Image De-noising using Double Density Discrete Wavelet Transform& Median Filtering

Image De-noising using Double Density Discrete Wavelet Transform& Median Filtering 2 NARAYAN DEV GUPTA 1, DEVANAND BHONSLE 2 1 ME Student, Department of ET&T, SSCET Bhilai, India Senior Assistant Professor, Department of EEE, SSCET Bhilai, India Abstract Noise affects images during transmission or processing. The quality of image is affected by noise so to retain the quality of image an operation is performed that is called de-noising. De-noising basically deals with the removal of noise from noise contaminated version of image. There are different method of image de-noising depend upon the noise that is present in the image. This paper presents image de-noising method that is based on double density discrete wavelet transform and median filtering. In this paper we presents different types of noise that can affect the image.when image is corrupted with Gaussian noise then double density discrete wavelet transform outperform the best and when image is corrupted with salt and paper noise then median filtering approach gives better result. In this proposed algorithm a new hybrid method is used to remove mixed noise and proposed method gives better result in terms of MSE, PSNR and SSIM. Keywords Image De-noising, Image Noise, Median Filter, Wavelet Domain De-noising, Image Decomposition, Wavelet Threshold I. INTRODUCTION The critical issue in image processing is restoration of image in noisy environment. When noise introduced in the image then pixel value get altered from its actual value that do not demonstrate true intensity of real scene. The process that deals with the manipulation of image data to produce high class image is called image de-noising. The image de-noising method can be classified in two categories that is spatial filtering method and transform domain method.in spatial filtering method we use a low pass filter on group of pixel in the image with pre-emption that noise affects higher frequency band of the spectrum. The spatial domain filtering method removes noise from the image but it also blur the image due to which edges became invisible. While the highpass filters can make edges even sharper and enhance the spatial resolution but will also amplify. There is a trade-off between the signal to noise ratio and spatial resolution of signal/image processed when we used Fourier transform domain filtering. When we used fast fourier transform for de-noising then edges in the de-noised image is not as sharp as in the original image. Because of the FFT basis functions which are not localized in time or space the edge information spread across frequencies. The FFT based denoising results in smearing of the edges but localized nature of wavelet transform in time and space gives us de-noising with edge preservation. II DIFFERENT TYPES OF NOISE IN IMAGE Any deterioration in the image signal due to any external disturbance is noise. Noise in the image occurs from different sources. It can affect image spatial resolution, details of the image and can produce distortion of important image features. Noise present in image can be modeled either as an additive noise or as a multiplicative noise. The noise signal that get added to the image is called additive noise and can be represented as z(x, y) = si(x, y) + no(x, y) Where, si(x, y) is the original image intensity and no(x, y) denotes the noise introduced to produce the corrupted signal z(x, y) at (x, y) pixel location. Noise signal gets multiplied to the original signal. The multiplicative noise model follows the following rule: z(x, y) = si(x, y) no(x, y) The different types of Noise are following Additive White Gaussian noise Salt-and-pepper noise Speckle Noise A. Additive White Gaussian noise Most of the time during transmission or acquisition when an image is corrupted with the channel noise generally we consider it as additive white Gaussian noise. Gaussian noise is equally distributed over the signal. This implies that each pixel in the corrupted image is the sum of the actual pixel value and a random Gaussian distributed noise value. This noise follows a Gaussian distribution, which has a bell shaped probability distribution function given by ISSN: 2231-5381 http://www.ijettjournal.org Page 462

A. Median Filter Where g shows the gray level, m is the mean or average of the function and σ is the standard deviation of the noise. B. Salt-and-pepper noise Salt and pepper noise is also known as impulse type of noise. This is originating generally because of errors in data transmission. It has only two probable values a and b. The expectation of occurring of each is typically less than0.1. The altered pixels are placed alternatively to the minimum or to the maximum value, giving the image a presence of salt and pepper noise. Unaltered pixels remain constant. If we consider an 8-bit image, the normal value for pepper noise is 0 and for salt noise 255. The salt and pepper noise is normally produced due to defect or fault in functioning of pixel elements in the camera sensors, faulty memory locations, or timing