 Open Access
 Total Downloads : 316
 Authors : Manvi, R. Swaminathan, Asif Iqbal
 Paper ID : IJERTV2IS60774
 Volume & Issue : Volume 02, Issue 06 (June 2013)
 Published (First Online): 20062013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Comparison of Noise Removal Technique for Image Enhancement
Manvi 
R. Swaminathan 
Asif Iqbal M.tech(E.C.E) 
MTech (Comm Engg) 
Assistant Professor (ECE) 
Research Engg. In Signal 
Galgotias University 
Galgotias University 
Processing & Image processing 
Abstract
An image enhancement scheme is presented by using cascaded blocks of nonlinear filtering and comparing it with the output presented by discrete wavelet transform and nonlinear filtering. In nonlinear filtering, the cascaded blocks performs smoothing and sharpening whose behaviour is finely controlled by a set of parameters. Smooth approximation of piecewise linear filter is done to obtain smoothing parameter. The smoothing parameter smoothens out the Gaussian noise present in any image. In the other technique, discrete wavelet transform (DWT) is used with piecewise linear filter. DWT decomposes the image into four subbands. The lower subband is smoothed and the higher subbands are sharpened by using non linear piecewise filter while removing noise. The experimental result shows the comparison of two techniques and gives an efficient noise removal technique.
Keywords: Gaussian noise, image enhancement, non linear filters, Discrete Wavelet Transform.

Introduction
Image enhancement plays very important role in image processing. Visual effects can be improved by enhancing some information and restraining other. The quality of image is mainly affected by the presence of noise in it. Many linear filtering approaches were used to remove noise but it resulted in the blurring of output image. To overcome the drawback of linear filters, non linear filtering approach is considered, as nonlinear models can effectively combine noise reduction and edge enhancement. If the sharpening is increased it results in increasing the noise, it (noise) can be limited during the sharpening process. Better results can be produced by nonlinear approaches, because they can realize a more satisfactory compromise between edge
enhancement and noise cancellation. A class of method which do not follow classical unsharp masking approach are the piecewise linear filters. Advantage of using this filter is easy control of sharpening and smoothing. Another technique for image enhancement is by using discrete wavelet transform and nonlinear piecewise filters. By using discrete wavelet transform image resolution enhancement technique was proposed by Demiral and Anbarjafari [1,2]. A satellite image enhancement based on the discrete wavelet transform (DWT) and singular value decomposition (SVD) was presented by Demirel [3]. Discrete wavelet transform decomposes the image in to four subbands. DWT helps in edge detection process.
In this paper, comparison of both the techniques is presented to obtain the efficient method for noise removal and image enhancement. Behaviour of non linear filters is analyzed with respect to the noise present in image.
This paper is organized as follows: section 2 gives the description about combination of DWT and Filtering method, section 3 gives the description about Non linear Filtering Method used for image enhancement, section 4 gives comparison of results of both the methods, section 5 is about the numerical comparison. Section 6 Concludes the paper.

