Australian Journal of Basic and Applied Sciences. Partial Differential Equation Based Denoising Technique for MRI Brain Images

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1 AENSI Journals Australian Journal of Basic and Applied Sciences Journal ome page: Partial Differential Equation Based Denoising Tecnique for MRI Brain Images 1 S. Jansi and P. Subasini 1 Researc Scolar, Avinasilingam Universit for Women, Coimbatore, India. Professor, Avinasilingam Universit for Women, Coimbatore, India. ARTICLE INFO Article istor: Received 17October 013 Accepted 013 Available online..013 Ke words: Medical Image Processing, Image Denoising, MRI Images, Partial Differential Equation, Filtering tecniques. ABSTRACT Image denoising is a common pre-processing step in man Magnetic Resonance (MR) image processing and analsis tasks, suc as segmentation, registration or parametric image sntesis. Image denoising remains a callenge for researcers because noise removal introduces artifacts and causes blurring of te images. In tis paper four different metods are proposed to reduce te image artifacts and noise in te MRI images. Tese metods use Partial Differential Equations (PDE) to get better results in MRI images. Te proposed metods are compared and evaluated based on te error rate and teir qualit of te image. Te performance of te proposed denoising metod is measured using quantitative performance as well as in terms of visual qualit of te images. 013 AENSI Publiser All rigts reserved. INTRODUCTION In medical image processing, medical images are corrupted b different tpe of noises. It is ver important to get precise images to elp eact observations for te given application (Nobi, M.N., M.A. Yousuf, 011). Image denoising is an active area of interest for image processing researcers for a long period. Te use of partial differential equations (PDEs) in image processing as grown over te past ears and man of PDE based metods ave particularl been proposed to tackle te problem of image denoising wit a good preservation of edges, and to eplicitl account for te intrinsic geometr (JenRajan, K., M.R. Kannan, Kaimal, 008). Tere ave been several publised algoritms and eac approac as its assumptions, advantages, and limitations (Mukes, C., Motwani, Mukes C. Gadia, 004). Image denoising is a procedure in digital image processing aiming at te removal of noise wic ma corrupt an image during its acquisition or transmission, wile retaining its qualit (Kavita, S., Dr.V.S.Jaanti, 01). All denoising metods depend on a filtering parameter (Buades, A., B. Coll, et al., 005). Te filtering value measures te degree of filtering applied to te image. For most metods, te value depends on te estimation of te noise variance. One can define te result of a denoising metod D as a decomposition of an image as v D n, D were, 1. D is more smoot tan.. n D, is te noise guessed b te denoising metod. In order to get a ig qualit MRI image, man filtering tecniques ad introduced in image denoising field. Te rest of tis paper is as follows: In section, te overview of metodologies and tecnical details of image filtering is described. In section 3, te eperimental results and discussions made. Finall, te conclusions are given in section 4. Metodolog: Non Local Means Filter: Non-Local (NL) means algoritm is based on te natural redundanc of information in images to remove noise (Pierrick Coupe, Pierre Yger, Cristian Barillot, 006). Te non-local means filter averages all observed piels to recover a single piel. Te weigt of eac piel is calculated b depending te distance between its Corresponding Autor: S. Jansi, Researc Scolar, Avinasilingam Universit for Women, Coimbatore, India.

