A NOVEL APPROACH FOR IMAGE DE- NOISING USING WAVELETS

Transcription

1 A NOVEL APPROACH FOR IMAGE DE- NOISING USING WAVELETS Tajinder Singh 1, Rajeev Bedi 2 1,2 Beant College of Engineering & Technology, Gurdaspur. Abstract: Wavelet thresholding is an admired move toward the de-noising, due to its unfussiness. This procedure operates in the orthogonal wavelet domain, where every coefficient is thresholded by comparing adjacent to a threshold. Because the information, which is transmitted in the form of digital images, is obsequious for Visual information, which is becoming a major means of communication in the recent era. But the image obtain after diffusion is often tarnished with noise. The received image demands processing before it can be used in applications. Image de-noising involves the manipulation of the image data to construct a visually high quality image. This p a p e r d e f i n e d a p r o p o s e d a p p r o a c h f o r i m a g e d e - n o i s i n g a n d the existing de-noising algorithms, such as Donoho Soft & Hard Thresholding De-noising, Standard wavelet de-noising, Baysian Thresholding de-noising, Bayes Shrinkage De-noising, and BLS De-noising for their comparative study. A quantitative measure of comparison is provided by the different parameter such as PSNR, MSE, and MAE of the image. By implementing the proposed approached we capture less time complexity as compare to the existing techniques having better result for MSE, MAE & PSNR. Keywords: De-noising, thresholding, SAR, symlet, PSNR, MSE, MAE. 1. INTRODUCTION is undesired information that contaminates the image. is present in an image either in an additive or multiplicative form. An additive noise follows the rule w( x, y) = s( x, y) + n( x, y), While the multiplicative noise satisfies, w( x, y) = s( x, y) * n( x, y), where s(x,y) is the original signal, n(x,y) denotes the noise introduced into the signal to produce the corrupted image w(x,y), and (x,y) represents the pixel location. The above image algebra is done at pixel level. By image multiplication, we mean the brightness of the image is speckled. 2. TYPES OF NOISE 2.1 Gaussian Gaussian noise is evenly scattered over the signal. This means that each pixel in the noisy image is the sum of the true pixel value and a random Gaussian distributed noise value. As the name indicates, this type of noise has a Gaussian distribution, which has a bell shaped probability distribution function given by Volume 2, Issue 2 March April 2013 Page 35 F g Figure 1 Gaussian distribution Where g represent the gray level, m is the mean or average of the function and σ is the standard deviation of the noise. Graphically, it is represented as shown in Figure 2.1. When introduced into an image, Gaussian noise with zero mean and variance as 0.05 would look as in Figure Salt and Pepper Salt and pepper noise is an impulse variety of noise, which is also referred to as intensity spikes. This is caused usually due to errors in data transmission. It has only two possible values, a and b. The probability of each is characteristically less than 0.1. The corrupted pixels are set alternatively to the minimum or to the maximum value, giving the image a salt and pepper like manifestation. Unaffected pixels remain unbothered. For an 8-bit image, the typical value for pepper noise is 0 and for salt noise 255. The salt and pepper noise is generally caused by faulty of pixel elements in the camera sensors, faulty memory locations, or timing errors in the digitization process. The probability density function for this type of noise is shown in Figure 2. Figure 2 Probability Density Function

