is transferred to the next state called idle.
3.4.2.1 Idle State:
The counters such as F, L, (noise determination counter) and the sum accumulator is
initialized to zero and points to Dat1 as next state.
3.4.2.2 DAT1 State:
Every element of the 3X3 is checked for 0 or 255. If 0 is encountered counter F is incremented by
1. If 255 are encountered L is incremented by 1. The total number of noisy pixel in the array is
stored to a variable called t_noise. When the counters F and L reaches the maximum value as 9
the program control is transferred to next state called index.

27
Figure 4 FSMD Scheduler for evaluation of Unsymmetrical trimmed median filter
3.4.2.3 Index State:
In this state two conditions are checked. First, when all the elements of the 3x3 window are
combination of 0 or 255 then a Look up table is formulated such that if all the elements are 0 then
variable op is 0. If all the values are 255 then op is 255. If both the above condition is failed then
Look up table is loaded with 198,170,141,113,85,56,28 indicating the mean of the elements in an
array with 2 0’s, 3 0’s 4 0’s 5 0’s 6 0’s 7 0’s 8 0’s respectively (i.e., sum of all 255 divided by 9).
On the second case, when all the elements are not the combination of 0 or 255 then non zero
entries index is checked. This state gives the procedure to point index of the elements to find
unsymmetrical trimmed median, if it is odd or even depending upon the number of noisy pixel
within the given window. The logic is to prefix certain index in the form of look up table so that
for an example when no 0’s and three 255’s is present then the number of non noisy pixel is even
i.e. 6. Index for finding the median is fixed as 3 and 4. In the case of four 255’s, then the number
of non noisy pixel is odd i.e. 5. So the index is prefixed as 3. Similarly the index positions are
prefixed in look up table for all possible combination. Depending upon the number of noisy
pixels in the given window the values are accessed from the look up table. If the number of noisy
elements are even then the index are stored in even_u and even_v respectively. If the number of
noisy elements are odd then the index are stored in odd. After finding the index the next state is
pointed to Decision state.
3.4.2.4 Decision State
After obtaining the index from the index state the value corresponding to the index state is
obtained. Initially the number of noisy pixels is evaluated and based on the noisy pixel the
unsymmetrical trimmed median is obtained. If the number of non-noisy pixel is odd then sum is
obtained as (memory (even_u) +memory (even_v)). In case of odd number, the non noisy pixel is
even then unsymmetrical trimmed median is obtained as memory (odd). If the number of non
noisy pixel is odd then the next state is pointed as out_even. If the number of non noisy pixel is
even then the next state pointed as out_odd.

28
3.4.2.5 Out_even State
After finding the number of noisy pixel as even the control is transferred to out_even state. In this
state the unsymmetrical trimmed median is obtained by finding the mean of memory (even_u)
and memory (even_v) and points to the next state called final process.
3.4.2.6 Out_odd State
After finding the number of noisy pixel as odd the control is transferred to out_odd state. In this
state the unsymmetrical trimmed median is obtained by finding the oddth
element of the trimmed
array i.e. memory (odd) and points to the next state called final process.
3.4.2.7 Final Process State:
The centre pixel, Unsymmetrical trimmed median value and median of the sorted array is loaded
into this state for the final process. This stage is done to obtain synchronization between the
output variables. The next state is pointed as out_final.
3.4.2.8 Out_final State:
Here the decision to check the centre pixel is noisy as follows. If the absolute difference between
centre pixel and unsymmetrical trimmed median is greater than 40. If the condition is true then
the processed pixel is considered as noisy. Now check for the median is noisy or not by finding
the absolute difference between computed median and unsymmetrical trimmed median is greater
than 20 then the computed median is noisy. Hence the processed pixel is replaced with
unsymmetrical trimmed median else if the median is not noisy then replace the processed pixel
with median of the array. If the centre pixel is not noisy it is left unaltered.
Figure 5. Simulation results of the architecture of Proposed algorithm

29
TABLE I
PERFORMANCE OF VARIOUS ALGORITHMS AT DIFFERENT FIXED VALUED IMPULSE NOISE
DENSITIES FOR PSNR AND IEF IN LENA IMAGE
TABLE II
PERFORMANCE OF VARIOUS ALGORITHMS AT DIFFERENT RANDOM VALUED IMPULSE NOISE
DENSITIES FOR PSNR AND IEF IN BABOON IMAGE
TABLE III
PERFORMANCE OF VARIOUS ALGORITHMS AT DIFFERENT FIXED AND RANDOM VALUED
IMPULSE NOISE DENSITIES FOR MSE IN LENA AND BABOON IMAGE.