2 0 S. Jansi and P. Subasini et al, 013 intensit gra level vector and tat of te target piel (Antoni Buades, Bartomeu Coll, et al., 005). Te NLM filter is a neigborood filter wic acieves denoising b averaging similar image piels according to teir intensit similarit. Te ke idea of te non-local means filter is tat a given nois image f: R R as filtered b f f d u, were written as w f (1), u : R is te denoised image and e e d f, d f were eqn () is te differences of, for d f, f f G, d f and deviation. Te map similar, ten te corresponding weigt weigt : R is a normalized weigt function f, weigted against a Gaussian window () G wit standard d f, measures te different patces of f centered in and. If two patces are, will be ig. Oterwise, if te patces are dissimilar, te, will be small (but positive) (Yifei Lou, et al., 009). Wile te parameter defines tat te dimensions of te patc were it is used to measure te similarit between two patces, te parameter regulates ow strict or relaed to consider te patces similarl. Finall, te result of te non-local means filter as several (similar) patc used to reconstruct anoter one. Anisotropic Diffusion Filter: Te anisotropic filter is non-optimal for MR images wit spatiall varing noise levels of suc sensitivitencoded data and intensit inomogeneit corrected images (Aleei, A., Samsonov, and Cris R. Jonson, 004). Te main aim of anisotropic diffusion filtering in image processing is to remove noise via a Partial Differential Equation (PDE), wit respect to te image function is as follows: u divku t were u u,, tte image is enanced in te continuous domain in an instantt. Te initial condition for tis equation of te input image is given b u,,0 (Larrabide, I., A.A. Novotn et al., 005). B appling values for tis equation, it produces blurred image edges of te input image. Bilateral Filtering: Te bilateral filter is an edge-preserving and noise reducing smooting filter. Tis filtering tecnique is acieved b te combinations of two Gaussian filters: one filter works wit spatial domain and te oter one works wit intensit domain (Devanand Bonsle,Vivek Candra,G.R. Sina, 01). Te intensit value of eac piel in an image is replaced b a weigted average of intensit values from nearb piels. Te weigt is mainl based on te Gaussian distribution. Bilateral filtering is a non-linear filtering tecnique for removing noise witout degrading important structures suc as edges. Several qualities of bilateral filter are listed below (Joakim Rdell, 007): 1. It is simple to formulate it. Eac piel is replaced b a weigted average of its neigbors.. It depends onl on two parameters tat indicate te size and contrast of te features to keep. 3. It is a non-iterative metod. Tis makes te parameters eas to set for teir effort is not cumulative over several iterations. Tis filtering is better tan man tecniques. One of te advantages of te bilateral filter is tat it smootes te areas were te piels are similar. Tis allows us to leave relativel unaffected edges in te image (Oliver, A. Nina, Bran S. Morse). (3)

3 03 S. Jansi and P. Subasini et al, 013 ROF Filter: ROF denoising metod is based on total-variation, originall proposed b Rudin, Oser, and Fatemi. Te total variation model is one of te most popular models. Te total- variation metod (Carles, A., Miccelli, Liin Sen, 011) is sensitive to geometric features of images but te lack of multiscale representation, wic is crucial for developing efficient computational algoritms. Tis metod can be iterated wic generall results in a partial differential equation formulation te denoised image function are given as follows: u u u u t u u,, t u, 0 0, Tis model preserves te edge of te image ver well, wereas produces te block effect wen dealing wit te flat areas, tus te local details caracteristics of te original image misplaced. RESULTS AND DISCUSSIONS In order to measure te image qualit and performance of te algoritm, metrics suc as PSNR, RMSE and SSIM to be calculated. PSNR is defined as te ratio of peak signal power to average noise power D MN PSNR db 10 log10 (5) i, j i, j i, j for 0 i M 1and0 j N 1, were D is te maimum peak-to-peak swing of te signal (55 for 8-bit images). Assume tat te noise i j i, j, is uncorrelated wit te signal. RMSE is often used to measure te difference between values predicted b a model or an estimator and te values actuall observed. It as a good measure of accurac ( Tese individual differences are also called residuals. RMSE MSE E(( ) ) (6) wit respect to te estimated value is defined as te square root of te Te RMSE of an estimator mean square error. Structural Similarit Inde Metric is a metod for measuring te similarit between two images. It is calculated on various windows of an image. Tis metric is designed to improve te metods like PSNR and MSE. Te measure between two windows and of common size 011): MN=size of te reference image and filtered image. SSIM, were, - te average of ; - te average of ; - te variance of ; c c 1 c c 1 N N is (Sata, S., R. Manavalan, (7)