Description about Discrete Wavelet Transform and nonlinear filtering Method.
The flow chart of this technique is shown in figure 1. The input image is decomposed by using Haar discrete wavelet transform into four subbands, as the decomposition is of 1 level. The four subbands are as follows : LowLow (LL), High Low (HL), LowHigh (LH), HighHigh (HH). The smoothing of lower frequency subband results in noise removal, it is achieved by smooth approximation of piecewise linear filter. The input images used in this paper are gray scale
images in which each pixel carries only intensity information. The value of gray level lies form 0 to 255. Where the lowest pixel indicates black and the highest pixel indicates white, this is known as gray scale of any image. The size of image considered is of 256×256.
Discrete Wavelet Transform
Input Image
Discrete Wavelet Transform
Input Image
High High (HH)
High High (HH)
High Low (HL)
High Low (HL)
Low Low (LL)
Low Low (LL)
Low High (LH)
PWL
Sharpening
Inverse DWT
PWL
Sharpening
Inverse DWT
LowLow (LL)
HighLow (HL)
LowHigh (LH)
HighHigh (HH)
Figure 2. Subbands
B. PWL Filtering
This is a class of nonlinear filters. In mathematics, a piecewise linear function is a function composed of straightline sections. It is a piecewisedefined function whose pieces are affine functions.
If the function is continuous, the graph will be a polygonal curve.
The function defined by:
3 3
Smooth approx. of PWL
filtering
Smooth approx. of PWL
filtering
=
=
+ 3 3 < < 0
Enhanced Image
Enhanced Image
2 + 3 0 < 3
6 3
(1)
Figure 1. Block diagram of Discrete Wavelet Transform Followed by nonlinear filtering.
A. Wavelet Transform
Wavelets transform is an efficient tool to represent an image. It allows multi resolution analysis of an image. The aim of this transform is to extract relevant information from an image. Wavelet transform has received considerable attention in the field of image processing due to its ability in adapting to human visual characteristics. It divides the signal into number of segments, each corresponds to a different frequency band. Wavelet transform provides a time frequency representation of the signal. Wavelets have been used for feature extraction, denoising, compression, face recognition and image resolution enhancement. Due to intrinsic deformation and extrinsic factors there is change in frequency of the pixels. Frequency components are isolated by using wavelet transform into certain subbands. Figure 2 shows the subbands obtained.
This block performs the smooth approximation of low frequency subband by using piecewise linear filter. This processing deals with four different pixels subsets as follows: W1, W2, W3, W4. The four different subset obtained is as follows:
i,j
i,j
i,j
i,j
W1 W2
i,j
i,j
i,j
i,j
W3 W4
Figure 3.Four Subsets of pixels
The four different subsets of pixels are defined as: W1={xi2,j,xi1,j,xi+1,j,xi+2,j} (i)
W2={xi,j2,xi,j1,xi,j+1,xi,j+2} (ii)
W3={xi2,j2,xi1,j1,xi+1,j+1,xi+2,j+2} (iii)
W4={xi+2,j2,xi+1,j1,xi1,j+1,xi2,j+2} (iv)
This blocks performs filtering while preserving thin lines in image.
The output yi,j is given by the relation:

Description about NonLinear Filtering Method.
The flow chart of this particular technique is shown in figure 4. The input image is filtered by two kind of PWL smoothers and the output of directional smoother 2 is sharpened by PWL sharpener. According to the intensity of Gaussian noise the amount of smoothing
, =
,
+ 1
,
( , , , , 1, 1, 1)
(2)
and sharpening are chosen. Input image chosen is a gray scale image of size 256×256, i.e. having L gray
Noise estimation
Noise estimation
Parameter assignment
Parameter assignment
4
4
Where (u,v,a,b,c) is a threeparameter sevensegment PWL function is shown in figure 5(a) and the set Wp is such that the following quantity is minimized.
levels where L=256. Let xi,j be the pixel luminance at location [i,j]. The image pixels luminance varies from (0<= xi,j <= L1).
,
( , , , , 1, 1, 1) (3)
where k= 1,2,3,4.
Input image
Input image
PWL
Smoother 1
PWL
Smoother 1
PWL
Smoother 2
PWL
Smoother 2
To further reduce the noise another pixel subset is selected by resorting to maximum operator:
, =
,
+ 1
,
( , , , , 2, 2, 2)
(4)
PWL
Sharpener
PWL
Sharpener
4
4
, ( , , , , 2, 2, 2) (5) where k= 1,2,3,4
For performing sharpening of higher subband by using
PWL sharpening filter, one pixel subset is chosen such
Enhanced image
Enhanced image
that:
W5= { xi1,j1
xi+1,j+1 }
, xi1,j , xi1,j+1
W5
i,j
i,j
, xi,j1 , xi,j+1 , xi+1,j1
, xi+1,j ,
(v)
Fig. 4 Block diagram of NonLinear Filtering using Piecewise Linear Filter