30
TABLE IV
PERFORMANCES OF VARIOUS ALGORITHMS AT DIFFERENT ZERO MEAN GAUSSIAN
NOISE DENSITIES FOR PSNR AND MSE IN BABOON IMAGE.
TABLE V
QUANTITATIVE PERFORMANCE OF VARIOUS EXISTING FILTERS CORRUPTED BY 70 % FIXED
VALUE IMPULSE NOISE FOR LENA IMAGE

31
TABLE VI
TABLE PERFORMANCE OF PROPOSED ALGORITHM ON VARIOUS IMAGES FOR MIXED NOISE (30%
FIXED VALUE IMPULSE NOISE PLUS ZERO VARIANCE 0.001 VARIANCE GAUSSIAN NOISE)
TABLE VII
COMPUTATION TIME OF DIFFERENT SORTING TECHNIQUES IMPLEMENTED IN MATLAB7 (R14)
PENTIUM DUAL CPU E2140 @1.6 GHZ OF 1 GB RAM
TABLE VIII
PERFORMANCE OF PROPOSED SNAKE LIKE SORTING ALGORITHM OVER CONVENTIONAL
ALGORITHMS TARGETED ON Xc3e5000-5fg900

32
TABLE IX
PERFORMANCE OF 3X3 WINDOW OF PROPOSED ALGORITHM TARGETED ON Xc3e5000-5fg900

33
Figure 6 Qualitative performance of Various algorithm For 70% Fixed value impulse noise a)
Corrupted image b) Smf(3x3) c)Smf(5x5) d)AMF e) CWF f)TDF g)Mean Det h) Med Det i)
RWCWMF j) PSMF k) DPF l) DBA m) CDMUTMF n) CUTMF o) CUMTPF p) MDBUTMF q)
PA

34
(a) (b) (c) (d) (e) (f) (g)
Figure 7. Performance of various filters for Baboon image corrupted by Random Valued Impulse
noise from 10% to 50% in row1 to 5 respectively. Output of various filters in column 1 to 8 (a)
Random valued impulse noise (b) output of SMF (c) output of AMF (d) output of Meandet (e)
output of Meddet (f) output of CUMTF (g) output of PA
(a) (b) (c) (d) (e) (f) (g)
Figure 8. Performances of various filters for Baboon image corrupted by Zero mean Gaussian
noise variance from 0.001 to 0.003 in row1 to 3 respectively. Output of various filters in column
1 to 7 (a) Random valued impulse noise (b) output of SMF (c) output of AMF (d) output of
Meandet (e) output of Meddet (f) output of CUMTF (g) output of PA

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(a) (b) (c) (d) (e) (f)
Figure 9. Performances of Proposed algorithm for various image corrupted by mixed noise (30%
impulse noise plus zero mean Gaussian noise variance of 0.001 in row1 to 3 respectively. (a d)
original image (b e) Mixed noise (c f) output of PA.
4. SIMULATION RESULTS DISCUSSIONS
The Quantitative performance of the proposed algorithm is evaluated based on Peak signal to
noise ratio (PSNR) ,Mean Square Error (MSE) and Image Enhancement Factor (IEF) which is
given in equations 4,5 ,6 respectively.
PSNR =
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MSE
2
10
255
log
10
(4)
MSE =
N
M
x
r ij
j
ij
i
×
−
∑
∑ 2
)
(
(5)
IEF =
2
2
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−
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−
∑
∑
∑
∑
j
ij
ij
i
ij
j
ij
i
r
x
r
n
(6)
Where r refers to Original image, n gives the corrupted image, x denotes restored image, M x N is
the size of Processed image [13]. The existing algorithms used for the comparison are SMF,
AMF, CWF, TDF, PSMF, DPF for comparing Fixed value impulse noise. To compare random

