Circuits and Systems, 2016, 7, 692-700
Published Online May 2016 in SciRes.
How to cite this paper: Amudha, J. and Sudhakar, R. (2016) Efficient Global Threshold Vector Outlyingness Ratio Filter for
the Removal of Random Valued Impulse Noise. Circuits and Systems, 7, 692-700.
Efficient Global Threshold Vector
Outlyingness Ratio Filter for the Removal
of Random Valued Impulse Noise
J. Amudha1*, R. Sudhakar2
1Department of Electrical and Electronics Engineering, Dr. Mahalingam College of Engineering and Technology,
Pollachi, India
2Department of Electronics and Communication Engineering, Dr. Mahalingam College of Engineering and
Technology, Pollachi, India
Received 9 March 2016; accepted 7 May 2016; published 11 May 2016
Copyright © 2016 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativ ecommon icenses/by /4.0/
This research paper proposes a filter to remove Random Valued Impulse Noise (RVIN) based on
Global Threshold Vector Outlyingness Ratio (GTVOR) that is applicable for real time image
processing. This filter works with the algorithm that breaks the images into various decomposi-
tion levels using Discrete Wavelet Transform ( DWT) and searches for the noisy pixels using the
outlyingness of the pixel. This algorithm has the capability of differentiating high frequency pixels
and the “noisy pixel” using the threshold as well as window adjustments. The damage and the loss
of information are p reven ted by means of interior mining. This global threshold based algorithm
uses different thresholds for different quadrants of DWT and thus helps in recovery of noisy image
even if it is 90% affected. Experimental results exhibit that this method outperforms other exist-
ing methods for accurate noise detection and removal, at the same time chain of connectivity is
not lost.
Image Resto ra ti on, Noise Detection, Noise Removal, Random Valued Impulse Noise,
Global Threshold Vector Outlyingness Ra tio
1. Introduction
Images are often corrupted by impulse noise because of sensors or channel transmission [1]. Impulse noise is
Corresponding author.
J. Amudha, R. Sudhakar
classified as fixed value impulse noise and random valued impulse noise. Generally the impulsive noise such as
salt and pepper noise has the nature of producing the highest p ixel val ue (25 5) and the lowe st pixel value ( zero)
in an eight bit image. This nature provid es the filtering algorithm to po int out possibilit ie s of the noise a nd has to
spend only li mited co mputation p ower to ident ify exact noise freep ixels. The problem in real time images is
that the salt and pepper noise may not occur in the form as mentioned above. Instead of pixel value 255 there
may be the val ue of 25 0, which is still a sa lt noise. I nstead of pixe l value 0 t here ma y be value 1 0, which i s still
a pepper noise. The existing algorithms will find difficulties in processing and removing this noise when the
above mentioned change occurred in an image.
In Gaussian filter [2], the Euclidean distance between the current pixel and its neighborhood is calculated. In
median filter, each pixel is replaced by the median value in its neighborhood, and thus destroys the significant
info rmatio n in the i mage. T o overc ome this, weighted -based median filters [3] are proposed. However, like me-
dian filter, the dra wback of weigh ted-based median filters [4] is that they replace each pixel with weighted me-
dian value in its neighborhood regardless of “noisy” or “noise free” pixel. The switching-based median filters
have been proposed to detect “noisy” pixels replaced by median value, whereas the “noise free” pixels are left
uncha nged, for exa mple, Ada ptive Switching Media n Filter (ASMF) [5]. However, these filters use median val-
ues or their variations to recover the “noisy” pixels, but they introduce blur in the image details [6].
To overcome this problem, edge-preserving regularization filters are introduced by employing two-stages. In
the first stage, the “noisy” pixels are identified by a noise detector. In the second stage, the “noisy” pixels are
recovered by an edge preserving regularization term without affecting the edges and “noise free” pixels which
have to be preserved. Papers [7]-[11] show that the noise removing capability depends on the accuracy of the
noise detector in these two stage methods. To this end, this paper will employ a better noise detector for two-
stage method. Local outlier-based impulse noise detectors are proposed in papers [12] recently. Local Outlier
Factor (LOF) and Robust Outlyingness Ratio (ROR) are employed to identify the fixed-valued impulse noise
and to measure the outlyingness of each and every pixel in the image respectively. Nor mall y ROR ha s the cap a-
bility of giving the outlyingness, but it always finds the outlyingness with fixed threshold [13] [ 14 ]. A global
threshold is used to find the outlyingness based on selecting better threshold for the data given. In this paper a
single algorithm is proposed using Global Threshold Vector Outlyingness Ratio (GTVOR) to detect the noise as
well as to remove the no ise. This technique uses the impulse-free information to r ecover the image.
