An adaptive method for noise removal from real world images

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  • 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN INTERNATIONAL JOURNAL OF ELECTRONICS AND 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMECOMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)ISSN 0976 – 6464(Print)ISSN 0976 – 6472(Online)Volume 4, Issue 1, January- February (2013), pp. 112-124 IJECET© IAEME: www.iaeme.com/ijecet.aspJournal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEMEwww.jifactor.com AN ADAPTIVE METHOD FOR NOISE REMOVAL FROM REAL WORLD IMAGES Krishnan Kutty1, Lipsa Mohanty2 1 (Center for Research in Engineering Sciences and Technology, KPIT Cummins, Pune, India, Krishnan.Kutty@kpitcummins.com) 2 (Center for Research in Engineering Sciences and Technology, KPIT Cummins, Pune, India, Lipsa.Mohanty@kpitcummins.com) ABSTRACT Noise removal is an important aspect in image processing. However, reduction of noise from images that contain textured regions or which have very fine details is difficult. Gaussian noise is very often encountered in acquired images. This paper presents a method to denoise the images corrupted by Additive White Gaussian Noise (AWGN). The noise removal technique proposed here is based on the modification of the well known bilateral filter, which encompasses both the spatial distance and amplitudinal distance between a centre point and its neighboring points. The proposed filter adapts its strength depending on the amount of local noise present in the image. The proposed technique attempts to smooth the image without deteriorating other visual aspects of the image. Experimental results show that the proposed method performs well with different types of images and for a large range of noise deviation. It is effective in removing additive Gaussian noise present in an image along with enhancing the perceptual quality, by virtue of retaining true edges and performing selective smoothing, of the image both qualitatively and quantitatively. Keywords: Noise Removal, Additive White Gaussian Noise, Spatial distance, Amplitudinal distance, Perceptual quality 1. INTRODUCTION Noise in an image, invariably degrades the interpretability of data present in the image. Image noise may be caused by different intrinsic and extrinsic conditions, which most of the times, becomes difficult to avoid. Therefore, realizing a smart filter enabling successful noise reduction without affecting the fine image details is of great importance. The noise reduction filter must be adaptive so as to change its strength of filtering according to the amount of noise present in the image. 112
  • 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Among many techniques that exist in the open literature, a conventional linear filtersuch as Gaussian filter [3] helps to smooth noises effectively but also tends to blur edges.Vijaykumar et al [1] proposed a method in which they keep increasing the window size untilthe number of elements within a factor multiplied with the image standard deviation is belowa particular threshold. However, this method will cease to work in case the image inherentlyhas high frequency component in it. The method proposed by Padole et al [6, 7] tends to oversmooth the image as is shown in their results thereby losing out on retaining the edges afternoise removal. Since the goal of filtering is not only to suppress the noise but also topreserve the edge and detail information of the image, the nonlinear approaches