36
valued impulse noise and Gaussian noise, the algorithms such as SMF, AMF, MEANDET,
MEDDET is used. The qualitative performance of the proposed algorithm is tested on various
images such as Lena, Cameraman, Baboon, Barbara, girl, pepper etc (Images are chosen as per
the details of the image). Quantitative analysis is made by varying noise densities in steps of ten
from 10% to 90% for Random valued impulse noise (RVIN) and Fixed valued impulse noise
(FVIN). The same is done by varying variance of zero mean Gaussian noise in increment of
0.001. The proposed algorithm is also tried for 70% of Fixed valued impulse noise and mixed
noise on low detail, medium detail and high detail images. Comparisons were made in terms of
PSNR, IEF and MSE. Results and graphs are given in Table I-VI and figure 10-17 respectively.
Figure 6-9 gives the qualitative performance of the proposed algorithm in terms of noise
elimination for FVIN, RVIN, Zero mean Gaussian noise, and mixed noise. All the simulation is
done in dual CPU E2140@1.6Ghz with 1GB RAM capacity. Better results were obtained when
the pre-defined threshold T was between 20 and 40. And the second threshold T1 was between
15 and 30. From the Table I we infer that for the proposed algorithm has high PSNR and IEF,
indicating how much the algorithm eliminates salt and pepper noise effectively. Table II gives the
performance of random valued impulse noise of various algorithms. The proposed algorithm is
found to work well for low density RVIN noise. From Table III we find the mean square error is
minimum for proposed algorithm at high noise densities for both FVIN and RVIN. It is evident
from figure 6 that the qualitative aspect of the proposed algorithm at 70% FVIN is found to
perform good against conventional algorithms. The proposed algorithm performs on par with the
recently proposed decision based filters for Lena (low detail image). Table IV and V gives the
quantitative performance of zero mean Gaussian noise and 70% FVIN respectively. It is shown
that the proposed algorithm fairs good for all these noises. Figure 7 gives the performance of
various filters for the baboon image corrupted by RVIN from 10% to 50%. It was found that the
existing algorithm either blurs the image or fails to remove the noise. The proposed algorithm is
effective in removing RVIN for noises up to 30%. Many traditional algorithms do not perform
well for high noise densities. Hence none of the single level detector algorithm is able to detect
and correct the long tailed noise at high noise densities. From table IV and figure 8 we understand
that the proposed algorithm fairs well for zero mean Gaussian noise for increasing variance. Table
VI and Figure 9 illustrates the performance of proposed algorithm for mixed noise (30% impulse
noise and zero mean 0.001 variance of Gaussian noise). It is found to perform well in eliminating
mixed noise also. The value of the threshold is updated based on the number of corrupted pixels
inside the corrupted window. Table 7 gives the computation time of different sorting technique
implemented in Matlab 7 on Pentium dual cpu E2140 @1.6 GHz of 1 GB RAM and found to
perform on par with various sorting algorithms. Figure 10 to 17 illustrates the graphical
performance of the proposed algorithm. The results illustrates that the proposed algorithm has a
good PSNR,IEF for high density FVIN noise, optimum results for high density Random valued
impulse noise, good quantitative measure on zero mean Gaussian noise. The proposed algorithm
was targeted on Spartan 3e family XC3S5000-5fg900 FPGA. The code was developed using
VHDL. The simulator tools used was a third party tool Modelsim 5.8i and synthesis tool XST
was used as part of Xilinx 7.1i suit for CPLD FPGA development. Table 8 gives the device
utilization summary, timing specification and power report for the target FPGA for various
median finding algorithms such as bubble sort, heap sort, insertion sort, Selection sort, Threshold
decomposition Filter. Table 9 illustrates the performance of proposed algorithm for the targeted
device. Figure 5 gives the simulation output of the PA which is found to generate its first output
in 13 clock cycles.
5. CONCLUSION
All the algorithms were tested on a fixed 3x3 window. From the exhaustive experiments, we
conclude that the proposed algorithm has a high PSNR, low MSE and high IEF for different

37
images and for different noise type at higher noise densities. However, on an average sense, PA
gives good performance in eliminating FVIN up to 70%, RVIN up to 30%, zero mean 0.5%
variance Gaussian noise and a mixed noise (30% impulse noise plus zero mean 0.001 variance
Gaussian noise). When compared to Conventional filters such as SMF, AMF, CWF,
TDF,PSMF,DPF etc , the PA exhibits good performance for Salt Pepper noise removal up to
70% and reduces smaller proportion of zero mean 0.3% variance Gaussian noise. The proposed
filter also exhibits good noise removal up to 30% RVIN and 30% of mixed noise. The proposed
algorithm works on par with the recently proposed algorithms such as DBA, MDBUTMF,
CUTMF etc., in our method, time complexity of the existing methods is eliminated by using the
pixel intensity itself as threshold. Hence, the proposed method shows optimum performance with
fewer comparison complexities. The Proposed algorithm has good average computation time.
FPGA implementation of the proposed algorithm for 3x3 window is implemented and
performance in terms of area, speed and power is illustrated in table 8, 9 respectively. Table 8
gives the device utilization summary, timing and power specification for the target device
XC3S5000-5fg900 required by the snake like algorithm with the existing sorting algorithm. The
proposed snake like algorithm utilizes 709 slices, which is 60% less when compared to other
sorting algorithms. The snake like sorting also has a low combinational delay path of 77.30ns
with a reduced gate count and slices flip flop of 7281 and 517 respectively, which is 7 times less
when compared to existing algorithm. The last part of the table deals with power required by each
sorting algorithm on the FPGA. The proposed logic for the entire algorithm is implemented on
the FPGA and found to consume 1034 slices with an operating frequency of 79.93 MHz and a
gate count of 11945 with optimum power consumption of 298mw. It was found that the proposed
parallel snake like sorting logic requires very less area and time with optimum power
consumption when compared to the existing sorting techniques. The proposed algorithm exhibits
very good results in restoration of images corrupted by non identical noise both quantitatively and
qualitatively and occupies a low area, good operating frequency and optimum power architecture
is proposed.
Figure 10. PSNR of various algorithms for Lena image corrupted by 70% FVIN

38
Figure 11. IEF of various algorithms for Lena image corrupted by 70% FVIN
Figure 12. PSNR of various algorithms for BABOON image corrupted by RVIN
Figure 13. IEF of various algorithms for BABOON image corrupted by RVIN

39
Figure 14. MSE of various algorithms for BABOON image corrupted by RVIN
Figure 15. PSNR of various algorithms for BABOON image corrupted by Zero mean Gaussian
noise
Figure 16. MSE of various algorithms for BABOON image corrupted by Zero mean Gaussian
noise

40
Figure 17. PSNR, IEF, MSE of various algorithms for images corrupted by Mixed noise
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2012

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