 Open Access
 Total Downloads : 290
 Authors : Juhi Mishra, Saurabh Mitra
 Paper ID : IJERTV3IS111247
 Volume & Issue : Volume 03, Issue 11 (November 2014)
 Published (First Online): 29112014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Evaluation of Spatial Domain Filtering with Brute Force Thresholding Algorithm for Image Denoising
Juhi Mishra M.Tech Scholar
Dept of Electronics & Communication Engineering, Dr. C.V. Raman University,
Kargi Road, Kota, Bilaspur (C.G.), India
Saurabh Mitra Assistant Professor
Dept of Electronics & Communication Engineering, Dr. C.V. Raman University,
d(x,y)
Formation of noisy image
Kargi Road, Kota, Bilaspur (C.G.), India
Abstract For researchers the extraction of noise from the original image is still a problem. Several algorithms have been developed and they all have their own merits and demerits. This paper is focused on the denoising of image which is a pre processing step for an image before it can be used in image processing applications. In this work to achieve these de noising, filtering approach and thresholding with wavelet based approach are used and their comparative performances are studied. Image filtering algorithms are applied on images to remove the different types of noise that are either present in the image during capturing or injected into the image during transmission. Here wavelet approach and special
i(x,y)
0(x,y)
n(x,y)
Denoising approach
Fig. 1 Denoising Concept
domain filter are used for the image reconstruction and denoising. In this paper, we propose an efficient algorithm for denoising of digital images.
Keywords – Spatial Filters, Denoising, Brute Force, Thresholding, Wavelet Sub bands.
INTRODUCTION
Image signals are often corrupted by acquisition channel or artificial editing. The main goal of image restoration techniques is to restore the original image from a noisy observation of it. Image noise problems arise when an image suffers with fluctuation or random variation in intensity level. Images may suffer with many of problems like additive multiplicative or impulse noise. It is undesirable because it degrades image quality and makes an image unpleasant to see. The several reasons due to which an image can reduce its quality or get corrupted are – motion between camera and object, improper opening of the shutter, atmospheric disturbances, misfocusing etc. Preprocessing can be done with image denoising and inpainting. Noise is the result of image acquisition system whereas image inpainting problems occur when some pixel values are missing. Denoising is a process of extracting useful information of image and to enhance the quality of image. Denoising is an enhancement technique to reconstruct a noiseless image which is better than the input image.
Generally in case of image denoising methods, the characteristics of the degrading system
and the noises are assumed to be known beforehand. The image i(x,y) is added with noise n(x,y) to form the degraded image d(x,y). This is convolved with the restoration procedure g(x,y) to produce the restored image o(x,y).
Denoising is a necessary step to be taken before the image
data is analyzed for further use. Because after introducing the noise in image, the important details and features of image are destroyed. It is necessary to apply efficient denoising technique to compensate for such data corruption So the main aim is to produce a noise free image from the noisy data. In this paper denoising of images which contain noise is defined by studying the actions of different special domain filters such as regular median filter, adaptive median filter, Gaussian filter and Bilateral filter. Also a thresholding technique called as brute force thresholding is used.
The organization of this paper is as follows: Section 2 is describes a noise models, Section 3 discusses about the filtering approach and thresholding technique, Section 4 describes simulation results on an image and Finally Section 5 gives conclusion.
NOISE MODELS
Noise can affect an image by different ways upto different extent depending on type of disturbance. Generally our focus is to remove certain kind of noise. So we identify certain kind of noise and apply different algorithms to remove the noise. The common types of noise that arises in the image are: a) Impulse noise, b) Additive noise, c) Multiplicative noise. Different noises have their own characteristics which make them distinguishable from others.
(i). Impulse noise This term is generally used for salt and pepper noise. They are also called as spike noise, random noise or independent noise. In image at random places black and white dots appears which makes image noisy. Over heated faulty component and dust particles on image
acquisition system is the main cause of such noise. Occurrence of such noise is independent of pixel values.