generallyprovide more satisfactory results than the linear approaches. Thus, there have been manyattempts to design digital filters which have the abilities of noise attenuation along with edgepreservation. In [4] C. Tomasi and R. Manduchi have proposed a bilateral filter to removeGaussian noise. In [8], Elad has detailed on improvements to the bilateral filtering technique.The bilateral filter is a nonlinear filtering technique utilizes both spatial and amplitudinaldistances. Here a local filter is defined based on the combination of spatial distances andamplitudinal distances between a centre point at (x, y) and its neighboring points. Howeverthe edge preservation performance of bilateral filter is debatable for images with fine detailsand for those that have a low signal to noise ratio (SNR). Moreover, it retains most of thefalse edges from the original noisy image. In this paper, we have proposed a new modifiedbilateral filter for reduction of Gaussian noise, wherein the noise standard deviation is knowna-priori. This filter shows improved performance in terms of MSE, PSNR and edge retentionover bilateral filter for the regions of input image that contains fine details. The paper is organized as follows: next section describes the assumed noise model.Section 3 illustrates the proposed noise removal method. Section 4 shows noise removalexperimental results and discussions, followed by conclusion in Section 5.2. NOISE MODEL Noise is modeled as Additive White Gaussian Noise (AWGN) where all the imagepixels deviate from their original values following a Gaussian curve. The probability densityfunction for the zero-mean Gaussian distribution is given by: ష࢔૛ ૚ ࡳሺ࢔ሻ ൌ ࢋ ૛࣌૛ ඥ૛࣊࣌૛ (1) For each image pixel with the intensity value O (i, j) (1 ≤ i ≤ M, 1 ≤ j ≤ N for an M x Nimage), the corresponding pixel of the noisy image X(i, j) is given by: ࢄሺ࢏,࢐ሻ ൌ ࡻሺ࢏,࢐ሻ ൅ ࡳሺ࢏,࢐ሻ (2) Where, each noise value G (i, j) is drawn from the zero-mean Gaussian distribution.3. PROPOSED METHOD The proposed noise reduction approach involves selective smoothening of image,wherein edges are relatively better preserved. The performance of our algorithm is dependenton prior knowledge about the standard deviation σ of the noise corrupted image. In this paper,we have used Swati et al’s [5] method of transfer function based technique for estimatingnoise standard deviation. 113
  • 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Having estimated the noise standard deviation, the proposed approach works in twophases: 1. Estimate the smoothening parameter and 2. Generate the modified bilateral filter. 3.1. ESTIMATE THE SMOOTHENING PARAMETER In order to estimate the smoothing parameter, blocks of three different window sizesare considered. This helps in estimating the strength of noise at diverse regions in the noisyimage based on a varying window size around the pixel of interest. Based on the strength ofthe Gaussian noise in the noise corrupted image, the smoothening parameter is estimated. The detailed algorithm for estimation of smoothening parameter is summarizedbelow:STEP 1: Initialise the block sizes. We have experimented with three window of sizes for theblock B (around the pixel of interest (i, j)), viz. 5×5, 7×7 and 9×9. Applying larger blocksizes could result in over estimation of smoothing parameter. The blocks are defined as: B ‫ א‬x|y|z (3) Where, x = ൣࢇ࢏,࢐ ൧ ࢏ୀሺ࢏ି૛:࢏ା૛ሻ;࢐ୀሺ࢐ି૛:࢐ା૛ሻ y = ൣࢇ࢏,࢐ ൧ ࢏ୀሺ࢏ି૜:࢏ା૜ሻ;࢐ୀሺ࢐ି૜:࢐ା૜ሻ z = ൣࢇ࢏,࢐ ൧ ࢏ୀሺ࢏ି૝:࢏ା૝ሻ;࢐ୀሺ࢐ି૝:࢐ା૝ሻWe first select the block B ‫.ݔ א‬STEP 2: We then compute the absolute difference D between the central pixel and itsneighborhood for the considered block. The local standard deviation ߪ஽ ሾ௖,௠ሿ is calculated forthe same block. ࡰሺࢉ,࢓ሻ ൌ |ࢉሺ࢏,࢐ሻ െ ࢓ሺ࢏,࢐ሻ |࢓ሺ࢏,࢐ሻ‫ࢠ|࢟|࢞א‬ (4) Where, c = central pixel m = neighbouring pixel ૚ ࣌ࡰ ሾࢉ,࢓ሿ ൌ ට ∑ ࢑ ሺࡰ ࢚ െ ࣆ ሻ૛ ࢚ୀ૚ ࢑ (5) ‫ࢠ|࢟|࢞ א‬ Where, k is the total number of elements ߤ denotes the mean value within the window and is given by: ૚ ࣆൌ ∑࢑ ࡰ࢚ ࢚ୀ૚ ࢑ (6) 114