2. Noise Detection and Removal
2.1. Noise Model
In fixed value impulse noise, “noisy” pixels take either minimum or maximum values i.e., ηF(i, j) є {Nmin,
Nmax}where Nmin = 0 and Nmax = 255, whereas Random Variable impulse noise,(RVIN) “noisy” pixels take any
value within the minimum range to maximum range i.e., ηV(i, j) є [Nmin, Nmax] ,where Nmin=[0, l], and Nmax =
[255 l, 255} denote the minimum range and maximum range. Consequently, removal of variable type impulse
noise is not easy compared to the removal of fixed value impulse noise. Let us consider the random valued im-
pulse noise model,
[ ]
[ ]
( )
( )
, max
,with probability
,with probability
,with probabiliy1
uN q
o pq
p is the probab ility o f noise whose values fall i n the range of [0, l],
q is the p robabili ty of noise whose values fa ll in the ra nge of [(255 l), 255],
noise probability r = p + q and p = q,
ox,y and ux,y is the current pixel value of original and noisy image at coordinate (x, y).
2.2. Proposed Method
( )
{ }
,,,1, 2,,ooxyxyM==
denote M × M original image to be recovered, M is integer power of 2.
J. Amudha, R. Sudhakar
RVIN is introduced during the signal acquisition stage the original image I gets corrupted. The noisy observa-
( )( )( )
,, ,uxy oxynxy
= +
is obtained. To recover o(x, y) from u(x, y) is our aim, such that the Mean
square Error (MSE) is less. DWT of u is matrix of wavele t c oefficie nts with 4 s ub band s ( LL, LH, HL, HH).The
sub bands LH, HL and HH are detailed coefficients and LL represents approximation coefficients. We can per-
form DWT of approximation sub band multiple times until the final approximation band contains only single
value. De note the ma ximu m number of deco mpositions by J. T he size of the sub band at scale k is M/2k × M/2k.
Figure 1 represents two level decomposition of an image.
Figure 2 depicts the process carried out in removing the noise and recovering the de-noised image from the
nois y ima ge.
Discrete Wavelet Transform is applied for the noisy image under consideration. The decomposition level can
be increased depending upon the noise level. DWT can slice the frequencies available in the image and able to
give them as spatial co-ordinates for processing. The coefficient of LL, LH, HL, HH are let in to further
processing. Separate the wavelet coefficients into Small Blocks with (2N + 1) × (2N + 1) window (for N = 1, 3 ×
3) for the all four Coefficients i. e . LL, LH, HL, HH. Let the 3 × 3 window of wavelet coefficient be
, For this data X compute GTVOR by computing the Median(MED),
Median Absolute Difference(MAD),and Global Threshold Interior Mining (GTIM) factor using the Equations
(2)-(6). Global Threshold (GT) is computed using the algorithm.
( )
MEDMedian X=
( )
MADMedianbsolute XMEDA
= −
3pass 1
GTIM 10 10
Figure 1 . Two-dimensional DWT with level-2 decomposition of an image.
Figure 2 . Prop os ed me thod over vie w.
J. Amudha, R. Sudhakar
[ ]
. The sign of each and every ratio should
be noted and floored. For example if GX3 is greate r than T h (Thr eshold), then the c orresp onding co efficie nt X3
will be suspected as noisy. The corresponding noisy pixel is rep laced by the average of th e noise free nei ghbors .
This is done in spatial image. Hence we need not to use inverse transform. If the noisy pixel is not detected in
this pass, the pass is incremented for further noise mining process. The iterative process of this filtering is done
to r emove the noise u ntil the GT VOR detec ts no outlyingness. Thus the noise free image is recovered. Figure 3
will provide the clarity in recovering the de-nois ed i mage in steps.
Algorithm to compute GT
Figure 3 . Flowchart.
J. Amudha, R. Sudhakar
3. Simulation Results
Standard test images of size 512 × 512 such a s Livi ng Ro om I mage , Bo at i mage, Le na I mage a nd G or illa i mage
are taken from data set USC-SIPI Image Database. GTVOR algorithm is evaluated and compared with many
other existing filters. For performance comparison, the Wiener filter, Median filter, Noise Adaptive Switched
Median filter and Proposed GTVOR filter have been simulated by programming models and the results were
tabulated in Table 1 for 80% of random valued impulse noise. The image outputs produced by various filters
were compared with proposed GTVOR filter with 70% noise was presented in Figure 4.
Figure 4. (a) Noise-free test images of size 512 × 512; (b) 70% noisy images; (c) Restored images by
Wiener Filter; (d) Restored images by Median Filter; (e) Restored images by Adaptive Switched Median
Filter; (f) Restored images by proposed GTVOR Filter.
