Wavelet Threshold De- Noising for Mammogram Images

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1 , pp Wavelet Threshold De- Noising for Mammogram Images Saima Anwar Lashari*, Rosziati Ibrahim and Norhalina Senan Universiti Tun Hussein Onn Malaysia, Parit Raja, Batu Pahat, Johor, Malaysia * hi120040@siswa.uthm.edu.my Abstract Digital mammograms are coupled with noise which makes de-noising a challenging problem. In the literature, few wavelets like daubechies db3 and haar have been used for de-noising medical images. However, wavelet filters such as sym8, daubechies db4 and coif1 at certain level of soft and hard threshold have not been taken into account for mammogram images. Therefore, in this study five wavelet filters namely: haar, sym8, daubechies db3, db4 and coif1 at certain level of soft and hard threshold have been considered. Later, peak signal to noise ratio and mean squared error values are calculated. From the obtained results, it can be concluded that db3 ( db for hard threshold and db for soft threshold) is more appropriate filter for de-noising mammogram images while compared with other wavelets filters. Keywords: Wavelet de-noising, hard thresholding, soft thresholding, peak signal to noise ratio 1. Introduction Digital Mammography is one of effective tools in early detection of breast cancer. Basically, mammography is an x-ray procedure for the visualization of internal structure of breast. It has been proven to be the most reliable method and it is the key screening tool for the early detection of breast cancer [1-2]. Mammography is highly accurate but like most medical tests, it is not perfect. On average mammography will detect about 80-90% of the breast cancers in women without symptoms. However, there are few common problems of the mammogram images such as: unknown noise, poor image contrast and inherent attenuation differences between normal and diseased breast tissues is so small that high quality mammogram images are required. These problems might be rectified by preprocessing techniques [3-6]. Therefore, the preprocessing is a fundamental step in the medical images to produce better image quality for segmentation and feature extraction procedures [7-9]. Moreover, noise present in the digital mammogram images directly influences the competence of a classification task. Study reveals that overall accuracy of classification systems decrease significantly with increase in noise and decrease can become as significant as 21%. This noise can be added due to several factors such as data acquisition and image preprocessing stage. Therefore, the main purpose of de-noising is to remove noisy components (low contrast resolutions, film noise, artifacts) while preserving the important signal as much as possible. De-noising is often done before the images are to be analyzed. Consequently, de-noising plays a very important role in image segmentation, feature extraction and in the classification task [10]. In general, noise filters can be divided into two types, linear methods and non-linear filtering methods. Linear methods involved methods like median, weiner, adaptive and mean filters. Non linear filtering methods include wavelet transform, multiwavelets and curvelet transform. Al Jumah [11] worked with various non-linear thresholding ISSN: IJSEIA Copyright c 2015 SERSC

2 techniques such as hard, soft, universal, modified universal and multivariate thresholding in multiwavelet transform domain such as Discrete Multiwavelet Transform Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite Bih52S) for different Multiwavelets at different levels to denoised an image and determine the best one out of it. It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results. Along with assorted efforts reported in the existing literature proposed algorithms, the major objective was to filter noise and provide better quality images for further processing such as feature extraction, feature selection and classification. In the work of Kim, et al., [9], the preprocessing method was cutting out background area and normalization for computed tomography (CT) brain images. In the proposed approach, an elliptical structure constructed based on skull contour and then the incline imaging angles were corrected. Likewise, in the study of Müller, et al., [12], authors worked with different filters such as median, weiner, adaptive median and mean filters in order to remove noise from mammogram images. From their results, adaptive median filter performed well than the others filters. The mean square error (MSE) value was small for adaptive median filter (mdb 001) and peak signal-to-noise ratio (PSNR) was reported as db (mdb 001). Later, Lashari & Ibrahim [13] proposed a framework for medical images based on soft set theory. Afterward, in their work [14], they assessed the performance of selected classification algorithms based on fuzzy soft set for classification of medical data (numerical data). The acquired results shows that the two approaches performed well, obtaining a classification accuracy reaching 90% for both techniques. However, the best results obtained with the breast cancer wisconsin (diagnostic) wdbc with accuracy for FSSCT and for FSSSM. Moreover, the experiments conducted demonstrated the use of and effectiveness of fuzzy soft set in medical data categorization. Among various proposed preprocessing techniques, wavelet gains high popularities in noise removal from images because of its distinctive features. So far, few wavelets like daubechies db3 and haar have been used for de-noising of medical images [15]. However, to the best of our knowledge, wavelet filters such as sym8, daubechies db4 and coif1 have not taken into account for mammogram images. Therefore, to conduct this study, five wavelets filter namely: haar, sym8, daubechies db3, daubechies db4 and coif1 at certain level of soft and hard threshold have been considered. The modeling process for mammogram images consists of four phases which are data collection, wavelet selection, hard & soft threshold, calculation and comparison of PSNR and MSE values. The rest of the paper as follows: a brief review of related work has been presented in Section 2. Wavelet thresholding de-nosing, hard and soft threshold functions are presented in Section 3. The modeling process for mammogram images is given in Section 4, experimental results and discussion are reported in Section 5 respectively. Finally, the overall conclusions of this study are presented in Section Related Work Due to the immense need of effective preprocessing techniques and accurate medical image classification, new trend for image preprocessing using automatic image classification has been investigated for the past few years. It is believed that quality of such automatic image classification system can be improved by a successful classification of images. The noise present in the mammogram images may appear as additive or multiplicative components and the main purpose of denoising is to remove these noisy components while preserving the important signal as much as possible [11, 19, 20]. Therefore, de-noising plays a very important role 216 Copyright c 2015 SERSC