  • 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEMESTEP 3: Compute the range filter ‫ܨ‬஺ to determine the amplitudinal distance for theconsidered block B. ૛ ൣࢅሺࢉሻ ି ࢅሺࢉష࢓ሻ ൧ ࡲ࡭ ൌ ࢋ࢞࢖ ቊെ ૛࣌ࡰ ሾࢉ,࢓ሿ ૛ ቋ (7)STEP 4: Here, we are taking into account the fact that for a Gaussian distributed variablewith mean µ and variance ߪ2, 95.5% of the samples (drawn from the normal distribution) lieswithin the rangeሾµ െ 2σ, µ ൅ 2σሿ.By applying this observation we compute P0, where P0 is the number of pixels ≤ 0.95. ࡼ૙ ൌ ሺ ࡮ ‫ ࢠ|࢟|࢞ א‬ሻ ൑ ૙. ૢ૞ (8)We then estimate ‘Noise Strength Factor (NSF)’ܴ ஻‫ , ୸|୷|୶ א‬which is the ratio between P0 andtotal number of elements k in the block. ࡼ૙ ࡾ࡮ ‫ ࢠ|࢟|࢞ א‬ൌ ࢑࡮‫ࢠ|࢟|࢞ א‬ (9)STEP 5: Similarly, we repeat Step 2, 3 and 4 for other window sizes, viz. B‫ ݕ א‬and B‫.ݖ א‬STEP 6: We now compute difference di where i=1, 2 and determine the smoothing factor fact. ࢊ૚ ൌ ࡾ࡮ ‫ ࢟ א‬െ ࡾ࡮ ‫࢞ א‬ (10) ࢊ૛ ൌ ࡾ࡮ ‫ ࢠ א‬െ ࡾ࡮ ‫࢟ א‬ (11)The differences d1 and d2 are used to analyse the strength of noise in the blocks where B ‫א‬ x|y|z. This provides three different conditions that will assist in estimation of fact. Theconditions that can possibly arise are as follows:Case 1: The normalized noise strength factor (NSF) present in the region of 5x5 block ishigher as compared to 7x7 and 9x9 blocks. This denotes that the strength of noise graduallydecreases with increase in the block size. 1.5 Noise strength 1 factor 0.5 0 (5x5) (7x7) (9x9) Block sizes Fig. 1: Noise strength factor (Case 1)For such condition, we use block size of 5x5 for estimating the smoothening factor (fact).Case 2: The normalized NSF in 5x5 block is the lowest. The strength gradually increases for7x7 block and then again decreases for 9x9 block. Thus, the NSF is highest for 7x7 block. 115
  • 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME 1.5 Noise strength 1 factor 0.5 0 (5x5) (7x7) (9x9) Block sizes Fig. 2: Noise strength factor (Case 2)For such condition, we use block size of 7x7 for estimating the smoothening factor (fact).Case 3: The 5x5 block has the least normalized NSF and the 9x9 block has relatively moreNSF. The strength of noise increases with increase in the block size. 1.5 Noise strength 1 factor 0.5 0 (5x5) (7x7) (9x9) Block sizes Fig. 3: Noise strength factor (Case 3)For such condition, we use block size of 9x9 for estimating the smoothening factor (fact).Thereafter, to calculate fact it is essential to know a-priori the level of Gaussian noiseߪ௘௦௧ present in the image. As discussed earlier, we use the approach detailed in [5] toestimate ߪ௘௦௧ .Based on Step 6, if ݀ଵ ൏ 0, this indicates that in 5x5 block, the level of noise is much morethan 7x7 block (Case 1). ࣌ࢋ࢙࢚ ࢌࢇࢉ࢚ ൌ ሺࡱ૚ ‫ ܠ א ۰ࡾ כ‬ሻ ‫ כ‬൬࣌ ൰ (12) ࡰ ሾࢉ,࢓ሿSimilarly, if ݀ଶ ൏ 0, this indicates that the amount of noise is more in 7x7 block as comparedto 9x9 block (Case 2). ࣌ࢋ࢙࢚ ࢌࢇࢉ࢚ ൌ ൫ࡱ૛ ‫ ࢟א ۰ࡾ כ‬൯ ‫ כ‬൬࣌ ൰ (13) ࡰ ሾࢉ,࢓ሿOtherwise, it specifies that the strength of noise is higher in block of size 9x9 (Case 3). 116