J. Amudha, R. Sudhakar
Table 1. Results in MSE, PSNR and SNR after filtering images corrupted by 80% Random valued impulse noise.
of Im age Image Quality
Parameter s 80%
Noisy ima ge Wiener Filter Median Filter ASMF Proposed
GTVOR Fil te r
Livin g Room
MSE 14,616.90 1997.87 9862.97 9898.38 256.58
PSNR 6.48 15.13 8.19 8.18 24.04
SNR 0.64 2.30 2.26 2.22 6.78
Boat Image
MSE 14,746.87 2082.65 9937.45 9976.38 238.32
PSNR 6.44 14.94 8.16 8.14 24.36
SNR 1.42 3.69 3.02 2.99 8.04
Lena Image
MSE 14,860.85 2138.40 9995.45 10,077.53 124 .69
PSNR 6.41 14.83 8.13 8.10 27.17
SNR 0.93 2.13 2.45 2.33 8.98
Gorilla Image
MSE 14,423.72 1906.30 9901.85 9943.86 589.32
PSNR 6.54 15.33 8.17 8.16 20.43
SNR 0.40 2.23 1.72 1.68 4.53
Through this comparison it is clear that the proposed GTVOR filter is the best among these. The reason be-
hind is the existing filters has no capability of differentiating “noisy” pixel among the group, and blindly process
all the pixels. Existing filters were explor ed fully on the spatial do main of the image and implemented id entical-
ly across the image, they tend to modify irrespective of noisy and noise free pixels and removes desirable details,
Our proposed algorithm break the images into various decomposition level and searches for the anomaly/odd
pixels by which the capability of noise detector is accurate than existing algorithms. Certa in algorithms such as
median filter has the capability of selecting the window to process, but the capability of adjusting the high fre-
quenc y noi se b y using its o wn t hresho ld val ue is not ha ndle d in t he swit ching seque nce. The se algorith ms were
flexible onl y up to cer tain limit to use mean, median and mod e operations. T he ability to differe ntiate high fre-
quency pixels and the “noisy pixels” using the thresholds is the best highlight of the proposed technique. The
damage and the loss of information is prevented by means of interior mining capability of this algorithm. The
inner mining will be more effective with bonded type noise since the proposed algorithm uses global threshold
for each window in process, which makes the algorithm adaptive to any image irrespective of nature of input.
The proposed GTVOR filter is tested for 512 × 512 Livin g roo m image . T he pe rfor mance of the prop ose d fil-
ter is tested for all levels of noise densities. Each time the test image is corrupted by random valued impulse
noise of different density ranging from 10% to 90% with an increment of 10% and tested for removal of noise
capabilit y. The performance at various noise den sities for living roo m image is shown in Table 2 and plotted in
Figure 5 and F igure 6.
From Figure 5 and Figure 6, it is clear that Median filter and Adaptive Median filters perform better than
Wie ner fi lt er whe n t he no ise l eve l i s l es s t han 40% and 50% respectively. But at high noise densities the median
of wind ow its elf ha ve the effec t of nois e resu lting i n poo r qualit y in rest ori ng ima ges. As Wiener filter have the
behavior of Linear time invariant that estimates the spatial intensity values of the 2D signal through which the
filtering or smoothening was done. At high noise levels the estimation values will also have the effect of noise
and hence restoration is poor. As the proposed filter has the capability of computing various thresholds in dif-
ferent quadrants, noise detection is more accurate than all other existing filters. Comparison of histograms for 70%
nois y “L iving Ro om Image” re stored by differe nt filter s is s ho wn in Figure 7. The r esul ts ar e pr o mine nt a nd t he
reconstruction quality is better even at higher level of noise densities.
4. Conclusions
This paper proposes a new filter, named Global Threshold Vector Outlyingness Ratio (GTVOR) Filter that
J. Amudha, R. Sudhakar
Figure 5 . MSE values for different filters operating on the image “Living Room” at various noise densities.
Figure 6 . PSNR values for different filters operating on the image “Living Room” at various nois e densi ties.
Table 2. PSNR in dB for different filters operating on the image “Living Room” at various noise densities .
Noise Density % Nois y Im a ge Weiner Filter Median Filter ASMF Proposed GTVOR Filter
10 12.54696 2 0. 45823 26.546 39 29.30889 31. 529 68
20 12.49474 2 0. 43171 26.477 96 29.15956 31. 478 64
30 10.74031 1 9. 27955 22.481 93 26.56197 29. 629 9
40 9.455607 1 8. 25742 18.418 2 23.42616 28. 279 6
50 8.524303 1 7. 45805 15.109 65 20.04897 27. 208 09
60 7.737345 1 6. 63694 12.328 69 12.318 2 6. 28682
70 7.071953 1 5. 9051 10.069 75 10.05166 25. 223 92
80 6.482251 1 5. 12513 8.1907 25 8.175163 24. 038 64
90 5.980825 1 4. 51399 6.7158 13 6.70808 21.56399
works in two stages namely detecting stage and filtering stage to recover highly-corrupted images effectively,
which can be used for many real-time image processing applications. The proposed GTVOR filter is capable of
suppr essing i mpulse noise e ven at high level of noise density (90%), especially, without affecting the edges and
textures. Extensive experimental results depict that the proposed GTVOR filter outperforms consistently com-
pared with other filters. Co mpa ring with the others existing filters, o ur filter has better ima ge r e storing cap a bility
with precise noise detection.