3 in the field of the medical image pre-processing. It is often done before the image is to be analyzed. De-noising is mainly used to remove noise that is present and retains the significant information, regardless of the frequency contents of the signal. In this process much attention is kept on how well the edges are preserved and how much of noise granularity has been removed. Hence, wavelet based noise removal has attracted much attention of the researchers for several years [15]. In the wavelet domain, the noise is uniformly spread throughout the coefficients while mostly the image information is concentrated in the few largest coefficients. The most important way of distinguishing information from noise in the wavelet domain consists of thresholding the wavelet coefficients. Mainly hard and soft thresholding techniques are performed [16-17]. In the work of Červinka & Provazník [4] the proposed method of the histogram of the intensity in CT images down sampled. Therefore, the low contrast and blurring regions in CT images enhanced. A Markov Random Filed model, which is consider the geometrical; constrains of the processed images used to develop the accuracy resulting from the down-sampling procedure. Table 1 summarizes four types of filters for mammogram images with gaussian noise. Adaptive median filter performed well than the others. The mean square error (MSE) value is small for adaptive median filter (mdb 001). Therefore, image quality is good for adaptive median filter since PSNR value is db (mdb 001) as shown in Table 1 which is high while compared with other filters [18]. Table 1. Different s for Mammogram Images with Gaussian Noise Author(s) Year Type PSNR (db) Ramani Vanitha & Valamathy 2013 Median (Mdb 001) (Mdb 155) (Mdb 322) Adaptive Median (Mdb 001) (Mdb 155) (Mdb 322) Weiner (Mdb 001) (Mdb 155) (Mdb 322) Mean (Mdb 001) (Mdb 155) (Mdb 322) MSE Table 2 summarizes medical images denoising in the wavelet domain using haar and db3 with speckle noise. It is found that db3 wavelet is more efficient than haar wavelet. De-noising was performed at speckle noise on =0.1with image type MRI image and PSNR value is db (hard threshold) and db (soft threshold) other than ultrasound, CT-scan and x-ray. The best PSNR value is calculated db (hard threshold) and db (soft threshold) respectively [15]. Table 2. Different Wavelets s for Medical Images with Speckle Noise Author(s) Year Type Sidhu, Khaira & Virk 2012 Haar Image type MRI image PSNR (db) (hard thresholing) (Soft thresholing) MSE Copyright c 2015 SERSC 217