  • 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME ࣌ࢋ࢙࢚ ࢌࢇࢉ࢚ ൌ ሺࡱ૜ ‫ ࢠ א ࡮ࡾ כ‬ሻ ‫ כ‬൬࣌ ൰ (14) ࡰ ሾࢉ,࢓ሿ Where, we have considered ହ ଻ ଽ ‫ܧ‬ଵ ൌ ቀ ቁ , ‫ܧ‬ଶ ൌ ቀ ቁ , ‫ܧ‬ଷ ൌ ቀ ቁ for our experiments. ଷ ହ ଻Looking at the way we calculated this factor, it is evident that it is some kind of weightedaverage of its neighbours.The value of fact is affected by two criteria: • How close (spatially) are the neighbouring pixels and centre pixel for a given block. • How similar (in terms of gray value) are the neighbouring pixels and the centre pixel for a given block.STEP 7: Consider the block of size 5×5 of the noisy image and repeat Step 2. We obtain‫ܦ‬ሺ௖,௠ሻ and ߪ஽ ሾ௖,௠ሿ as given in Eqn. (4) and (5). We now compute the new local standarddeviation ߪ௡௘௪ for the considered block: ࣌࢔ࢋ࢝ ൌ ࡰሾࢉ,࢓ሿ ‫࢚ࢉࢇࢌ כ‬ (15)We then repeat Step 3 to obtain ‫ܨ‬஺ from Eqn. (7).STEP 8: Convolve the noisy image with the Laplacian mask given in Eqn. (16) to generate aLaplacian image. This helps in suppression of a large amount of smooth regions in the noisyimage, mostly leaving behind the high frequency noisy regions. ૚ െ૛ ૚ Laplacian mask = ൥െ૛ ૝ െ૛൩ (16) ૚ െ૛ ૚We then consider a 5x5 block BLap of the Laplacian image and calculate the local standarddeviation σ୐ୟ୮ . 3.2. GENERATE MODIFIED BILATERAL FILTER Conventional bilateral filter [4] is a non-linear and non-iterative filtering techniquewhich utilizes both spatial and amplitudinal distances to preserve the image details.In the Gaussian case, the bilateral filter can be defined as follows: ෡ ∑ࡺ ࢄሾ࢑ሿ ൌ ࢔సషࡺ ࡺ ࢃሾ࢑,࢔ሿࢅሾ࢑ି࢔ሿ ∑࢔సషࡺ ࢃሾ࢑,࢔ሿ (17) Where, ࢔૛ ࢃ࢙ ሾ࢑, ࢔ሿ ൌ ࢋ࢞࢖ ቄെ ቅ ૛࢙࣌ ૛ (18) ૛ ൣࢅሾ࢑ሿିࢅሾ࢑ି࢔ሿ൧ ࢃ࢘ ሾ࢑, ࢔ሿ ൌ ࢋ࢞࢖ ൜െ ૛࣌࢘ ૛ ൠ (19) 117
  • 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME ࢃሾ࢑, ࢔ሿ ൌ ࢃ࢙ ሾ࢑, ࢔ሿ · ࢃ࢘ ሾ࢑, ࢔ሿ (20)Ws [k, n] computes the spatial distance and Wr[k,n] computes the amplitudinal distance.W[k, n] is a local filter defined by combination of both spatial and amplitudinal distances.In our approach, we have used the Laplacian image (generated in Step 8) for determining theamplitudinal distances ‫ܨ‬஺_௅௔௣ሾ௖,௠ሿ for BLap, which is given as: ࡲ࡭ሾࢉ,࢓ሿ ࡲ࡭_ࡸࢇ࢖ሾࢉ,࢓ሿ ൌ ࣌ࡸࢇ࢖ (21)Compute the spatial distance using the domain filter ‫ܨ‬ௌሾ௖,௠ሿ for the noisy image with block ࢉ૛B ‫ࡿࡲ.ݔ א‬ሾࢉ,࢓ሿ ൌ ࢋ࢞࢖ ቄെ ૛ሺ࣌ ቅ ࢙ሻ ૛ (22)Combine the two filters ‫ܨ‬஺_௅௔௣ሾ௖,௠ሿ and ‫ܨ‬ௌሾ௖,௠ሿ to create a local filter ‫ܨ‬ሾ௖,௠ሿ . ࡲሾࢉ,࢓ሿ ൌ ࡲࡿሾࢉ,࢓ሿ ‫࢖ࢇࡸ_࡭ࡲ כ‬ሾࢉ,࢓ሿ (23)The modified bilateral filter is now defined as: ෢ ૚ ࢌሾࢉሿ ൌ ∑శࡹ ࡲ ∑ࢉୀ ିࡹሺࡲሾࢉ,࢓ሿ ࡺሾࢉି࢓ሿሻ ାࡹ (24) ࢉస షࡹ ሾࢉ,࢓ሿ4. RESULTS AND DISCUSSIONS 4.1. CONFIGURATION In this section we compare the performance of our proposed approach (PA) with otherstandard noise reduction filters. Some of the test images that we have used are as shown in Fig. 4. The performance ofthe proposed algorithm is tested for various levels of noise (with standard deviation varyingfrom 5 to 40) and the results are compared with standard filters like Gaussian filter [3],bilateral filter [4] and Wigner filter [6]. In addition to the visual quality, the performance ofthe proposed algorithm and other standard algorithms are quantitatively measured. Leaves Flower Lena . Baboon Barbara Fig. 4: Test Images 118
