Image Denoising Using Non Linear Filter

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Abstract: Noise in an image is a serious problem In this
project, the various noise conditions are studied which are:
Additive white Gaussian noise (AWGN), Bipolar fixedvalued impulse noise, also called salt and pepper noise
(SPN), Random-valued impulse noise (RVIN), Mixed noise
(MN). Digital images are often corrupted by impulse noise
during the acquisition or transmission through
communication channels the developed filters are meant for
online and real-time applications. In this paper, the
following activities are taken up to draw the results: Study
of various impulse noise types and their effect on digital
images; Study and implementation of various efficient
nonlinear digital image filters available in the literature
and their relative performance comparison;

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Image Denoising Using Non Linear Filter

  1. 1. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4543-4546 ISSN: 2249-6645 Image Denoising Using Non Linear Filter Mr. Vijay R. Tripathi Assistant Professor IN College of Engg & Technology, Akola-444004.Abstract: Noise in an image is a serious problem In this the noise-free pixels should be kept unchanged. This can beproject, the various noise conditions are studied which are: achieved by determining whether the current pixel isAdditive white Gaussian noise (AWGN), Bipolar fixed- corrupted, prior to possibly replacing it with a new value.valued impulse noise, also called salt and pepper noise Decision-based filters correspond to a well-known class of(SPN), Random-valued impulse noise (RVIN), Mixed noise filters that appear to be particularly efficient to reduced(MN). Digital images are often corrupted by impulse noise impulse noise. In this work, we propose an impulseduring the acquisition or transmission through detection scheme by successfully combining the SM filtercommunication channels the developed filters are meant for with CWM filter.online and real-time applications. In this paper, thefollowing activities are taken up to draw the results: Study PROGRESSIVE SWITCHING MEDIAN FILTERof various impulse noise types and their effect on digital A median-based filter, progressive switchingimages; Study and implementation of various efficient median (PSM) filter, is implemented to restore imagesnonlinear digital image filters available in the literature corrupted by salt–pepper impulse noise. The algorithm isand their relative performance comparison; developed by the following two main points: 1) switching scheme—an impulse detection algorithm is used before I. Introduction filtering, thus only a proportion of all the pixels will be Today digital imaging is required in many filtered and 2) progressive methods—both the impulseapplications e.g., object recognition, satellite imaginary, detection and the noise filtering procedures arebiomedical instrumentation, digital entertainment media, progressively applied through several iterations. The noiseinternet etc. The quality of image degrades due to pixels processed in the current iteration are used to help thecontamination of various types of noise. Noise corrupts the process of the other pixels in the subsequent iterations. Aimage during the process of acquisition, transmission, main advantage of such a method is that some impulsestorage etc[1]. For a meaningful and useful processing such pixels located in the middle of large noise blotches can alsoas image segmentation and object recognition, and to have be properly detected and filtered. Therefore, bettervery good visual display in applications like television, restoration results are expected, especially for the casesphoto-phone, etc., the acquired image signal must be noise where the images are highly corrupted.free and made deblurred. The noise suppression (filtering)and deblurring come under a common class of imageprocessing tasks known as image restoration. In common use the word noise means unwantedsignal. In electronics noise can refer to the electronic signalcorresponding to acoustic noise (in an audio system) or theelectronic signal corresponding to the (visual) noisecommonly seen as snow on a degraded television or videoimage. In signal processing or computing it can beconsidered data without meaning; that is, data that is notbeing used to transmit a signal, but is simply produced as anunwanted by-product of other activities. In Information Fig. 1. A general framework of switching scheme-basedTheory, however, noise is still considered to be image filters.information. In a broader sense, film grain or evenadvertisements in web pages can be considered noise. PSM Filter In early days, linear filters were the primary toolsin signal and image processing However; linear filters 1. Impulse Detectionhave poor