4 Ultra image sound (hard thresholing) (soft thresholing) X ray image (hard thresholing) (soft thresholing) CT scan image (hard thresholing) (soft thresholing) MRI image (hard thresholing) (Soft thresholing) Db3 Ultra sound image X -ray image (hard thresholing) (soft thresholing) (hard thresholing) (soft thresholing) CT scan image (hard thresholing) (soft thresholing) Wavelet Thresholding De-Noising Wavelet thresholding de-noising is based on the idea that the energy of the signal to be defined concentrates on some wavelet coefficients, while the energy of noise spreads throughout all wavelet coefficients. Wavelet threshold de-noising is a very efficient method, the purpose of which is to remove independent and identically distributed gaussian noise. Let x ( t) x1 t, x2 t..., xn t be the signal series acquired by means of a senor. This signal series consists of impulses and noise. x (t) can be expressed as follows [16]. x( t) p t n t (1) Where p ( t) p1 t, p2 t..., pn t indicates identically distributed and in depended Gaussian noise with mean zero and standard deviation. The wavelet threshold denoising producer has following steps: 1. Transform signal x (t) to the time-scale plane by means of a wavelet transform. It is possible to acquire the results of the wavelet coefficients on different scales. 2. Assess the threshold and in accordance with the establish rules, shrink the wavelets coefficients 3. Use the shrunken coefficients to carry out the inverse wavelet transform. The series recovers is the estimation of impulse p (t) The second step has a great impact upon the effectiveness of the procedure. According to Donoho, the universal threshold rule should be applied in the second step. According to him, the universal threshold is defined as follows [5]. 2InN (2) where refers to the standard deviation of the noise and if it is not known, a robust median estimator is used from the finest scale wavelet coefficients : MAD / Where MAD refers to the median absolute value of the finest scale wavelet coefficients, whereas N refers to the number of data samples in the measured signal Thresholding Thresholding is one of important steps to remove noise. Thresholding is used to segment an image by setting all pixels whose intensity values are above a threshold to a foreground value and all the remaining pixels to a background value. Thresholding is mainly divided into two categories: hard thresholding and soft thresholding. 218 Copyright c 2015 SERSC

5 3.2. Hard Thresholding The hard-thresholding function used by Donoho is [6-7] (5) It is called keep or kill, keep the elements whose absolute value is greater than the threshold. Set the elements lower than the threshold to zero, where w ~ j, k the signal is, is the threshold Soft Thresholding The soft thresholding function used by Donoho is [6-7] (6) It is called shrink or kill which is an extension of hard thresholding, first setting the elements whose absolute values are lower than the threshold to zero and then shrinking the other coefficients where sgn( ) is symbol function: (7) 4. Modeling process The modeling process for preprocessing of mammogram images consist of four phases which are: data collection, wavelet selection, hard & soft threshold, calculation and comparison of PSNR and MSE (as shown in Figure 1). Each of the phases is discussed in details in next sub-sections. Data Collection Wavelet Selection (Sym8, Haar, Coif1 Db3 & Db4) Hard & soft Threshold Calculation & Comparison of PSNR & MSE Figure 1. Modeling Process for Mammogram Images Copyright c 2015 SERSC 219

6 4.1. Data collection The data was collection from the Mammographic Image Analysis Society (MIAS). There are 322 images, which belong to three categories: normal, benign and malign. There are 208 normal images, 63 benign and 51 malign. Every of the mammograms are an x-ray image with a size of 1024*1024 pixels with 256 level gray scale. All the mammograms are medio-lateral oblique view Wavelet Selection For medical images many wavelets like db1, sym8, coif3 etc. can be used for denoising of a medical images, however in this study, sym8, haar, db3 and db4 at certain level of hard and soft threshold and then decomposed and reconstructed the de-noised image. PSNR and MSE values are calculated for comparing these wavelets filters Hard and Soft Threshold The hard-and soft threshold functions used by Donoho [6, 12] as stated in Section III are used with different wavelets filter types Calculation & Comparison of PSNR and MSE Peak Signal-to-Noise Ratio (PSNR) values 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 [15]; R 2 PSNR 10 log 10 db MSE (8) Where R is the maximum fluctuation in the input image data. For example, if the input image has a double precision floating point data type, then R is 1. If it has an 8-bit unsigned integer data type, R is 255, etc Mean squared error [15]. 1 2 (9) MSE M,, 1 N x i j y i j I J 1 MN where x i, j represents the original image and y i, j represents the de-noised (modified) image and I and j are pixels of N i j y i, j 5. Experimental Results and Discussion M image. MSE is zero when x, = In this paper, five types of filters are used for de-noising mammogram images mainly concentrating on the mean square error (MSE) and peak signal to noise ratio (PSNR) parameters. These parameters are calculated and tabulated in Table 3. Different PSNR and MSE values are calculated at different levels of gaussian noise at hard and soft thresholding levels by applying these filters one after the other and then comparison is made. The best PSNR value is db (hard threshold) and db (soft threshold) which occurs in db3 wavelet filter. The lowest MSE value occurs in db3 wavelet which is The highest MSE value occurs in Coif1 wavelet which is Table 3 depicts different filters with obtained best PSNR values for hard and soft threshold functions. From the observations, db3 provides better results while compare with the other filters for purpose of de-noising in the mammogram images. The best PSNR value is db (hard thresholding) and db (soft thresholding). 220 Copyright c 2015 SERSC