Additive noise Gaussian noise comes under the category of additive noise. This noise model follows Gaussian distribution model. The resultant noisy pixel is a sum of original pixel value and randomly distributed Gaussian noise value. This can be expressed by following equation:
w(x, y) = i(x, y) + n(x, y) (1)
its probability distribution function can be given by:
( )2
mathematically than the nonlinear filters. Nonlinear filters have accurate results because they are able to reduce noise levels without blurring the edges. Some of the filtering techniques have been discussed below:

Gaussian filter Gaussian filters are linear low pass filters. It is basically a smoothing filter. Smoothness depends upon the deviation. To get intensive smoothness deviation must be larger.

Regular median filter Median filter is one of the most popular nonlinear filters. It is very simple to implement and much efficient as well. In median filter a central pixel which appears to be noisy is replaced with the median values of neighbouring
f(g)= 1
2 2
2 2 (2)
pixel values. Median filtering tends to remove image detail such as thin lines and corners while reducing noise. A limitation of median filter is
where is standard deviation, g is gray level of image and
m is mean.
(iii). Multiplicative noise This type of noise occurs in almost all coherent imaging systems such as laser, acoustics and SAR (Synthetic Aperture Radar) imagery. Speckle noise is a multiplicative noise. The source of this noise is attributed to random interference between the coherent backscattered signals. Fully developed speckle noise has the characteristic of multiplicative noise. Speckle noise follows a gamma distribution. It can be given as
w(x, y) = i(x, y)Ã—n(x, y) (3)
SPATIAL FILTERING AND THRESHOLDING APPROACH FOR IMAGE DENOISING

Spatial domain filters Enhanced images can be reconstructed via filteration process. Image filters may be used to highlight parts or edges of image or boundaries. Filters provide an image better visualization. Image denoising is the process of obtaining original image from the degraded one. It helps to retain the edges and other major detail without modifying the visual information of image. Filtering in image processing is used to accomplish many things, including interpolation, noise reduction, and resampling. The choice of filter is often determined by the nature of the task and the type and behaviour of the data. Noise, dynamic range, color accuracy, optical artifacts, and many more details affect the outcome of filter functions in image processing.
A traditional way to remove noise is to employ spatial filters. Spatial filtering is commonly used to clean up the output of lasers, removing aberrations in the beam due to imperfect, dirty or damaged optics. Thespecial filtering works directly on image plane and manipulates the pixel value of corrupted pixel by applying various algorithms of filters. The values of neighbourhood pixels decide the value of processed pixel therefore it is also known as neighbourhood process. Spatial filters can be further classified into nonlinear and linear filters. In linear filters output values are linear function of the pixels in the original image. Linear methods are easy to analyse
that it acts as a low pass filter so it passes low frequencies while attenuates high frequency components of image like edges and noise. So it blurs the image.


Adaptive median filter Images affected by impulse noise can be denoised by the application of adaptive median filters. Its algorithm is simple and easy to implement. It is being used to remove high density of impulse noise as well as non impulse noise while preserving fine details. Its algorithm works on two levels. In first level it the presence of residual impulse in a median filter output is tested. If there is an impulse then it will increase window size and repeat the test. If no impulse is present in median filter output then second level test is carried out to check whether central pixel is corrupted or not. If yes then the value of central pixel will be replaced with the median value.
Bilateral filter Bilateral filter smooth the image as well as preserves edge information. It extends the concept of Gaussian smoothing by weighting the filter coefficients with their corresponding relative pixel intensities. Pixels that are very different in intensity from the central pixel are weighted less even though they may be in close proximity to the central pixel. This is effectively a convolution with a nonlinear Gaussian filter, with weights based on pixel intensities. Its formulation is very simple.

Discrete Wavelet Transform
A wavelet is a small wave which has its energy concentrated in time. It has an oscillating wavelike characteristic & it as timescale and timefrequency analysis tools have been widely used in topographic reconstruction and still growing. Working in the wavelet domain is advantageous because the DWT tends to concentrate the energy of the desired signal in a small number of coefficients, hence, the DWT of the noisy image consists of a small number of coefficients with high Signal Noise Ratio (SNR) and a large number of coefficients with low SNR. After discarding the coefficients with low SNR (i.e., noisy coefficients) the image is reconstructed using inverse DWT. As a result,
noise is removed or filtered from the observations[3]. The DWT is identical to a hierarchical sub band system where the sub bands are logarithmically spaced in frequency and represent octaveband decomposition. By applying DWT, the image is actually divided i.e., decomposed into four sub bands and critically sub sampled as shown in Figure.1(a). These four sub bands arise from separable applications of vertical and horizontal filters. The sub bands labeled LH1, HL1 and HH1 represent the finest scale wavelet coefficients, i.e., detail images while the sub band LL1 corresponds to coarse level coefficients, i.e., approximation image. To obtain the next coarse level of wavelet coefficients, the sub band LL1 alone is further decomposed and critically sampled. This results in two level.