PWL Directional Smoother 1
This block in particular performs noise smoothing based on the directional filter, which aims at preserving thin lines in the image. The processing deals with four
The output yi,j of sharpener is defines as:
different subsets of pixels:
, =
,
+ 1
,
5
( , , , , , , , )
(5)
W1= { xi2,j , xi1,j , xi+1,j , xi+2,j } (vi)
W2= { xi,j2 , xi,j1 , xi,j+1 , xi,j+2 } (vii)
8
8
Where (u,v,d,e,f,g) is the four parameter three segment PWL function as shown in figure 5(b).
After applying the above mentioned technique Inverse Discrete Wavelet Transform (IDWT) is applied on the output of the smooth approximation and sharpening to obtain enhanced output.
W3= { xi2,j2 , xi1,j1 , xi+1,j+1 , xi+2,j+2 } (viii)
W4= { xi+2,j2 , xi+1,j1 , xi1,j+1 , xi2,j+2 } (ix) The output yi,j is given by the relation:
, =
,
+ 1
,
( , , , , 1, 1, 1)
(6)
This block further performs the smoothing by resorting to the maximum operator. This block further aims at
4
4
Where (u,v,a,b,c) is a threeparameter sevensegment
noise removal. The output of this filter is given by:
PWL function is shown in figure and the set Wp is such
+ 1 (
,
, 2, 2, 2)
(8)
that the following quantity is minimized.
, = ,
4 ,
,
,
, ( , , , , 1, 1, 1) (7) where k= 1,2,3,4
One pixel subset is selected and the filtering is performed by using PWL type 1 smoother. This operation is performed by resorting to minimum operator. This block preserves thin lines, and it performs well in the uniform regions. It reduces noisy pixels having large amplitude corresponding to the Gaussian noise present. The behaviour of this type of filter is of main consideration as during the sharpening process amplification of such pixels intensity can cause annoying sharpening which is considered as noise. To avoid such condition smoothing is done as a pre processing step for image enhancement using non linear filter.
For performing piecewise linear filtering the luminance difference between the central pixel and neighbouring
, ( , , , , 2, 2, 2) (9) where k= 1,2,3,4
This filter is used with PWL directional smoother1 in cascaded form so as to give more efficient output. The output of this filter which is smoothed and is of less noise content is sharpened with the help of PWL sharpener.
C. PWL Sharpening
This block performs sharpening of the image output of cascaded smoothers. A subset of pixels is considered as follows:
W5= { xi1,j1 , xi1,j , xi1,j+1 , xi,j1 , xi,j+1 , xi+1,j1 , xi+1,j , xi+1,j+1 } (x)
The output yi,j of the sharpener is as follows:
pixels is taken into account. In this approach, small
+ 1 (
,
, , , , )
(10)
differences (uv <= a) are interpreted as noise which is smoothed out using this filtering mechanism. The
, = , 8 , 5 ,
,
output is the arithmetic mean of the luminance values, according to the function . For large luminance difference between the pixels (uv >= a), it dente object contours. If the values obtained are very different from the central element pixel value, then smoothing is not applicable to them and so the image obtained is not blurred. In this paper, a trapezoid shaped function is considered to achieve transition for luminance differences varying from medium value (a<=uv<ba) to large(ba<=uv<ca). Three parameters a, b and c give flexibility in choosing the useful information in defining filtering action. Through this it can be decide how much luminance difference should be considered as useful information or unwanted noise by appropriately choosing these parameters. It aims at noise cancellation and detail preservation for a given noise variance. Parameter a is the most important of all as the length of whole function depends on it. The choice of parameter b and c is less critical. The value of a is chosen according to the noise variance.
B. PWL Directional Smoother 2
Where (u,v,d,e,f,g) is the four parameter three segment PWL function.
Sharpening is used to highlight edges in any image, it is quite opposite of smoothing [4],[5]. If <= 0 when u v>= 0 and >= 0 when uv< 0. effective sharpening results are obtained. function aims at better controlling of sharpening. Function states that if the luminance difference is small (uv<d), no sharpening is performed the function is flat in order to avoid noise increase. When the luminance differences are not small (uv>=d), sharpening of image starts. For medium differences (d<uv<=e), the output gives stronger sharpening in order to highlight image details. But if the differences are very large (e<uv<=g) the sharpening again gets reduced as to avoid annoying sharpening which is considered as noise. By choosing a set of parameters {d, e, f, g, L}the effect of sharpening can be obtained. Where m1= f /(ed) and m2= (L1 f)/(ge) denote the slope of the function.
After applying the above mentioned technique the output image obtained is more sharpened and noise level is comparatively smoothened.
a
ca ba a
a ba ca uv
a
(a)
L1
f
d e g
(b) (d)
Fig. 6 (a) input image with no noise

input image with less noise

output enhanced image

output enhanced image
Based on Discrete Wavelet Transform, the input image corrupted with internal noise and external Gaussian noise is considered as above. The input images are
g e d uv
f
L+1
(b)
Fig. 5. Parameterized PWL functions
(a) Function . (b) Function .



