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\title{Image Fusion Algorithm for Impulse Noise Reduction in Digital Images}
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             \author[1]{hari  kiran}

             \affil[1]{  GITAM University Visakhapatnam}

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\date{\small \em Received: 22 April 2011 Accepted: 20 May 2011 Published: 2 June 2011}

\maketitle


\begin{abstract}
        


This paper introduces the concept of image fusion technique for impulse noise reduction in digital images. Image fusion is the process of combining two or more images into a single image while retaining the important features of each image. Multiple image fusion is an important technique used in military, remote sensing and medical applications. The images captured by different sensors undergo filtering using pixel restoration median filter and the filtered images are fused into a single image, which combines the uncorrupted pixels from each one of the filtered image The fusion algorithm is based on selecting the sharper regions from the individual de-noised images. The performance evaluation of the fusion algorithm is evaluated using structural similarity index (SSIM) between original and fused image. Experimental results show that this fusion algorithm produce a high quality image compared to individually de-noised images.

\end{abstract}


\keywords{Image Fusion, Image Restoration, Image Processing, Impulse Noise.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
igital images are often corrupted during acquisition, transmission or due to faulty memory locations in hardware \hyperref[b0]{[1]}. The impulse noise can be caused by a camera due to the faulty nature of the sensor or during transmission of coded images in a noisy communication channel \hyperref[b1]{[2]}. Consequently, some pixel intensities are altered while others remain noise free. The noise density (severity of the noise) varies depending on various factors namely reflective surfaces, atmospheric variations, noisy communication channels and so on.\par
In most image processing applications the images captured by different sensors are combined into a single image, which retains the important features of the images from the individual sensors, this process is known as image fusion  {\ref [3][4]}. In this paper, the images captured by multiple sensors are differently noised depending on the proximity to the object, environmental disturbances and sensor features. These noise images are filtered using pixel restoration median filter and the filtered images are fused into a single image based on the sharpness of the regions from the de-noised images, thus producing a high quality image. The entire process of our technique is shown in figure \hyperref[fig_0]{1}. The performance evaluation of the image fusion is evaluated using SSIM \hyperref[b6]{[7]} index between the original and fused image.\par
This paper is organized as follows: Section II present the impulse noise in images, Section III present the method for noise density calculation in an image, Section IV present the pixel restoration median filter Section V present the image fusion algorithm, Section VI present experimental results and finally Section VII reports conclusion.  
\section[{Impulse Noise In Images}]{Impulse Noise In Images}\par
Impulse noise \hyperref[b4]{[5]} corruption is very common in digital images. Impulse noise is always independent and uncorrelated to the image pixels and is randomly distributed over the image. Hence unlike Gaussian noise, for an impulse noise corrupted image all the image pixels are not noisy, a number of image pixels will be noisy and the rest of pixels will be noise free.\par
There are different types of impulse noise namely salt and pepper type of noise and random valued impulse noise.\par
In salt and pepper type of noise the noisy pixels takes either salt value (gray level -225) or pepper value (gray level -0) and it appears as black and white spots on the images. If p is the total noise density then salt noise and pepper noise will have a noise density of p/2.This can be mathematically represented by (1)   zero or 255 with probability p y ij =\par
x ij with probability 1-p\par
Where y ij represents the noisy image pixel, p is the total noise density of impulse noise and x ij is the uncorrupted image pixel. At times the salt noise and pepper noise may have different noise densities p 1 and p 2 and the total noise density will be p=p 1 + p 2 .\par
In case of random valued impulse noise, noise can take any gray level value from zero to 225. In this case also noise is randomly distributed over the entire image and probability of occurrence of any gray level value as noise will be same. We can mathematically represent random valued impulse noise as in \hyperref[b1]{(2)}. n ij with probability p y ij =\par
x ij with probability 1-p\par
where n ij is the gray level value of the noisy pixel. 
\section[{III.}]{III.} 
\section[{Noise Density Calculation}]{Noise Density Calculation}\par
Algorithm:\par
1. Let I be the noisy image of size NXN of an object or scene captured by sensor. The value of ND ranges from 0 to 1. 
\section[{IV.}]{IV.} 
\section[{Pixel Restoration Median Filter}]{Pixel Restoration Median Filter}\par
Image X and Binary Map of the image BM are inputs to the PRMF algorithm \hyperref[b5]{[6]}.\par
[1] Let pixel x ij and corresponding b ij are selected from image X and binary map BM respectively, where i=2?? (n-1) and j=2?.. (n-1) for an image of size nxn. If b ij = '0', then pixel x ij is 'uncorrupted'. Hence go to step \hyperref[b4]{[5]}.\par
[2] Select a 3x3 window W x in X and W b in BM centered around (i,j) th pixel x ij in X and b ij in BM respectively.\par