4 04 S. Jansi and P. Subasini et al, te variance of ; - te covariance of and In tis section, te performance of various de-noising tecniques suc as Non Local Means filter, Anisotropic Diffusion filter, bilateral filter and ROF filter are analzed for te MRI images. Te resultant images for various de-noising metods operated on original images are sown in Fig.1 and te corresponding performance metrics obtained suc as Peak Signal to Noise Ratio (PSNR), Root Mean Square Error (RMSE) and Structured Similarit Inde Metric (SSIM) values are tabulated in Table1. In general te PSNR for an filter sould be ig wereas te RMSE is ver low. Te value of SSIM for an filter sould be ig wit respect to RMSE. Conclusion: MRI denoising is an important step, used to increase image qualit and to improve performance for image analsis. Te various denoising algoritms are applied to remove noise from MRI brain images. For obtaining te better denoising metod in MRI images te performance metrics are evaluated. From te above table, te average value of performance metrics for te ROF denoising tecnique gives a iger qualit of PSNR value, wic is and gives lowest error rate and te SSIM is evaluated to measure te similarit between two images, wic gives iger value compared to te oter tree algoritms for MRI brain images. Te simulation result sows, te ROF algoritm as better denoising performance for te MRI images. Table1: Performance Metrics for denoising metods Metodolog/Performance Metrics PSNR RMSE SSIM Non Local Means Filter Anisotropic Diffusion Filter Bilateral Filter ROF Filter Fig. 1: Resultant Images for denoising metods

5 05 S. Jansi and P. Subasini et al, 013 REFERENCES Aleei, A., Samsonov, and Cris R. Jonson, 004. Noise-Adaptive Nonlinear Diffusion Filtering of MR Images wit Spatiall Varing Noise Levels, Journal of Magnetic Resonance in Medicine, pp: Antoni Buades, Bartomeu Coll, et al., 005. A non-local algoritm for image denoising, IEEE Conference on Computer Vision and Pattern Recognition, : Buades, A., B. Coll, et al., 005. A Review of Image Denoising Algoritms, wit A New One, Societ for Industrial and Applied Matematics, 4(): Carles, A., Miccelli, Liin Sen, 011. Proimit Algoritms for image models: denoising, IOP Science Journals, 7: 4. Devanand Bonsle,Vivek Candra,G.R. Sina, 01. Medical Image Denoising using Bilateral Filter, International Journal of Image, Grapics and Signal Processing (IJIGSP), ISSN: Frank Lenzen, Florian Becker, 01. Variational Image Denoising wit Solution-Adaptive Constraint Sets, Proceedings of te 3rd conference on Scale Space and Variational Metods in Computer Vision 011 (SSVM), LNCS JenRajan, K., M.R. Kannan, Kaimal, 008. An Improved Hbrid Model for Molecular Image Denoising, Journal of Matmetical Imaging and Vision, 31(1): Joakim Rdell, 007. Advanced MRI data processing, Link oping Universit PD, Tesis Kavita, S., Dr.V.S.Jaanti, 01. A Metod for Denoising and Compression of Medical Images, International Journal of Communication and Engineering, 03(04). Larrabide, I., A.A. Novotn et al., 005. A Medical Image Enancement Algoritm based on Topological Derivative and Anisotropic Diffusion, Proceedings of te XXVI Iberian Latin-American Congress on Computational Metods in Engineering. Mukes, C., Motwani, Mukes C. Gadia, 004. Surve of image denoising tecniques, Proceedings of Global Signal Processing Epo and Conference, Santa Clara, Calif, USA. Nobi, M.N., M.A. Yousuf, 011. A New Metod to Remove Noise in Magnetic Resonance and Ultrasound Images, Journal of Scientific Researc, 3(1): Oliver, A. Nina, Bran S. Morse, Interactive Smooting of Handwritten Tet Images Using a Bilateral filter, Professor of Computer Science, BYU. Pierrick Coupe, Pierre Yger, Cristian Barillot, 006. Fast Non-Local Means Denoising for 3D MR Images, International Conference on Medical Image Computing and Computer-Assisted Intervention, : Sata, S., R. Manavalan, 011 Analsis of Background Detection and Contrast Enancement of MRI Images, International Journal of Computer Applications ( ), Yifei Lou, Paolo Favaro, Stefano Soatto and Andrea L. Bertozzi, 009. Non-local Similarit Image Filtering, Proceedings of te International Conference on Image Analsis and Processing (ICIAP).