Brute force thresholding brute force is
Finding an optimized value () for threshold is a major problem. A small change in optimum threshold value destroys some important image details that may cause blur and artifacts. So, optimum threshold value should be found out, which is adaptive to different sub band characteristics. Here we proposed a Brute Force Thresholding technique which gives an efficient threshold value for noise to get high value of PSNR as compared to previously explained methods.
Threshold follows the same concept as in basic electronics, Brute force Threshold is given 5 times the maximum pixel intensity, which will be 127 in most of the images. Brute force thresholding always outclass other existing thresholding techniques in terms of better results. Algorithm for brute force thresholding is given

Input wavelet sub band.

Find maximum (max) and minimum (min) value of sub band coefficients.

loop through (threshold=min to max) and execute desired algorithm

save the results in array for each loop such that F= [threshold, result]

When loop completed, select the (threshold) that gives best result.


Flow diagram for proposed algorithm
Fig 2 Flow diagram of proposed algorithem
PERFORMANCE EVALUATION AND SIMULATION RESULTS
This work has been implemented using MATLAB as a simulation tool. The proposed method is tested on image
SAR_Image.JPG of size 1232 X 803. The image is corrupted by different type of noises like salt and pepper noise, random noise and Gaussian noise at various noise densities and the performance of algorithm is evaluated on the basis of peak signal to noise ratio, mean square error and root mean square error.

Mean Square Error Mean square error or MSE is the average square difference of pixels between orginal and denoised image throughout the image. Lower the MSE better will be the system response.
MSE= [Is r,c I(r,c)]Â²
R x c

Peak Signal To Noise Ratio the phrase peak signal to noise ratio abbreviated as PSNR represents the ratio between maximum possible power of signal and power of corrupting noise. Because of wide dynamic range
PSNR is usually expressed in logarithmic decibel scale. PSNR may be expressed as:
of RMSE is very common and it makes an excellent general purpose error metric for numerical predictions.
PSNR=
MAXi Â²
20 log10 MSE
255
RMSE=
10 20

Root Mean Square Error The term root mean square error also known as root mean square deviation, also referred as standard deviation as it is the square value of variance. It represents the square root of the mean/average of the square of all of the error.The use
Take an example of SAR image. The stimulation results and data are shown in below and Table respectively.
GAUSSIAN NOISE 

Noise Value 
Regular Median Filter 
Adaptive Median Filter 
Gaussian Filter 
Bilateral Filter 

PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 

0.1 
21.3714 
21.7756 
276.4523 
23.286 
17.4678 
474.1768 
36.1425 
3.9757 
15.8063 
30.1365 
7.93807 
63.013 

0.2 
20.4 
25.5 
593.035 
19.1592 
28.0918 
789.15 
33.5457 
5.36148 
28.74156 
22.5818 
18.9431 
358.8395 

0.3 
18.7122 
29.5754 
874.7025 
16.7906 
36.898 
1361.5 
31.9569 
6.4372 
41.4372 
17.6824 
33.2982 
1108.767 

0.4 
17.6329 
33.4885 
1121.477 
15.4605 
43.0046 
1849.397 
30.8811 
7.2859 
53.0848 
14.6932 
46.97645 
2206.786 

0.5 
16.9449 
36.2489 
1313.985 
14.7916 
46.4473 
2157.348 
30.072 
7.99724 
63.95586 
12.8509 
58.07579 
3372.798 

0.6 
16.1297 
39.8157 
1585.295 
14.4675 
48.21311 
2324.504 
29.4268 
8.61391 
74.1993 
11.935 
64.5342 
4163.805 

0.7 
15.5911 
39.8157 
1794.6111 
14.3926 
48.6306 
2364.94 
29.3621 
8.6783 
75.31307 
11.2258 
70.0245 
903.4343 