performance in the presence of noise that is not Similar to other impulse detection algorithms, thisadditive as well as in systems where system nonlinearities impulse detector is implemented by prior information onor non-Gaussian statistics are encountered. Linear filters natural images, i.e., a noise-free image should be locallytend to blur edges, do not remove impulsive noise smoothly varying, and is separated by edges [4]. The noiseeffectively, and do not perform well in the presence of considered for this algorithm is only salt–pepper impulsivesignal dependent noise. To overcome these shortcomings, noise which means: 1) only a proportion of all the imagevarious types of nonlinear filters have been proposed in the pixels are corrupted while other pixels are noise-free and 2)literature. a noise pixel takes either a very large value as a positive impulse or a very small value as a negative impulse. In this II. Median Based Filters chapter, we use noise ratio R(0  R  1) to represent how In order to effectively remove impulse noise asdescribed in while preserving image details, ideally the much an image is corrupted. For example, if an image isfiltering should be applied only to the corrupted pixels, and corrupted by R = 30% impulse noise, then 15% of the www.ijmer.com 4543 | Page
  2. 2. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4543-4546 ISSN: 2249-6645pixels in the image are corrupted by positive impulses and (0) (1) flag image sequence {g(i , j ) , g(i , j ) ,....g(i , j ) .....} . In the ( n)15% of the pixels by negative impulses. (0) Two image sequences are generated during the gray scale image sequence, we still use y( i , j ) to denote theimpulse detection procedure. The first is a sequence of gray (0) (1) (2) ( n) pixel value at position (i, j) in the noisy image to be filteredscale images, {x(i , j ) , x(i , j ) , x(i , j ) ,....x(i , j ) .....} , where the (n) and use y( i , j ) to represent the pixel value at position (i, j) (0)initial image x (i , j ) is noisy image itself , (i , j) is position of in the image after the nth iteration. In a binary flagpixel in image, it can be 1  i  M, 1  j  N where M (n) (n) image g ( i , j ) , the value g ( i , j ) =0 means the pixel (i, j) isand N are the number of the pixel in horizontal and vertical (n) (n) good and g ( i , j ) = 1 means it is an impulse that should bedirection respectively, and x( i , j ) is image after nth iteration. filtered. A difference between the impulse detection and The second is a binary flag image sequence, noise-filtering procedures is that the initial flag image{ f((0)) , f((1)j ) , f((2)) ,.... f((i ,nj)) } where the binary flag f ((i ,nj)) is i, j i, i, j g ((0)j ) of the noise-filtering procedure is not a blank image, i,used to indicate whether the pixel at (i, j) in noisy image (N ) (0) (N ) (n) but the impulse detection result f ( i , j D , i.e., g ( i , j ) = f ( i , j D .detected as noisy or noise-free after nth iteration. If f ( i , j ) =0 ) ) In the nth iteration (n = 1; 2; ….), for eachmeans pixel at (i, j) has been found as noise-free after nth ( n 1) ( n 1) (n) pixel y , we also first find its median value m( i , j ) of aiteration and if f ( i , j ) =1 means pixel at (i, j) has been found (i , j ) WF×WF (WF is an odd integer and not smaller than 3)as noisy after nth iteration. Before the first iteration, we window centered about it. However, unlike that in the (0)assume that all the image pixels are good, i.e. f ( i , j ) =0 for impulse detection procedure, the median value here is ( n 1)all (i, j). selected from only good pixels with g ( i , j ) = 0 in the In the nth iteration (n= 1, 2, 3…) for each pixel window. ( n 1)x (i , j ) we first find out the median value of the samples in a Let M denote the number of all the pixels with ( n 1)WD ×WD (WD is an odd integer not smaller than 3) window g (i , j ) = 0 in the WF×WF window. If M is odd, thencentered about it. To represent the set of the pixels within aWD ×WD window centered about x( i , j ) is x(i  k , j l ) where ( n 1) ( n 1) m((in, 1) = median{ y((in, 1) g((in, 1)  0,(i, j ) WF WF } j) j) j) (n)W  k  W , W  l  W k  W, -W  l  W and The value of y( i , j ) is modified only when the pixel (i, j) is ( n 1) an impulse and M is greater than 0:W≥1, then we have median value of this window m( i , j ) is m((in, 1) = median ( x((ink1)j l ) ) m((in, 1) , if g ((in, 1)  1; M  0 j) ,  j) j) ( n 1)The difference between m( i , j ) and x( i , j ) provides us with ( n 1) y (n) (i , j )   ( n 1)  y(i , j ) ,  elsea simple measurement to detect impulses Once an impulse pixel is modified, it is considered as a  f ((i ,nj)1) ,  if x((in, 1)  m((in, 1)  T good pixel in the subsequent iterations f ((i ,nj))  j) j) 1,  g((in, 1) ,  j) if y((in, )j )  y((in, 1)  otherwise g (n)  j) if y((in, )j )  m((in, 1) (i , j )Where T is a predefined threshold value. Once a pixel (i, j) 0,  j)is detected as an impulse, the value of The procedure stops after the NFth iteration when all of thex((in, )j ) is subsequently modified impulse pixels have been modified, i.e., g NF (i , j ) =0 m ,  ( n 1) (i , j ) if f (n) (i , j )  f ( n 1) (i, j ) (i , j )x((in, )j )   ( n 1) Then we obtain the image { y(i , jF) } which is our restored (N )  x(i , j ) ,  if f ((i ,nj))  f ((i ,nj)1) output image.