7 To sum up analysis, db3 wavelet with noise level =10 might be suitable for mammogram images whilst =20 and =40 might not be appropriate to add that much of noise to de-noised mammogram images. On other hand, mammogram images have good PSNR values, it might be they have a high fine details edge that is the reason that hard thresholding produce enhanced results than soft thresholding. Table 3. Psnr and Mse Values of Mias after Processing Through Different Wavelet s Types of filters Sym8 Db3 Db4 haar Coif1 Types of threshold Hard Soft Hard Soft Hard Soft Hard Soft Hard Soft Noise Levels PSNR(db) MSE = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Table 4 depicts different wavelet filters attaining best PSNR values from hard and soft threshold functions. From the observations, db3 filter provides better results when compared with the other filters for purpose of de-noising of mammogram images. The best PSNR value obtained db (hard thresholding) and db (soft thresholding). Copyright c 2015 SERSC 221

8 Table 4. Psnr Values for Mias after Processing Through Different Wavelet s Types of threshold Sym8 Db3 Db4 haar Coif1 Mammogra m Images Hard Soft From Table 5, illustrates comparison of different medical images with different filters. It can be observed that the PSNR values for soft threshold operator are better than hard threshold in MRI images with speckle noise. The reason might be that MRI dataset have low fine details and edges. Whereas, images like CT scan and X-ray, there is no statically difference in both threshold functions. However, in this study MIAS dataset have better hard threshold value than soft threshold, the reason for this occurrence might MIAS dataset have high fine details and edges. Therefore, PSNR values for hard threshold is better than soft threshold. Table 5. Comparing Of Different Medical Images with Different s Author(s),Year Image Type Type PSNR (db) Ramani et al., MIAS [18] Adaptive Median (Mdb 001) (Mdb 155) (Mdb 322) MSE Sidhu, Khaira & Virk [15] Taujuddin & Ibrahim [17] MRI image CT scan image X-ray image Barbara Haar Db3 Haar Db3 Haar Db3 Sym8 ( =25 ) This study MIAS Db (hard thresholing) (Soft thresholing) (hard thresholing) (Soft thresholing) (hard thresholing) (Soft thresholing) (hard thresholing) (Soft thresholing) (hard thresholing) (Soft thresholing (hard thresholing) (Soft thresholing (hard thresholing) (soft thresholing) (hard thresholing) (soft thresholing) Conclusion and Future Scope In this paper, de-noising of mammogram images based on wavelet filters has been presented. Empirical results for five filters namely: sym8, haar, coif1, db3 and db4 tested for 114 mammogram images were reported. From the observations, it can be concluded that db3 is more appropriate filter while compared with the other wavelet filters. These experimental evidences are also helpful to select the best wavelet transform for de-noising of mammogram images. Thus, this paper provides an alternative filtering method for mammogram images. On the other hand, it will 222 Copyright c 2015 SERSC