0.8 
15.2226 
44.19876 
1953.53 
14.3449 
48.8985 
2391.0593 
29.0507 
8.9951 
80.91152 
10.5726 
67.28374 
5699.285 

SALT AND PEPPER NOISE 

Noise Value 
Regular Median Filter 
Adaptive Median Filter 
Gaussian Filter 
Bilateral Filter 

PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 

0.1 
36.0275 
4.0287023 
16.2304 
27.5213 
10.7269 
115.067 
33.8419 
5.18137 
26.8466 
16.2096 
39.4511 
1556.3969 

0.2 
35.2163 
4.423 
19.5636 
27.2825 
11.0254 
121.5711 
32.247 
6.22572 
38.7596 
13.565 
53.49216 
2861.4118 

0.3 
34.9112 
4.58121 
20.9874 
27.036 
11.3433 
128.671 
31.1325 
7.0781 
50.099 
11.9158 
64.67704 
4183.1204 

0.4 
36.8114 
3.681 
13.55 
26.8444 
11.59632 
134.4746 
29.9744 
8.0876 
73.3905 
10.8019 
73.8267 
5406.178 

0.5 
35.8235 
4.12444 
17.011 
26.6975 
11.7941 
130.4789 
29.9508 
8.1096 
65.765 
9.9297 
81.2934 
6608.614 

0.6 
32.127 
6.31233 
39.8455 
26.0661 
12.6831 
160.868 
29.4495 
8.5914 
73.8125 
9.153 
88.8976 
7902.789 

0.7 
26.2069 
12.4794 
155.736 
25.9473 
12.8581 
165.3295 
28.917 
9.1346 
83.4411 
8.5801 
94.95879 
9017.172 

0.8 
20.2085 
24.8951 
619.7697 
25.4429 
13.6268 
185.691 
28.4272 
9.6645 
93.4029 
8.0864 
100.5125 
10102.768 

0.9 
15.457 
43.0219 
1850.888 
22.8269 
18.41599 
339.14885 
28.5174 
9.5647 
91.4829 
7.6896 
105.21077 
11069.305 

RANDOM NOISE 

Noise Value 
Regular Median Filter 
Adaptive Median Filter 
Gaussian Filter 
Bilateral Filter 

PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 
PSNR 
RMSE 
MSE 

0.1 
21.0084 
22.70493 
515.5138 
23.3076 
17.424494 
303.612 
36.0585 
4.01435 
15.115 
30.207 
7.8734 
61.9912 

0.2 
20.3529 
24.48472 
599.502 
19.1113 
28.24718 
797.903 
33.4539 
5.4181 
29.3555 
22.726 
18.630 
347.089 

0.3 
18.8756 
29.024195 
842.404 
16.7276 
37.16723 
1381.40 
32.2994 
6.18828 
38.2948 
17.794 
32.871 
1080.51 

0.4 
17.3755 
34.49572 
1189.955 
15.4373 
43.11965 
1859.30 
31.2187 
7.00818 
49.1145 
14.687 
47.007 
2209.73 

0.5 
16.8269 
36.74474 
1350.1759 
14.7832 
46.49221 
2161.52 
29.9892 
8.07384 
65.1869 
13.018 
56.964 
3244.96 

0.6 
16.3177 
38.96325 
1518.1348 
14.4902 
48.08728 
2312.38 
29.5818 
8.46155 
71.5979 
11.915 
66.187 
4183.60 

0.7 
15.6572 
42.04169 
1767.5038 
14.3893 
48.64914 
239.465 
29.2333 
8.80796 
77.5801 
11.167 
70.493 
4969.35 

0.8 
14.7754 
46.83397 
2165.411 
14.2026 
49.7062 
2470.70 
28.7082 
9.35686 
87.5508 
10.586 
75.738 
5681.20 

0.9 
14.8013 
46.39543 
2152.536 
14.2363 
49.513677 
2451.60 
28.7894 
9.26979 
85.9291 
10.181 
78.975 
6237.06 
CONCLUSION
In this work image denoising is achieved by various special filtering approach with a thresholding method named as brute force thresholding. Simulation is performed on image with various types of noises that are either present during acquisition or transmission of image. In this work three types of noises are added to image and special domain filtering is performed on each of them. The performances of the filters are compared using the Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE). The performance of brute force thresholding algorithm is very efficient in denoising.
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