% Noise Density
Noisy Image
Wiener Filter
Median Filter
Adaptive Swit ched
Median Filter
Proposed G TVOR Filter
% Noise Density
Noisy Image
Wiener Filter
Median Filter
Adaptive Switched
Median Filter
Proposed G TVOR Filter
J. Amudha, R. Sudhakar
(a) (b )
(c) (d)
(e) (f)
Figure 7. Comparison of histograms for 70% noisy “living room image” restored by different filters. (a) Noise free living
room image; (b) 70% noisy image; (c) Wiener filter output; (d) Median filter output; (e) Adaptive switching median filter
output; (f) Proposed GTVOR filter output.
According to the current research the GTVOR filter perfectly wo rk s with 8 bit images, which is used for gen-
eral purp ose applic ations. T his filter has so me limitatio ns w hile worki ng with medical im ages. T he medical field
has the intensive requirement for image restoration and denoising, since the medical images such as DICOM,
multispectral images may involve such noise. But these images are 16 bit and the combination of pixels varies
from 0 to 65535 (65536 pixel values). Therefore it is a real challenge at window decomposition of the image and
in computing the outlyingness. Also the information constrained with the global threshold value varies with
large interval which should be addressed in the future.
J. Amudha, R. Sudhakar
[1] Gonzalez, R.C. and Woods, R.E. (2002) Di gi tal Image Process ing. Prentice-Hall, Englewood Cliffs.
[2] Wang, Z. and Zhang, D. (1999) Progressive Switching Median Filter for the Removal of Impulse Noise from Highly
Corrupted Images. IEEE Transactions on Circuits and SystemsII: Analog and Digital Signal Processing, 46, 78-80.
[3] Brownrigg, D.R.K. (1984) The Weighted Median Filter. Communications of the ACM, 27, 807-818.
[4] Ko, S.J. and Lee, S.J. (1991) Center weighted Median Filters and Their Applications to Image Enhancement. IEEE
Transactions on Circuits and Systems, 38, 984-993.
[5] Akkoul.S, Ledee, R., Leconge, R. and Harba, R. (2010) A New Adaptive Switching Median Filter. IEEE Signal
Processi ng Lett er s, 17,587-590.
[6] Nikolova, M. (2004) Avariational Approach to Remove Outl iers and Impulse Noise. Journal of Mathematical Imaging
and Vision, 20, 99-120.
[7] Chan, R.H., Hu, C. and Nikolova, M. (2004) An Iterative Procedure for Removing Random-Valued Impulse Noise.
IEEE Signal Process ing Letters , 11, 921-924.
[8] Dong, Y., Chan, R.H. and Xu, S. (2007) A Detection Statistic for Random Valued Impulse Noise. IEEE Transactions
on Ima ge Processing, 16, 1112-1120.
[9] Chan, R.H., Ho, C.W. and Nikolova, M. (2005) Salt-and-Pepper Noise Removal b y Median-Type Noise Det ectors a nd
Detail Preserving Regularization. IEEE Trans ac tions on Im age Pr oce s s ing, 14, 1 479-1485.
[10] Huang, Y., Ng, M.K. and Wen, Y. (2009) Fast Image Restoration Methods for Impulse and Gaussian Noise Removal.
IEEE Signal Pr oc e s s ing Letters, 16, 457-460.
[11] Allard, W.K. (2008) Total Variation Regularization for Image Denoising. SIAM Journal on Imaging Sciences, 1,
[12] Wang, W. and Lu, P. (2011) An Efficient Switching Median Filter Based on Local Outlier Factor. IEEE Signal
Processi ng Lett er s, 18, 551-554.
[13] X iong, B. and Yin, Z. (2012 ) A Universal Den oising Framework with A New Impulse Detector and Nonlocal M eans.
IEEE Tra ns ac t i ons on Image P r o c e s s i ng, 21, 1663-1675.
[14] Breuig, M.M. (2000) LOF: Identifying Density-Based Local Outliers. Proceedings of the ACM SIGMOD Conference
on Management of Data, Dallas, 15-18 May 2000, 93-104.