2 2.3 Speckle Speckle noise is a multiplicative noise. This type of noise occurs in almost all coherent imaging systems such as laser, acoustics and SAR (Synthetic Aperture Radar) descriptions. The source of this noise is attributed to random interference between the coherent returns. Fully developed speckle noise has the characteristic of multiplicative noise. Speckle noise follows a gamma distribution and is given as Where variance is a 2 α and g is the gray level. On an image, speckle noise (with variance 0.05) looks as shown in Fig 2.4 [Im01]. The gamma distribution is given below in Figure.3. energy does not. It is this important principle that enables the separation of signal from noise. The procedure in which small coefficients are removed while others are left untouched is called Hard Thresholding [5]. But the hard thresholding includes some demerits so to overcome the demerits of hard thresholding, wavelet transform using soft thresholding was also introduced in [5]. In this scheme, coefficients above the threshold are shrunk by the absolute value of the threshold itself. Similar to soft thresholding, other techniques of applying thresholds are semi-soft thresholding and Garrote thresholding [6]. Most of the wavelet shrinkage literature is based on methods for choosing the optimal threshold which can be adaptive or non-adaptive to the image. Figure 3 Gamma Distribution 3. WAVELET DOMAIN 3.1 Filters In wavelet Filtering progression can be separated in two categories Linear nlinear Linear Filters Linear filters such as Wiener filter in the wavelet domain give up optimal results when the signal corruption can be modeled as a Gaussian process and the accuracy measure is the mean square error (MSE) [14, 15]. However, scheming a filter based on this assumption frequently results in a filtered image that is more visually displeasing than the original noisy signal, even though the filtering operation successfully reduces the MSE. n-linear Threshold Filtering The most investigated domain in de-noising using Wavelet Transform is the non-linear coefficient thresholding based methods. The procedure exploits sparsity property of the wavelet transform and the fact that the Wavelet Transform maps white noise in the signal domain to white noise in the transform domain. Thus, while signal energy becomes more concentrated into fewer coefficients in the transform domain, noise Figure 4 Image De-noising Methods 4. ROLE OF FILTERS IN IMAGE DE-NOISING Filters play a major role in the image restoration process. Let w(x) be the input signal subjected to filtering, and z(x) be the filtered output. If the filter satisfies certain conditions such as linearity and shift invariance, then the output filter can be expressed mathematically in simple form as z(x) = w(t)h(x t)dt (1) where h(t) is called the point spread function or impulse response and is a function that completely characterizes the filter. For a discrete case, the integral turns into a summation as z(i)= (2) Although the limits on the summation in Equation (2) are, the function h(t) is usually zero outside some range. If Volume 2, Issue 2 March April 2013 Page 36

3 the range over which h(t) is non-zero is (-k, +k), then the above Equation (2) can be written as z(i)= (3) This means that the output z(i) at point i is given by a weighted sum of input pixels surrounding i where the weights are given by h(t). To create the output at the next pixel i+1, the function h(t) is shifted by one and the weighted sum is recomputed. The total output is created by a series of shift-multiply-sum operations, and this forms a discrete convolution. For the 2-dimensional case, h(t) is h(t,u), and Equation (3) becomes z(i, j)= (4) Values of h(t,u) are referred to as the filter weights, the filter kernel, or filter mask. For reasons of symmetry h(t,u) is always chosen to be of size m n where m and n are both odd (often m=n). In physical systems, the kernel h(t,u) must always be non-negative which results in some blurring or averaging of the image. If the coefficients are alternating positive and negative, the mask is a filter that returns edge information only. 5. WAVELET DE-NOISING In wavelet De-noising firstly apply Discrete Wavelet Transform using Standard wavelet symlet upto 2 level decomposition which is as shown in Fig 5(a). 2. Different types of s are introduced into the original image. Such as Salt and Pepper, Speckle and Gaussian. Various De-noising techniques like Donoho (Hard & Soft Thresholding), BLS, along with proposed method is applied to the test image. 3. For the verifications of result a comparative study between various De-noising methods is made which is based upon two performance metrics namely Peak Signal to Ratio (PSNR) and Mean Square error(mse), Mean Absolute Error(MAE), Simulation ( ). 7. RESULT AND DISCUSSIONS (SALT AND PEPPER NOISE) Figure 6 Original Image Figure 5(a) Lena: Original Image Figure 6.1 isy version of Camera man Figure 5(b) Lena: Two-Level Decomposition of DWT by Symlet 6. PROPOSED APPROACH 1. First of all a image is randomly selected from a data base of 4-5 images. Figure 6.2 De-d by using Wavelet David Donoho Soft Thresholding De-ising, Type= Salt and Pepper = 0.1 Volume 2, Issue 2 March April 2013 Page 37