errors in the different digitization method used. C. Speckle Noise Speckle noise comes under the category of multiplicative noise unlike the Gaussian or Salt and Pepper type noise. Speckle noise is granular noise that naturally be present in and reduces the feature of the active radar and synthetic aperture radar (SAR) images. Speckle noise in traditional radar occurs from random fluctuations in the return signal from an object that is no larger than a single image-processing segment. It extended the mean grey level of a local area. Speckle noise is generated by signals from fundamental scatterers, the gravitycapillary ripples, and demonstrates as a pedestal image, underneath the image of the sea waves. All coherent imaging system suffers from this noise such as laser, acoustics and SAR (Synthetic Aperture Radar) imagery. The origin of this noise is made from random interference between the coherent returns. Speckle noise pursues a gamma distribution and can be given as [11]. Where variance is andg is the gray level III.DENOISING OF IMAGES BY FILTERING When the images are processed through channels, they are corrupted with impulse noise due to noisy channels. This impulse noise comprise of large positive and negative spikes. The positive spikes have values much larger than the background and thus they appear as bright spots, while the negative spikes have values smaller than the background and they appear as darker spots. Both the spots for the Positive and negative spikes are observable to the human eye. Gaussian noise also affects the image. Thus, filters are required for removing noises before processing. The median filter comes under the class of nonlinear filter generally used to eliminate noise. Such noise elimination is a normal pre-processing step to enhance the results of subsequent processing (for example, edge detection on an image).as median filter preserves edges while removing noise from images it is generally used in digital image processing. It is also known as a rank filter, this spatial filter suppresses isolated noise by replacing each pixel s intensity by the median of the intensities of the pixels in its neighbourhood. Median filter is used extensively in de-noising and image smoothing applications. Due to the edge-keeping feature of median filter (cf. linear methods such as average filtering tends to blur edges), which is very advantageous for many image processing application as edges carry significant information for labelling, segmenting and keeping details in image. This filter may be represented by Eq. (1) Where IV.WAVELET BASED DENOISING...1 Filter window with pixel (,) as its middle. The term wavelet indicates an oscillatory vanishing wave with time-limited extend, which has the capability to illustrate the time-frequency plane, with atoms of divergent time supports. The wavelet transform provides a multi resolution representation using a set of analyzing functions that are dilations and translations of a few functions. It is preferred to work in Wavelet domain because the Discrete Wavelet Transform (DWT) make the signal energy concentrate in a small number of coefficients, hence, the DWT of the noisy image contains a small number of coefficients having high Signal to Noise Ratio (SNR) while comparatively huge number of coefficients is having low SNR. After discarding the noisy sub band having low SNR the image is reconstructed by using inverse DWT. Due to which noise is throw out from observation[12]. The basic principle of image de-noising using discrete wavelet transform consists of following three steps [15]. 1. Apply wavelet transform to the noisy image to produce the noisy wavelet coefficients. 2. Select appropriate threshold limit at each level by using threshold method to remove the noises. 3. Inverse wavelet transform is applied to threshold wavelet coefficients to obtain a de-noised image. V.DOUBLE DENSITY DISCRETE WAVELET TRANSFORM The Undecimated DWT is exactly shift-invariant and for de-noising, it performs substantially better than the critically ISSN: 2231-5381 http://www.ijettjournal.org Page 463

sampled DWT. The Double-Density discrete wavelet transform is based on a single scaling function and two distinct wavelets where the two wavelets are designed to be offset from one another by one half, the integer translates of one wavelet fall midway between the integer translates of the other wavelet. In this way, the Double-Density DWT approximates the continuous wavelet transform (having more wavelets than necessary gives a closer spacing between adjacent wavelets within the same scale). The Double-Density DWT is two-times expansive regardless of the number of scales implemented-potentially much less than the Undecimated DWT. The Double-Density DWT has twice as many coefficients as the critically sampled DWT. The double density DWT is an improvement upon the critically sampled DWT with important additional properties. 1. In double density discrete wavelet transform we use two wavelet and one scaling function which are offset from one another. 