(4.3) Table 1.WF(3 * 3) Median Filter,CWM Filter&PWM FilterSuppose the impulse detection procedure is stopped after Noise PSNR PSNR After Filtering (N ) Withthe NDth iteration, then two output images- x( i , jD) and Noise f ((i ,Nj D ) are obtained, but only f ((i ,Nj D ) is useful for our noise ) ) Median CWM PWM Filter Filter Filterfiltering algorithm. 10% 15 12 13.5 29 2. Noise Filtering 20% Like the impulse detection procedure, the noise 12 12 13 27filtering procedure also generates a gray scale image 30% 11 12 13 26 (0) (1) (2) ( n)sequence, { y (i , j ) ,y (i , j ) ,y (i , j ) ,.... y (i , j ) .....} and a binary 40% 9.5 12 13 24 www.ijmer.com 4544 | Page
  3. 3. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4543-4546 ISSN: 2249-6645 The Experimental results are shown in Table.2 for WF (5 * 5) PWM Filter Table 2. WF (5 * 5) PWM Filter PSNR with PSNR after Noise Noisy Filtering 10 15 21 20 12 19 (d) 30 11 19 40 9.5 19The Experimental results are shown inTable.3 for WF (7 * 7) PWM Filter Table 3. WF (7 * 7) PWM Filter PSNR with PSNR after (e) Noise Noisy Filtering 10 15 14 20 12 7. 3 30 11 6 40 9.5 5.9. <f> (a) (g) (b) (h) (c) <i> www.ijmer.com 4545 | Page
  4. 4. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4543-4546 ISSN: 2249-6645Figure 2. a, b, c, d are noisy images of Lena (512×512) Referencecorrupted by salt and pepper noise with noise density of [1] R.C. Gonzalez and R.E. Woods Digital Image10%, 20%, 30%, 40% respectively and corresponding Processing Second Edition.restored image by PWM are in e, f, g, h for WF (3 * 3) [2] A. C. Bovik, T. S. Huang, and D. C. Munson, ―A generalization of median filtering using Linear III. Conclusion combinations of order statistics,‖ IEEE Tran Acoust., In this entire dissertation work, two different non-linear Speech, Signal Process., volASSP-31, no.6, pp.1342–filters are implemented and extensive experiments are 1350, Dec. 1983.performed to obtain the results with various parameters to [3] J. Astola and P. Kuosmanen, Fundamental ofassess the performance of each filter. The plot of PSNR for Nonlinear Filtering, Boca Raton, CRC Press, 1997.these two filters is given below. The Table.1, 2 &3 below [4] T. Sun and Y. Neuvo, ―Detail-preserving medianshows the PSNR value obtain using Lena Image of size 512 based filters in image processing,‖ Pattern Recognit.x 512. Lett., vol. 15, pp. 341–347, Apr. 1994From the PSNR value mention in the simulation result it isvery clear that PWM Filter shows better performance in [5] I. Pitas and A. N. Venetsanopoulos, Nonlinear Digitalsuppressing impulsive noise compare to above mention Filters: Principles and Applications, Boston, Kluwer,filter in suppressing impulse noise when noise exceeds from 1990.10 % to 40 %. [6] B. I. Justus son, ―Median filtering: Statistical& Secondly extensive experimental result show that if we properties, ―Two-Dimensional Digital Signalincrease window size i.e. 5 * 5 & 7 * 7,we find that by Processing II, T. S. Huang Ed., New York;increasing the window size image get more & more Springer Verlag, 1981.corrupted & filter is not able to suppress impulsive noise [7] S-J. KO and Y. H. Lee, ―Center-weightedeffectively compare to when window size in filter was (3 * median filters and their applications to image3) in filter. Though simulation time required is less, which enhancement,‖ IEEE Trans. Circuits and Syst.,is given in table below. vol. 38, pp. 984-993, Sept. 1991. [8] J.-H. Wang, ―Rescanned minmax center- Filter Used PSM weighted filters for image restoration,‖ Proc. Window Size Time In Inst. Elect. Eng., vol. 146, no. 2, pp. 101–107, Sec 1999. WF (3 * 3) 16sec [9] ―Tri-State Median Filter for Image Image Denoising‖, WF (5 * 5) 13sec T Chen, K-K.Ma, and L-H Chen IEEE 10sec TRANSACTIONS ON IMAGE PROCESSING, WF (7 * 7) VOL. 8, NO. 12, DECEMBER 1999. Table4: Average Run Time in Sec [10] T. Kasparis, N. S. Tzannes, and Q., ―Detail- preserving adaptive conditional median filters,‖ J. Therefore from the above table it is very cleared Electron. Imag, vol. 1, no. 14, pp. 358–364, 1992.that as window size increases image get more & moreblurred & distorted though it requires less simulation timecompare to that when window size in filter was (3 * 3). Somostly window size of WF (3 * 3) is preferred compare tothat of WF (5 * 5) & WF (7 * 7). www.ijmer.com 4546 | Page

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