4 Figure 6.3 De-d by using Wavelet David Donoho Hard Thresholding De-ising, Type= Salt and Pepper = 0.1 Figure 6.7 BLS De-ising, Type= Salt and Pepper = 0.1 Figure 6.4 De-d by using Wavelet Thresholding, Type= Salt and Pepper = 0.1 Figure 6.8 Proposed Approach. Type= Salt and Pepper = SIMULATION RESULTS 8.1 MSE (Mean Square Error) Figure 6.5 Basian De-ising,. Type= Salt and Pepper = 0.1 Figure 6.6 Bayes Shrinkage De-ising, Type= Salt and Pepper = 0.1 Figure 7 MSE Representation ( Standard Deviation for Salt and Pepper OF Cameraman 256X256) In figure the MSE (Mean Square Error) is calculated w.r.t standard deviation of Salt and Ppepper noise applied to the noiseless image. It is very clear from the plot the significant improvement in MSE value which is obtained with the use of proposed technique over the other techniques which is already explained in the above section of paper. Volume 2, Issue 2 March April 2013 Page 38

5 8.2 PSNR (Peak Signal to Ratio) Representation Table 1 PSNR, MSE,MAE, for Salt and pepper. Donoho Soft Thresholding Table 2 PSNR, MSE,MAE, for Salt and pepper. Figure 8 PSNR (in db) Vs Standard deviation Factor for Cameraman(256x256) image In figure PSNR is calculated w.r.t standard deviation of salt and pepper noise applied to the noiseless image. It is very clear from the plot the significant improvement in PSNR value that is obtained with the use of proposed technique over the other techniques. 8.3 Graphical Representation of MAE (Mean Average Error) In figure differentiate the Existing approach and proposed approach where MAE is calculated w.r.t standard deviation of salt and pepper noise applied to the noiseless image. It is very clear from the plot the significant improvement in MAE value that is obtained with the use of proposed technique over the other techniques Donoho Hard Thresholding Table 3 PSNR, MSE,MAE, for Salt and pepper. Sr. N o Standard Wavelet Thresholding Complexit y Table 4 PSNR, MSE,MAE, for Salt and pepper. Figure 9 MAE Vs Standard deviation Factor for Cameraman(256x256) image 9. PROPOSED APPROACH VS EXISTING APPROACHES NOISE VARIANCE Bayes Shrinkage Denoising Volume 2, Issue 2 March April 2013 Page 39