[3] Check for '0's (uncorrupted pixels) in W b and store corresponding elements of W x in vector A. \hyperref[b3]{[4]} If A is a null vector go to step V. Else replace x ij with median of vector A.\par
x ij = median(A).\par
(5) \hyperref[b4]{[5]} Increment i, j and consider next x ij, b ij and go to step \hyperref[b1]{[2]}. 
\section[{V.}]{V.}\par
Image Fusion Algorithm [1] Let I 1 , I 2 ,......, I n be the noisy images of an object or scene captured by sensors S 1 ,S 2 ,......,S n respectively. Let I i be of size NXN where i =1,2,?,n. Iteration index k i .\par
[2] Compute the noise densities of the images I i . Noise densities are computed for the iteration count k i . If K i =1 compute ND i \hyperref[b2]{[3]} Filter the noisy images using pixel restoration median filter. The filtered images are denoted as R i\par
shown in figure \hyperref[fig_0]{1}. \hyperref[b3]{[4]} Check for the noise in the processed images. If the images are still noisy, then increment the iteration index k i , k i = k i +1 and goto step [2]. [5] The recovered images R i for i=1,2,..,n are divided into non-overlapping rectangular blocks (or regions) with size of mxn (10x10 blocks). The j th image blocks of R i are referred by R i j [6] Variance (VAR) of R i j is calculated for determining the sharpness values of the corresponding blocks and the results of R i j are denoted by VAR i j . VAR is defined as:'0' if L 1 < y<L 2 BM = '1' if y<L 1 or y>L 2 (3) = 1. 
\section[{= 1}]{= 1}\par
By using this algorithm iteratively along with updated binary map of the recovered image, noise fades from the noisy image.  
\section[{Conclusion}]{Conclusion}\par
In this paper, an image fusion technique for impulse noise reduction in digital images is presented. The proposed technique helps to attain high quality images. Images of an object or scene, captured by multiple sensors undergo filtering using pixel restoration median filter individually and these de-noised images are fused by the proposed technique. The proposed method is simple and can be used for real-time imaging applications.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.7732851985559567\textwidth}P{0.009205776173285198\textwidth}P{0.05216606498194946\textwidth}P{0.006137184115523466\textwidth}P{0.009205776173285198\textwidth}}
2. The noise boundaries of noisy image I are computed by spike detection technique [6]. Let L 1 and L 2 be the lower and upper noise boundaries for the noisy image. 3. The binary map (BM) of the noisy image is developed using the noise boundaries L ND=\tabcellsep sum\tabcellsep N in s * '1' N of\tabcellsep BM\tabcellsep (4)\end{longtable} \par
  {\small\itshape [Note: 1 and L 2 . If the image pixel 'y' lies within the noise boundaries, then it is uncorrupted and represented by a '0' in the binary map. The corrupted pixel is represented by a '1'in binary map.4]} 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.24605263157894738\textwidth}P{0.1174342105263158\textwidth}P{0.05032894736842105\textwidth}P{0.4361842105263158\textwidth}}
\tabcellsep \tabcellsep \tabcellsep SSIM value of fused\\
\multicolumn{3}{l}{Noise densities of 3}\tabcellsep image with respect\\
\multicolumn{2}{l}{input images}\tabcellsep \tabcellsep to original image\\
0.2\tabcellsep \multicolumn{2}{l}{0.35 0.4}\tabcellsep 0.8436\\
0.3\tabcellsep 0.4\tabcellsep 0.5\tabcellsep 0.7342\\
0.5\tabcellsep 0.6\tabcellsep 0.7\tabcellsep 0.5743\\
0.6\tabcellsep 0.7\tabcellsep 0.8\tabcellsep 0.4468\\
\tabcellsep \multicolumn{2}{l}{VII.}\tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 			\footnote{© 2011 Global Journals Inc. (US)} 			\footnote{© 2011 Global Journals Inc. (US) :} 			\footnote{© 2011 Global Journals Inc. (US) Global Journal of Computer Science and Technology Volume XI Issue XII Version I July} 		 		\backmatter  			 \par
In order to determine the sharper image block, the variances of image blocks from n recovered images are sorted in descending order and the same ordering is associated with image blocks. The block with the maximum variance is kept in the fused image. The fusion mechanism is represented as follows:\par
If VAR (k) is the variance of block R i j , where k denotes the rank, the ordering of variances is given by\par
and this implies the same ordering to the corresponding blocks\par
Where the subscripts are the ranks of the image blocks.\par
Since the block with the largest variance is in the fused image, it will correspond to rank 1 of the ordered blocks ie;\par
VI. 
\subsection[{Experimental Results}]{Experimental Results}\par
The proposed method of image fusion for impulse noise reduction in images was tested on the true color parrot image with 290x290 pixels. The i mpulse noise is added into the image with noise density 0.45, 0.5, 0.6 . The noisy images are processed using pixel restoration median filter individually. The filtered images are fused into a single image using the Image fusion method. The experimental res ults are shown in Figure  {\ref 2}. Table  {\ref (1} 			 			  				\begin{bibitemlist}{1}
\bibitem[Indu and Ramesh]{b4}\label{b4} 	 		‘A noise fading technique for images corrupted with impulse noise’.  		 			S Indu 		,  		 			Chaveli Ramesh 		.  	 	 		\textit{Proceedings of ICCTA07},  				 (ICCTA07)  		IEEE.  	 
\bibitem[Wang and Bovik (2002)]{b6}\label{b6} 	 		‘A universal image quality index’.  		 			Z Wang 		,  		 			A C Bovik 		.  	 	 		\textit{IEEE Signal Processing Letters}  		Mar. 2002. 9 p. .  	 
\bibitem[Berstein ()]{b1}\label{b1} 	 		‘Adaptive nonlinear filters for simultaneous removal of different kinds of noise in images’.  		 			Reihard Berstein 		.  	 	 		\textit{IEEE Trans on circuits and systems}  		1987. 34  (11)  p. .  	 
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