IMAGE DENOISING USING WAVELETS

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1 IMAGE DENOISING USING WAVELETS Aashish Singhal 1, Mr. Diwaker Mourya 2 1 Student M.Tech, JBIT, Dehradun (U.K) 2 Assistant Professor JBIT, Dehradun (UK) 1 aashish.singhal1@yahoo.com Abstract- Image denoising involves the manipulation of the image data to produce a visually high quality image. This report reviews the existing denoising algorithms, such as filtering approach and wavelet based approach, and performs their comparative study. Different noise models including additive and multiplicative types are used. They include Gaussian noise, salt and pepper noise and speckle noise. Selection of the denoising algorithm is application dependent. Hence, it is necessary to have knowledge about the noise present in the image so as to select the appropriate denoising algorithm. The filtering approach has been proved to be the best when the image is corrupted with salt and pepper noise. The wavelet based approach finds applications in denoising images corrupted with Gaussian noise. A quantitative measure of comparison is provided by the PSNR (peak signal to noise ratio) of the image. This report aims to let the reader understand the project work which I have done. Keywords: - GGD, DWT, PSNR, CPU, Coif5 I. INTRODUCTION A. Preliminaries: A very large portion of digital image processing is devoted to image restoration. This includes research in algorithm development and routine goal oriented image processing. Image restoration is the removal or reduction of degradations that are incurred while the image is being obtained [2]. Degradation comes from blurring as well as noise due to electronic and photometric sources. Blurring is a form of bandwidth reduction of the image caused by the imperfect image formation process such as relative motion between the camera and the original scene or by an optical system that is out of focus [10]. When aerial photographs are produced for remote sensing purposes, blurs are introduced by atmospheric turbulence, aberrations in the optical system and relative motion between camera and ground. In addition to these blurring effects, the recorded image is corrupted by noises too. A noise is introduced in the transmission medium due to a noisy channel, errors during the measurement process and during quantization of the data for digital storage. Each element in the imaging chain such as lenses, film, digitizer, etc. contributes to the degradation. B. Digital Images: Let us now consider the representation of a digital image. A 2-dimensional digital image can be represented as a 2-dimensional array of data s(x,y), where (x,y) represent the pixel location. The pixel value corresponds to the brightness of the image at location (x,y). Some of the most frequently used image types are binary, gray-scale and color images. Binary images are the simplest type of images and can take only two discrete values, black and white. Black is represented with the value 0 while white with 1. Note that a binary image is generally created from a gray-scale image. A binary image finds applications in computer vision areas where the general shape or outline information of the image is needed. They are also referred to as 1 bit/pixel images. Gray-scale images are known as monochrome or one-color images. The images used for experimentation purposes in this thesis are all gray-scale images. They contain no color information. They represent the brightness of the image. This image contains 8 bits/pixel data, which means it can have up to 256 (0-255) different brightness levels. A 0 represents black and 255 denotes white. In between values from 1 to 254 represent the different gray levels. As they contain the intensity information, they are also referred to as intensity images. Color images are considered as three band monochrome images, where each band is of a different color. Each band provides the brightness information of the corresponding spectral band. Typical color images are red, green and blue images and are also referred to as RGB images. This is a 24 bits/pixel image. 171