6 Table 5 PSNR, MSE,MAE, for Salt and pepper BLS De-noising Table 6 PSNR, MSE,MAE, for Salt and pepper Basian Thresholding Table 7 PSNR, MSE,MAE, for Salt and pepper CONCLUSION Proposed Approach From the investigational and mathematical results it can be concluded that for salt and pepper noise (Speckle and Gaussian as well), the median filter is optimal compared to Mean Filter and LMS adaptive filter. It produces the ceiling SNR for the output image compared to the linear filters considered. The LMS adaptive filter proves to be better than the mean filter but has more time complexity. From the output images shown in above given results the image obtained from the modified median filter gives a fine quality of image which is close to the high quality image. Denoising salt and pepper noise using proposed method has proved to be efficient due to adaptive median filter used in it. It does a superior job in de-noising images that are highly irregular and are corrupted with noise that has a complex nature. We conclude that the proposed approach gives the paramount results as PSNR(Peak Signal to Ratio), MSE (Mean Square Error), MAR(Mean Average Error) and complexity has been improved as compare to the Existing approaches FUTURE SCOPE As future research, we would like to work further on the comparison of the de-noising techniques on color images as well. It can also be extended in which the denoised signals can be fed into Neural Networks pattern reorganization as well. By this way, rate of successful classification should determine the ultimate measure by which to compare various de-noising procedures. These two points would be considered as an extension to the present work done. REFERENCES [1] Aliaa A.A.Youssif Adaptive Algorithm for Image Denoising Based on Curvelet Threshold IJCSNS International Journal of Computer Science and Network Security, VOL.10.1, January [2] A. Buades, B. Coll, and J. Morel, Neighborhood Filters and PDE s, Numerische Mathematik, 105,. 1,pp. 1-34,2006. [3] A.Pizurica, W.Philips, I.Lemahieu, and M.Acheroy, A joint inter- and intrascale statistical model for bayesian wavelet based image denoising," IEEE Trans. on ImageProc., vol. 11, no. 5, pp , [4] Babak Nasersharif, Ahmad Akbari, Application of Wavelet Transform and Wavelet Thresholding in Robust Subband Speech Recognition, 12th European Signal Processing Conferences (EUSIPCO), pp , 2004,Vienna,Austria. [5] G.Fan and X.Xia, Wavelet-based texture analysis and synthesis using hidden markov models," IEEE Trans. Circuits and Systems I: Fundamental theory and applications, vol. 50, no. 1, pp , [6] J.L.Starck, E.J.Candes, and D.L.Donoho, The curvelet transform for image denoising," IEEE Trans. on Image Proc., vol. 11, no. 6, pp , [7] J.Portilla, V.Strela, M.Wainwright, and E.Simoncelli, Image denoising using scale mixtures of gaussians in the wavelet domain," IEEE Trans. Image Proc., vol. 12, no. 11, pp , [8] Kashif Rajpoot, Nasir Rajpoot and J. Alison ble, Discrete Wavelet Diffusion for Image Denoising IEEE Transactions on Pattern Analysis and Machine Intelligence, vol Volume 2, Issue 2 March April 2013 Page 40

7 [9] Mukesh C. Motwani, Mukesh C. Gadiya, Rakhi C. Motwani, Frederick C. Harris, Jr, (2004) Survey of Image Denoising Techniques, Proc. of GSPx 2004, Santa Clara Convention Center, Santa Clara, CA, pp Engineering and currently one of the potential emerging areas Cloud Computing. [10] N.Kingsbury, Image processing with complex wavelets," Phil. Trans. Royal Society London A, vol. 357, pp ,1999. [11] Pankaj Hedaoo and Swati S Godbole, Wavelet Thresholding Approach For Image Denoising, International Journal of Network Security & Its Applications (IJNSA), Vol.3,.4, pp , [12] Rong Bai, Wavelet Shrinkage Based Image Denoising Using Soft Computing, Thesis for Master of Applied Science in University of Waterloo, Waterloo, Ontario, Canada [13] Rudra Pratap Singh Chauhan, A vel Approach To Overcome The Intertwined Shortcomings Of DWT for Image Processing and De-ising International Journal of Engineering Research and Applications (IJERA) ISSN: [14] S.G. Chang, Y. Bin, and M. Vetterli, Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Trans. on Image Proc., vol. 9, no. 9, pp , [15] S.G. Chang, Y. Bin, and M. Vetterli, Adaptive wavelet thresholding for image denoising and compression," IEEE Trans. on Image Proc., vol. 9, no. 9, pp {1531, Tajinder Singh received his bachelor s Degree in Information Technology (IT) from PTU, Jalandhar, Punjab (India) in 2009, and pursuing master degree in CSE from Punjab Technical University Jalandhar, Punjab, India. His research interest includes Software Engineering, Digital Image processing especially in Image De-noising, Image segmentation & Enhancement. Rajeev Bedi received his bachelor s Degree in Computer Science & Engineering (CSE) from Punjab Technical University, Jalandhar, Punjab (India) in 2000, and his master degree in Computer Science & Engineering (CSE) from Punjab Technical University, Jalandhar, Punjab (India) in 2000, and his master degree in Computer Science & Engineering (CSE) from Punjab Technical University, Jalandhar, Punjab (India) in He is currently working as Assistant Professor in Computer Science and Engineering (CSE) department of Beant College of Engineering & Technology, Gurdaspur, Punjab, (India). His area of interest includes Programming Languages,.NET Technologies, Software Volume 2, Issue 2 March April 2013 Page 41