  • 8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME All the filters are implemented in MATLAB 7.1. The filtering window used forGaussian filter and bilateral filter is of size 5×5 and that for Wigner filter is 7×7. 4.2. DENOISING PROPERTY The denoising performance of the proposed algorithm and other standard methods aretested for gray scale images. In order to quantitatively evaluate the performance of ourapproach we have used two metrics, Mean Square error (MSE) and Peak Signal to NoiseRatio (PSNR). ૚ ૛ MSE ൌ ‫ିܕ∑ ܖכܕ‬૚ ∑‫ିܖ‬૚ൣ۷ሺܑ,‫ܒ‬ሻ െ ۹ሺܑ,‫ܒ‬ሻ൧ ܑୀ૙ ‫ܒ‬ୀ૙ ሻ ሻ (25) ࡹ࡭ࢄ૛ ࡵ ࡼࡿࡺࡾ ൌ ૚૙. ࢒࢕ࢍ૚૙ ࡹࡿࡱ ࡹ࡭ࢄࡵ ൌ ૛૙. ࢒࢕ࢍ૚૙ √ࡹࡿࡱ (26) Where, m×n = size of the image MAXI = maximum intensity value of the image I = noise free original image K = noisy test image The results of the proposed algorithm are presented in the Fig. 5 and Fig. 6. (a) (b) (c) (d) (e) (f) Fig. 5: (a) Input Image (b) Noisy image (σ =30) (c) Gaussian Filter output (d) Proposed approach output (e) Bilateral Filter output (f) Wigner Filter output 119
  • 9. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME (a) (b) (c) (d) (e) (f) Fig. 6: (a) Input Image (b) Image with high noise (σ =40) (c) Gaussian Filter output (d) Proposed approach output (e) Bilateral Filter output (f) Wigner Filter output The quantitative performance in terms of PSNR and MSE with different values of sigmafor mentioned standard filters and the proposed approach are shown in Fig. 7, Fig. 8, Fig. 9and Fig. 10. Fig. 7: Comparison of MSE of [3], [4] and PA for test images with σ = 10 120
  • 10. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Fig. 8: Comparison of PSNR of [3], [4], [6] and PA for test images with σ = 10 Comparision of MSE for test images with σ =20 4.50E+02 4.00E+02 Mean Square Error (MSE) 3.50E+02 3.00E+02 2.50E+02 LEAVES 2.00E+02 FLOWER 1.50E+02 LENA 1.00E+02 BARBARA 5.00E+01 BABOON 0.00E+00 Noisy Gaussian Bilateral Proposed Approach Noise Reduction method Fig. 9: Comparison of MSE of [3], [4] and PA for test images with σ = 20 121
  • 11. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME Comparision of PSNR for test images with σ =20 Peak Signal to Noise Ratio (PSNR) 30 25 20 LEAVES 15 FLOWER 10 LENA 5 BARBARA BABOON 0 Noisy Wigner Gaussian Bilateral Proposed Approach Noise Reduction method Fig. 10: Comparison of PSNR of [3], [4], [6] and PA for test images with σ = 20 4.3. EDGE RETENTION Fig. 11 shows the comparison and analysis of the proposed approach and other standard filters for edge preservation. (a) (b) (c) (d) (e) (f) Fig. 11: (a) Input Image (b) Noisy image (σ =20) (c) Gaussian Filter output (d) Proposed approach output (e) Bilateral Filter output (f) Wigner Filter output 122
  • 12. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME In the Fig. 11, we can notice that the edges are better preserved in our proposedalgorithm as compared to methods proposed in [3], [4] and [6]. For instance the fine edges ofthe hat are retained more precisely in 4(d) than in 4(c), 4(e), 4(f). The quantitative edge retention performance of the proposed approach (PA) and [3],[4], [6] is shown in Table I in terms of percentage of Edge Preserved factor (EP), Edge Lostfactor (EL), False Edge factor (FE) and number of Edges Not Match (ENM) with respect tothe edges present in the original image. The EP, EL and FE tests are performed by “pixel to pixel” comparison of the originalinput image and the filtered output image. The edge at a particular pixel position in theoriginal input image is being matched with that of the processed image. If an edge existsthere then, it’s considered as edge preserved else the edge is lost. And if there exist an edge ata particular pixel position in the processed image but there does not exist a correspondingedge at that particular pixel position in the original image then, we consider it as false edge. The constraint behind “pixel to pixel matching” method is that it does not hold good ifthere is any pixel shifting for the