9 improve the accuracy and efficiency of mammogram images classification, since before applying classifier there is a need to identify inappropriate attributes like noise and outliers which in turn slow down the classifier performance. Future work is to make it valuable to extract statistical features for mammogram images. Later, to perform classification based on fuzzy soft set algorithms and to observe the viability of fuzzy soft set for mammogram images. Acknowledgements The authors would like to thank Universiti Tun Hussein Onn Malaysia (UTHM) and office for Research, Innovation, Commercialization and Consultancy Management (ORICC) for supporting this research under the grant vote No.U110. References [1] V. P. Baligar, Low complexity and high fidelity image compression using fixed threshold method, vol. [2] 176, (2006), pp [3] V. Bruni and D. A. Vitulano, Combined image compression and denoising using wavelets, Signal Process Image Commun., vol. 22, (2007), pp [4] Z. Chang-Ming, G. Guo-Chang, L. Hai-Bo, S. Jing and Y. Hualong, Segmentation of ultrasound image based on texture feature and graph cut, In Computer Science and Software Engineering, International Conference on IEEE, vol. 1, (2008), pp [5] T. Červinka and I. Provazník, Pre-processing for Segmentation of Computer Tomography Images, Proceedings of RADIOELEKTRONIKA, (2005), pp [6] I. Daubechies, Ten lectures on wavelets, Philadelphia: Society for industrial and applied mathematics, vol. 61, (1992), pp [7] D. L Donoho, De-noising by soft-thresholding, Information Theory, IEEE Transactions on, vol. 41, no. 3, (1995), pp [8] D. L. Donoho, I. M Johnstone, G. Kerkyacharian and D. Picard, Wavelet shrinkage: asymptopia?, Journal of the Royal Statistical Society. Series B (Methodological), (1995), pp [9] F. P. K. Y. S. Feng and W. Chen, Pre-processing of CT brain images for content-based image retrieval, BioMedical Engineering, (2008). [10] S. H. Kim, J. H. Lee, B. Ko and J. Y. Nam, X-ray image classification using random forests with local binary patterns, In Machine Learning and Cybernetics (ICMLC), International Conference on IEEE, vol. 6, (2010), pp [11] N. Naveed, A. Hussain, M. A. Jaffar and T. S. Choi, Quantum and impulse noise filtering from breast mammogram images, Computer methods and programs in biomedicine, vol. 108, no. 3, (2012), pp [12] A. Al Jumah, M. G. Ahamad and S. A. Ali, Denoising of Medical Images Using Multiwavelet Transforms and Various Thresholding Techniques, Journal of Signal and Information Processing, vol. 4, (2013), pp [13] H. Müller, N. Michoux, D. Bandon and A. Geissbuhler, A review of content-based image retrieval systems in medical applications clinical benefits and future directions, International journal of medical informatics,vol. 73, no. 1, (2004), pp [14] S. A Lashari and R. Ibrahim, A Framework for Medical Images Classification Using Soft Set, Procedia Technology, vol. 11, (2013), pp [15] S. A. Lashari and R. Ibrahim, Performance Comparison of Selected Classification Algorithms Based on Fuzzy Soft Set for Medical Data, InAdvanced Computer and Communication Engineering Technology, Springer International Publishing, (2015), pp [16] K. Sidh, B. Khaira and I. Virk, Medical image denoising in the wavelet domain using haar and DB3 filtering, International Refereed Journal of Engineering and Science, vol. 1, (2012), pp [17] H. Zang, Z. Wang and Y Zheng, Analysis of signal de-noising method based on an improved wavelet thresholding, In Electronic Measurement & Instruments, ICEMI'09. 9th International Conference on, IEEE, (2009) August, pp [18] N. S. A. M. Taujuddin and R. Ibrahim, Enhancement of Medical Image Compression by Using Threshold Predicting Wavelet-Based Algorithm, InAdvanced Computer and Communication Engineering Technology. Springer International Publishing, (2015), pp [19] R. Ramani, N. S. Vanitha and S.Valarmathy, The Pre-Processing Techniques for Breast Cancer Detection in Mammography Images, International Journal of Image, Graphics & Signal Processing, vol. 5, no. 4, (2013). [20] M. R. Zare, W. C. Seng and A. Mueen, Automatic Classification of medical X-ray Images, Malaysian Journal of Computer Science, vol. 26, no. 1, (2013), pp Copyright c 2015 SERSC 223

10 [21] Z. Chang-Ming, G. Guo-Chang, L. Hai-Bo, S. Jing and Y. Hualong, Segmentation of ultrasound image based on texture feature and graph cut, In Computer Science and Software Engineering, International Conference on IEEE, vol. 1, (2008), pp Authors Saima Anwar Lashari, was admitted to the PhD degree at Faculty: of Computer Science and Information Technology at Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia in She received her MSc degree in Information Technology in 2012, Universiti Tun Hussein Onn Malaysia (UTHM), and her Bachelors (Hons) in Computer Science in 2004 at University of Engineering & Technology (UET), Pakistan. Her research interest includes data mining, classification, soft set. Rosziati Ibrahim, obtained her Bachelor of Science (Hons) in Applied Mathematics from University Of Adelaide in She holds an Msc degree in Applied Mathematics from the same university in She completed her PhD in Information Technology (Software Specification) at Queensland University of Technology (QUT) in Her research interest includes software engineering, image processing and machine learning. Norhalina Senan, obtained her Bachelor of Science in 2000 and Msc degree in 2004 from Universiti Teknologi Malaysia, Malaysia. She completed her PhD in Information Technology (soft computing) at Universiti Tun Hussein Onn Malaysia (UTHM) in Her research interest includes data mining, classification, rough set, feature selection, signal processing, multimedia content development. 224 Copyright c 2015 SERSC

11 Appendix A: Results with Visu Shirnk Original l image (mdb001) Gaussian Noise 10% Original l image (mdb001) Gaussian Noise 20% Visu Shirnk by Hard Thresholding Sym8 at level 1 Visu Shirnk by Soft Thresholding Sym8 at level 1 Visu Shirnk by Hard Thresholding Sym8 at level 1 Visu Shirnk by Soft Thresholding Sym8 at level 1 Copyright c 2015 SERSC 225

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