Experimental Observation
Based on Piecewise linear filtering, the input image when there is no external added noise present and when corrupted with less amount of Gaussian noise is presented in (a) and (b) respectively. The output image is depicted in (c) and (d) after applying the nonlinear filtering in fig 6.
(a) (c)
shown in (e) and (f) respectively and output is shown in

and (h) respectively.

(g)

(h)

Fig. 7 (e) input image with no noise

input image with less noise

output image

output image


Result Analysis
A number of quantitative measuring parameters can be used to evaluate the performance of the various types of filters in terms of restoring damage signals quality and quantity after filtering out impulse noise (salt and pepper). The following measuring parameters are used:

Mean Square Error (MSE)

Peak SignaltoNoise Ratio
Mean square error of two separate images is computed for various types of filters. The MSE is the cumulative squared error between the noisy image and the filtered image. The mathematical formula for the MSE is:
1 1
Table 1 PSNR and MSE
= 1
[ , (, )]2
Technique used
PSNR
MSE
Using Nonlinear filtering(for noise present internally)
36.831
21.68
Using Nonlinear filtering(for noise present externally)
35.172
23.13
Using DWT and nonlinear filtering.(for noise present internally)
27.46
116.4241
Using DWT and nonlinear filtering.(for noise added to the image)
27.18
124.2661
Technique used
PSNR
MSE
Using Nonlinear filtering(for noise present internally)
36.831
21.68
Using Nonlinear filtering(for noise present externally)
35.172
23.13
Using DWT and nonlinear filtering.(for noise present internally)
27.46
116.4241
Using DWT and nonlinear filtering.(for noise added to the image)
27.18
124.2661
=0 =0
Where, M and N are the total number of pixels in the column and row of the image respectively. f denotes the noisy image and denotes the filtered image.
The peak signaltonoise ratio is one of the best known techniques for assessing the amount of noise that an image is polluted with and, for that matter, the amount of noise left in a filtered image. The peak signalto noise criterion is adopted to measure the performance of various digital filtering techniques quantitatively. It is the measure of the peak error:
2552
= 10 10
A lower value for MSE means lesser error, and as seen from the inverse relation between the MSE and PSNR, this translates to a high value of PSNR. Logically, a higher value of PSNR is good because it means that the ratio of Signal to Noise is higher. Here, the 'signal' is the original image, and the 'noise' is the error in reconstruction or restoration. So, if you find a filtering or compression scheme having a lower MSE and a high PSNR, you can recognize that it is a better one.
Table 1 shows the quantitative result of peak signal to noise ratio values and mean square error values.


Conclusion
By comparing nonlinear filtering technique and noise removal filtering( based on discrete wavelet transform), it is concluded that the nonlinear filtering technique using PWL filter is more efficient and appropriate.

References

H. Demirel and G. Anbarjafari, Image Resolution Enhancement by Using Discrete and Stationary Wavelet Decomposition, IEEE Trans. on Image Processing, Vol.20, May2011,No. 4, pp 14581460 .

H.Demirel and G.Anbarjafari, Discrete Wavelet TransformBased Satellite Image Resolution Enhancement, IEEE Trans. on Geoscience and Remote Sensing,Vol.49 Jun 2011,No. 6, 1997 2000.

H.Demirel , C.Ozcinar, and G. Anbarjafari, Satellite Image Contrast Enhancement Using Discrete Wavelet Transform and Singular Value Decomposition, IEEE Trans. On Geoscience and Remote Sensing Letters, vol.70, April 2010 ,No. 2, pp 333337.

F. Russo, Design of piecewise linear sharpeners, in Proc. IEEE Int.Workshop IST, Niagara Falls, ON, Canada, May 13, 2005, pp. 2731.

F. Russo, Automatic enhancement of noisy images using objective evaluationof image quality, IEEE Trans. Instrum. Meas., vol. 54, no. 4,pp. 16001606, Aug. 2005.

F. Russo, An ImageEnhancement system Based on Noise estimation, IEEE Trans. on on Instrumentation and Measurement, vol.56,no.4,pp 14351442,2007.