2 C. Image Denoising: Image denoising is often used in the field of photography or publishing where an image was somehow degraded but needs to be improved before it can be printed. For this type of application we need to know something about the degradation process in order to develop a model for it. When we have a model for the degradation process, the inverse process can be applied to the image to restore it back to the original form. This type of image restoration is often used in space exploration to help eliminate artifacts generated by mechanical jitter in a spacecraft or to compensate for distortion in the optical system of a telescope. Image denoising finds applications in fields such as astronomy where the resolution limitations are severe, in medical imaging where the physical requirements for science where potentially useful photographic evidence is sometimes of extremely bad quality [10]. II. LITERATURE SURVEY 1. Wavelet Based Image Denoising Technique: Sachin D Ruikar (2011) In this paper, we extend the existing technique and providing a comprehensive evaluation of the proposed method. Results based on different noise, such as Gaussian, Poisson s, Salt and Pepper, and Speckle performed in this paper. A signal to noise ratio as a measure of the quality of denoising was preferred. 2. De -noising Of Image and Its Performance Evaluation: Karamveer Kaur Uppal1, Ashwani Kumar2(2014) The most important task in image processing is denoising the image. Lots of research is conducted in this era but the compelling challenge in this field is to get the efficient denoised image.in this paper three noises are added to the image one by one and then denoised with the bayes shrink and vishu shrink. Different authors had proposed the simple formulas for these methods. Comparison of both filters wih effect of noise is done using the various image matrics such as BER,MSE,PSNR.The filters are impleted on the matlab (R2012a). 3. Wavelet Estimators in Nonparametric Regression, A Comparative Simulation Study: Anestis Antoniadis, Jeremie Bigot(2001) We compare various estimators in an extensive simulation study on a variety of sample sizes, test functions, signal-to-noise ratios and wavelet filters. Because there is no single criterion that can adequately summarise the behaviour of an estimator, we use various criteria to measure performance in finite sample situations. Insight into the performance of these estimators is obtained from graphical outputs and numerical tables. In order to provide some hints of how these estimators should be used to analyse real-life data sets, a detailed practical step-by-step illustration of a wavelet denoising analysis on electrical consumption is provided. Matlab codes are provided so that all figures and tables in this paper can be reproduced. 4. Image de-noising using wavelets: J. N. Ellinas, T. Mandadelis, A. Tzortzis, L. Aslanoglou(2011) In this paper, we propose an adaptive method of image de-noising in the wavelet subband domain. This approach is based on threshold estimation for each subband of the wavelet decomposition of a noise-contaminated image, by considering that the subband coefficients have a Generalized Gaussian Distribution (GGD). Under this framework, the proposed technique estimates the threshold level by applying a robust median estimator on either all the detail coefficients or every detail subband of each decomposition level. 5. Comparative Performance Analysis of Image Denoising Techniques: Vivek Kumar, Pranay Yadav, Atul Samadhiya, Sandeep Jain, and Prayag Tiwari(2013) Objective of this paper is to present brief account on types of noises, its types and different noise removal algorithms. In the first section types of noises 172

3 on the basis of their additive and multiplicative nature are being discussed. In second section a precise classification and analysis of the different potential image denoising algorithm is presented. At the end of paper, a comparative study of all these algorithms in context of performance evaluation is done and concluded with several promising directions for future research work. 6. Image Denoising using Wavelet Thresholding: Lakhwinder Kaur Savita Gupta R.C. Chauhan(2010). In this paper, a near optimal threshold estimation technique for image denoising is proposed which is subband dependent i.e. the parameters for computing the threshold are estimated from the observed data, one set for each subband. The paper is organized as follows. Section 2 introduces the concept of wavelet thresholding. Section 3 explains the parameter estimation for Normal Shrink. Section 4 describes the proposed denoising algorithm. Experimental results & discussions are given in section 5 for three test images at various noise levels. Finally the concluding remarks are given in section Survey on Prevention of Black Hole Nodes in Mobile Adhoc Networks: Puja vij, V. K. Banga, TanuPreet Singh (2012). This paper states that a wireless Adhoc network is a collection of mobile nodes with no pre-established infrastructure, forming a temporary network. In the absence of a fixed infrastructure, nodes have to cooperate in order to provide the necessary network functionality. III. PROPOSED ALGORITHM 1. Discrete Wavelet Transform (DWT) Principles: Wavelets are mathematical functions that analyze data according to scale or resolution. They aid in studying a signal in different windows or at different resolutions. For instance, if the signal is viewed in a large window, gross features can be noticed, but if viewed in a small window, only small features can be noticed. The term wavelets is used to refer to a set of orthonormal basis functions generated by dilation and translation of scaling function φ and a mother wavelet ψ [1]. The finite scale multiresolution representation of a discrete function can be called as a discrete wavelet transforms [27]. DWT is a fast linear operation on a data vector, whose length is an integer power of 2. This transform is invertible and orthogonal, where the inverse transform expressed as a matrix is the transpose of the transform matrix. The wavelet basis or function, unlike sines and cosines as in Fourier transform, is quite localized in space. But similar to sines and cosines, individual wavelet functions are localized in frequency. 2. Wavelet Thresholding: Donoho and Johnstone [4] pioneered the work on filtering of additive Gaussian noise using wavelet thresholding. From their properties and behavior, wavelets play a major role in image compression and image denoising. Since our topic of interest is image denoising, the latter application is discussed in detail. Wavelet coefficients calculated by a wavelet transform represent change in the time series at a particular resolution. By considering the time series at various resolutions, it is then possible to filter out noise. 3. Mean Filter: A mean filter [22] acts on an image by smoothing it; that is, it reduces the intensity variation between adjacent pixels. The mean filter is nothing but a simple sliding window spatial filter that replaces the center value in the window with the average of all the neighboring pixel values including it. By doing this, it replaces pixels that are unrepresentative of their surroundings. It is implemented with a convolution mask, which provides a result that is a weighted sum of the values of a pixel and its neighbors. It is also called a linear filter. The mask or k=ernel is a square. Often a 3 3 square kernel is used. If the coefficients of the 173