2. The double density DWT is over completing by a factor of two. 3. Shift invariant property exists in double density discrete wavelet transform. There is a difference between un-decimated discrete wavelet transform and oversampled discrete wavelet transforms. Shift-invariant property exists in un-decimated discrete wavelet transforms and it has an expansion factor of logn. It expands an N-sample data vector to N logn samples. For de-noising of the image, there are different thresholding methods that can be used. The selection of the thresholding technique is one of the important steps which affect the quality of the image during de-noising of image. Hard and soft thresholding is used in discrete wavelet transform. The thresholding technique which is based on keep and kill rule is called hard thresholding and thresholding technique which is based on shrink or kill rule is called soft thresholding. As soft thresholding gives more pleasant image and also reduces abrupt sharp changes in the image as compared to hard thresholding, soft thresholding is preferred over hard thresholding. By default, hard thresholding is used for compression and soft thresholding is used for de-noising in MATLAB [13]. A. Threshold Selection Rules During the selection of the threshold value in de-noising we should select threshold value in such a manner that it gives us maximum peak signal to noise ratio. If we select a small threshold then it will pass noisy sub band of the image so we get noisy image and if we select a large threshold it will make more coefficients to zero, which results in blurring of the image and we may loss some pixel value. Selection of threshold can be divided into two parts that is non adaptive threshold and adaptive threshold. B. Non Adaptive Threshold VI. IMAGE DECOMPOSITION By using discrete wavelet transform an image can be decomposed into sequence of different spatial resolution images. If we consider N level decomposition of the image (2 D image) then it results in 3N+1 different frequency bands denoted as, LL, LH, HL and HH.When we apply discrete wavelet transform on the image due to the decomposition of an image the original image is decomposed into four pieces which is normally denoted as LL1, LH1, HL1 and HH1 as shown in the fig.1a. When we again decomposed LL1 band then it gives us four sub bands denoted as LL2, LH2, HL2 and HH2 as shown in the fig 1 (b). Fig. 1 Image decomposition by using DWT VII.WAVELET THRESHOLD VIII.METHODOLOGY A thresholding method that depends only on a number of data points is called visu shrink and it comes under the category of non adaptive threshold. When number of pixel reaches infinity, it gives us best performance in terms of mean square error. As it depends on large number of pixel its threshold value is quite large. It is suitable for only additive noise because it cannot remove multiplicative noise. The formula that is used for calculating threshold is given by 2log M T= Where σ is the noise level and M is the length of the noisy signal [1]. C. Adaptive Threshold There are two types of adaptive threshold i.e. Sure Shrink and Bayes Shrink. Sure Shrink derived from minimizing Stein s Unbiased Risk Estimator, an estimate of MSE risk. It is a combination of universal threshold and SURE threshold. It is used for suppression of noise by thresholding the empirical wavelet coefficient. The aim of Sure Shrink is to minimize the mean square error. Sure shrink suppresses the noise by thresholding the empirical wavelet coefficient [1]. The Bayes Shrink technique has been attracting attention latterly as an algorithm for setting different thresholds for every sub band. Here sub bands are frequency bands that differ from each other in level and direction [14]. In our implementation we are trying to get original image from noise contaminated version of image. The images taken ISSN: 2231-5381 http://www.ijettjournal.org Page 464

are corrupted with two different types of noises. We will take a portable network graphic format image available in matlab. Gray scale conversion of the image is performed. Gray scale conversion is done in order to make a single page matrix for processing of data through digital filter structure and then the intensity values in a gray scale image are equalized through Histogram Equalization. Now noise is added to the image. Here two different types of noise are added to the image that is Gaussian noise and salt and pepper noise. When addition of noise is completed then we will apply double density discrete wavelet transform and then median filtering and try to get denoised image. In this proposed method we will use single level decomposition of the image. The flow chart of proposed method is shown in fig.2.. Input Image used for image quality measurement. By subtracting the test signal from the reference, and then computing the average energy of the error signal. Let f = {f i i = 1, 2 M} and g = {g i i=1, 2 M} be the original and the de-noised images respectively.mse may be defined by MSE = Where M is the number of elements in the image. PSNR: This can be calculated by comparing two images one is original image and other is distorted image. The PSNR