processed output image. Therefore, in order to obtain aproper quantitative result for edge preservation, we have proposed an approach where we firstestimate the number of edges that do not match (ENM) in the processed image with respect tothe original image for a particular pixel position. Taking into consideration the pixel shift, wethen consider the 8 neighbours of the pixel. If there is an edge found in this eight neighboursof the pixel, it is regarded as the sought after pixel and is marked so that the same edge is notaccounted for the next consideration. Thus, this approach assists in determining the numberof edges preserved in the processed output image with respect to the original image. Table I. Comparison of percentage of EP, EL, FE and ENM of [3], [4], [6] and PA for σ =5 and σ =15 of test images 123
  • 13. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 1, January- February (2013), © IAEME As seen in Table I, the Edge Preserving factor (EP) of the proposed algorithm ishigher than those in [3], [4], and [6]. At the same time, the Edge Lost factor (EL) and theFalse Edge factor (FE) is low for the proposed approach. Moreover, the number of Edges notmatched (ENM) is low for the proposed method. All this, along with the fact that the MSE islow and the PSNR is high substantiates the enhanced performance of the proposed algorithmboth in terms of noise removal as well as edge retention.5. CONCLUSION The proposed noise estimation technique performs well for images with wide range ofnoise deviation and also gives encouraging results for noisy images that have inherent highfrequency or textured regions in it. The proposed approach removes Gaussian noise with edgepreservation for a wide range of Gaussian noise corrupted images and has improvedperformances in terms of MSE and PSNR. Experimental results show that the proposedmethod also preserves better the fine details of the processed image as compared to thestandard Gaussian filter, bilateral filter and Wigner filter. This approach can be easilyextended to color images as well.REFERENCES[1] V.R.Vijaykumar, P.T.Vanathi, P.Kanagasabapathy, Fast and Efficient Algorithm to Remove Gaussian Noise in Digital Images, IAENG International Journal of Computer Science, 37:1, IJCS_37_1_09, Feb 2010.[2] A.K.Jain, “Fundamentals of Digital Image Processing”, Prentice Hall, Englewood cliffs, 1989.[3] Gonzalez and woods,” Digital image Processing”, Prentice Hall, 2nd edition, 2001.[4] C.Tomasi, R.Manduchi, “Bilateral Filtering for Gray and Colour Images”, Proceedings of 1998 IEEE International Conference on Computer Vision, Bombay, India.[5] Krishnan Kutty, Swati Ojha, “A Generic Transfer Function Based Technique for Noise Estimation”, IJCA Journal, Volume 51- Number 10, 2012.[6] Padole, C.N.; Vaidya, V.G.; "Image restoration using Wigner distribution for night vision system" 9th Int. Conf. on Signal Processing, 2008. ICSP 2008. Page(s): 844 - 848[7] Vinay Vaidya, C Padole," Night Vision Enhancement using Wigner Distribution", IEEE 3rd International Symposium on Communications, Control and Signal Processing, 2008., ISCCSP2008, March, pp 1268-1272[8] M. Elad, “On the origin of the bilateral filter and ways to improve it”, IEEE Trans. Image Process. 11 (10) (2002) 1141–1151.[9] Mr. J.Rajarajan and Dr. G.Kalivarathan, “Influence Of Local Segmentation In The Context Of Digital Image Processing – A Feasibility Study” International journal of Computer Engineering & Technology (IJCET), Volume 3, Issue 3, 2010, pp. 340 - 347, Published by IAEME. 124