4 mask sum up to one, then the average brightness of the image is not changed. If the coefficients sum to zero, the average brightness is lost, and it returns a dark image. The mean or average filter works on the shift-multiply-sum principle. 4. Median Filter: A median filter belongs to the class of nonlinear filters unlike the mean filter. The median filter also follows the moving window principle similar to the mean filter. A 3 3, 5 5, or 7 7 kernel of pixels is scanned over pixel matrix of the entire image. The median of the pixel values in the window is computed, and the center pixel of the window is replaced with the computed median. Median filtering is done by, first sorting all the pixel values from the surrounding neighborhood into numerical order and then replacing the pixel being considered with the middle pixel value. Note that the median value must be written to a separate array or buffer so that the results are not corrupted as the process is performed. Figure 3.6 illustrates the methodology. III. CONCLUSION AND FUTURE WORK From the experimental and mathematical results it can be concluded that PSNR is basically a comparison between original and de-noised image as how the de-noised image is close to original image. For Gaussian Noise- Coif5 and bior6.8 wavelets results high PSNR against haar, db10, sym4 wavelets and wiener filter for Smooth images. For Textured images Coif5 and sym4 gives best results. Smooth images results high PSNR against Textured images. Decomposition level 4 is the saturation level for Smooth images. For Textured images if sigma is low(८=10,15,20), level 1 decomposition results high PSNR but for large value of sigma ८=(30,35,40), level 2 decomposition gives high PSNR. Bal. Sparity Norm Thresholding results high PSNR against Fixed Form Thresholding. Level dependent Thresholding best PSNR in comparison with Global Thresholding. It can also concluded that for salt and pepper noise, the median filter is optimal compared to mean filter and Weiner filter. It produces the maximum PSNR for the output image compared to the linear filters considered. The Weiner filter proves to be better than the mean filter but has more time complexity. In the case where an image is corrupted with Gaussian noise, the wavelet shrinkage denoising has proved to be nearly optimal. Since selection of the right denoising procedure plays a major role, it is important to experiment and compare the methods. As future research, we would like to work further on the comparison of the denoising techniques. If the features of the denoised signal are fed into a neural network pattern recognizer, then the rate of successful classification should determine the ultimate measure by which to compare various denoising procedures [19]. Besides, the complexity of the algorithms can be measured according to the CPU computing time flops. This can produce a time complexity standard for each algorithm. These two points would be considered as an extension to the present work done. IV. REFERENCES [1] Anestis Antoniadis, Jeremie Bigot, Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study, Journal of Statistical Software, Vol 6, I 06, [2] Castleman Kenneth R, Digital Image Processing, Prentice Hall, New Jersey, [3] David L. Donoho, De-noising by soft-thresholding, stanford.eduzszreportszszdonohozszdenoiserelease3.pdf/donoho94de noising.pdf, Dept of Statistics, Stanford University, [4] David L. Donoho and Iain M. Johnstone, Adapting to Unknown Smoothness via Wavelet Shrinkage, Journal of American Statistical Association, 90(432): , December [5] 1/f noise, Brownian Noise, [6] Langis Gagnon, Wavelet Filtering of Speckle Noise-Some Numerical Results, Proceedings of the Conference Vision Interface 1999, Trois- Riveres. 174

5 [7] Amara Graps, An Introduction to Wavelets, IEEE Computational Science and Engineering, summer 1995, Vol 2, No. 2. [8] David Harte, Multifractals Theory and applications, Chapman and Hall/CRC, New York, [9] Matlab 7.8, Image Processing Toolbox, shtml [16] C. Schmid and R. Mohr, Local grayvalue invariants for image retrieval, IEEE Trans on PAMI, Vol. 19, No. 5, pp , May [10] Reginald L. Lagendijk, Jan Biemond, Iterative Identification and Restoration of Images, Kulwer Academic, Boston,