has been computed using the following formula PSNR = 10 log10 (R 2 /MSE) R is the maximum fluctuation in the input image data type. RGB to gray scale conversion X. EXPERIMENTAL RESULTS Histogram equalization Set variance of noise distribution Add noise Compute forward Double density DWT Filter structure for cut-off thresholding The proposed image de-noising algorithm has been applied on natural grayscale Lena images (512 512) that are contaminated by additive Gaussian noise and salt and pepper noise. The implementation of this work is performed in MATLAB 7.8 software. Performance measure is shown in the Table 1.The PSNR, MSE, SSIM value is calculated for different value of noise variance and accordingly de-noised image is shown in fig.3. Table1. Performance Measure Noise variance PSNR(db) MSE Correlation SSIM 0.01 31.30 48.15 0.87 0.79 0.05 31.18 49.55 0.80 0.72 0.10 31.08 50.66 0.74 0.76 Compute Inverse Double Density DWT Median Filter Noisy Image (Gaussian and Salt and Pepper) De-noised Image using proposed method Noise Variance=0.01 De-noised image Fig.2. flow chart of proposed method IX. PERFORMANCE PARAMETER Performance of proposed algorithm is evaluated by using MSE (Mean Square error) and PSNR (Peak signal to noise ratio). Mean square error is Simplest, and the most widely Noise Variance=0.05 ISSN: 2231-5381 http://www.ijettjournal.org Page 465

[6]. Mrs. C. Mythili and Dr. V. Kavitha Efficient Technique for Color Image Noise Reduction, T h e Research Bulletin of Jordan ACM, V o l. I I (I I I). [7] Mr. R. K. Sarawale, Dr. Mrs. S.R. Chougule Image Denoising using Dual-Tree Complex DWT and Double-Density Dual-Tree Complex DWT, International Journal of Advanced Research in Computer Engineering & Technology (IJARCET), Volume 2, Issue 6, June 2013. Noise Variance=0.10 [8]. S.Kother Mohideen, Dr. S. Arumuga Perumal, Dr. M.Mohamed Sathik Image De-noising using Discrete Wavelet transform, IJCSNS International Journal of Computer Science and Network Security, VOL.8 No.1, January 2008. [9]. S.Arivazhagan, S.Deivalakshmi, K.Kannan, Performance Analysis of Image Denoising System for different levels of Wavelet decomposition, International Journal of Imaging Science and Engineering (IJISE), GA, USA, ISSN: 1934-9955, VOL.1, NO.3, July 2007. [10]. Mukesh C. Motwani, Mukesh C. Gadiya, Rakhi C. Motwani survey of image denoising techniques, Proceedings of GSPx 2004, Santa Clara Convention Center, Santa Clara, CA. P.27-30, 2004. [11]. Er.Ravi Garg and Er. Abhijeet Kumar, Comparison of Various Noise Removals Using Bayesian Framework, International Journal of Modern Engineering Research (IJMER), Jan-Feb 2012, Vol.2, Issue.1, 265-270. Fig.3 various de-noised Lena image using proposed method XI.CONCLUSIONS In this paper a new method is proposed by hybridizing double density discrete wavelet transform and median filter to deal with the mixed noise (Gaussian and salt and pepper noise). The performance of proposed algorithm is tested at different noise level and evaluated in terms of PSNR, MSE and SSIM. The proposed algorithm gives us better noise removal of mixed noise than individual algorithm on particular noise. ACKNOWLEDGMENT [12]. S.Arivazhagan, S.Deivalakshmi, K.Kannan, Performance Analysis of Image Denoising System for different levels of Wavelet decomposition, International Journal of Imaging Science and Engineering (IJISE), July 2007, Vol.1, No.3. [13]. Akhilesh Bijalwan, Aditya Goyal, Nidhi Sethi, Wavelet Transform Based Image De-noise Using Threshold Approaches, International Journal of Engineering and Advanced Technology (IJEAT), June 2012, Vol.1, Issue-5. [14]. E.Jebamalar, Leavline, S.Sutha, D.Asir Antony Gnana Singh, Wavelet Domain Shrinkage Methods for Noise Removal in Images: A Compendium, International Journal of Computer Applications, November 2011, Vol. 33, No. 10. [15]. Sudipta Roy, Nidul Sinha & Asoke K. Sen, A New Hybrid image denoising method, International Journal of Information Technology and Knowledge Management, Vol. 2, No. 2, P. 491-497,2010. The authors are greatly indebted to the Department of Electronics & Telecom, SSCET Bhilai, CSVTU, India for providing necessary support and facilities that made this work possible. REFERENCES [1]. Sachin D Ruikar & Dharmpal D Doye Wavelet Based Image Denoising Technique, International Journal of Advanced Computer Science and Applications, March 2011, Vol.2, No.3 [2]. Kanika Gupta, S.K. Gupta, Image Denoising Techniques A Review paper, International Journal of Innovative Technology and Exploring Engineering (IJITEE), March 2013, Vol.2, Issue-4. [3]. Asoke Nath, Image Denoising Algorithms: A Comparative study of Different Filtration approaches used in image restoration, IEEE, 978-0-7695-4958-3/13 $26.00 [4]. R. Vijaya Arjunan and V. Vijaya Kumar Intelligent & Adaptive Image Denoising Based on Wavelets with Shrinkage Rule, International Journal of Information & Computation Technology., ISSN 0974-2239 Volume 2, Number 2 (2012). [5]. Pankaj Hedaoo and Swati S Godbole Wavelet Thresholding Approach for Image Denoising, IJNSA, Vol.3, No.4, July 2011. ISSN: 2231-5381 http://www.ijettjournal.org Page 466