The objective of the work is to denoise the image and to provide better Peak Signal to Noise Ratio (PSNR) with edge preservation by using the hidden Bayesian network constructed from the wavelet coefficients. A Bayesian network which is also called as a directed acyclic graph is a graphical model with a set of conditional probabilities. Each node in the graph represents a random variable which is used to denote an attribute, feature and hypothesis. Bayesian network is constructed to model the priori probability of the original image for the image denoising problem, which involves removing white and homogeneous Gaussian noise with zero mean and known variance from an image. Two Maximum A Posteriori (MAP) techniques are used such as Bivariate Cauchy MAP (BCMAP) and Multivariate Cauchy MAP (MCMAP). From the simulation analysis, it is very clear that for various noise levels, the wavelet Bayesian network based on MAP estimation provides better PSNR value by preserving edges compared with the existing methods. For Lena image with noise variance of 15, the percentage increase in PSNR values are 2.08%, 4.16% and 7.38% for wavelet Bayesian, BCMAP and MCMAP compared with Bayesian Least Square Gaussian Scale Mixture (BLS-GSM) and for the same, the percentage increase in PSNR are 0.12%, 2.15% and 5.32% compared with Block Matching and 3-D filtering (BM3D).
Denoising, Bayesian network, Wavelet coefficients, MAP, bivariate and multivariate
. Cooper G.F, Herskovits E (1992) A Bayesian method for the induction of probabilistic networks from data, Mach. Learn., 9(4):309– 347.
. Heckerman D, Geiger D, Chickering D.M (1995) Learning Bayesian networks: The combination of knowledge and statistical data, Mach. Learn., 20(3):197– 243.
. Srivastava A, Lee, A.B, Simoncelli E.P, Zhu S.C (2003), On advances in statistical modeling of natural images, Journal of Mathematical Imaging and Vision, 18(1) : 17– 33.
. Goossens B, Pizurica A, Philips W (2009), Image denoising using mixtures of projected Gaussian scale mixtures, IEEE Trans. Image Process., 18(8):1689–1702.
. Money E.S, Reckhow K.H, Wiesner M.R (2012) The use of Bayesian networks for nanoparticle risk forecasting: model formulation and baseline evaluation, Science of the Total Environment, 42(6) : 436–445.
. Madadgar S, Moradkhani H (2014) Spatiotemporal drought forecasting within Bayesian networks, Journal of Hydrology, 512(6) :134– 146.
. Heckerman D (2008) A tutorial on learning Bayesian networks, Innovations in Bayesian Networks : 33-82.
. Chatterjee P, Milanfar P (2010) Is denoising dead? IEEE Trans. Image Process., 19(4): 895–911.
. Kervrann C, Boulanger J (2006) Optimal spatial adaptation for patch based image denoising, IEEE Trans. Image Process., 15(10): 2866–2878.
. Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-D transform-domain collaborative filtering, IEEE Trans. Image Process., 16(8):2080– 2095. 11]. Crouse M.S, Nowak R.D, Baraniuk R.G (1998) Wavelet-based statistical signal processing using hidden Markov models, IEEE Trans. Signal Process., 46(4): 886–902.
. Milanfar P (2013) A tour of modern image filtering: New Insights and methods, both practical and theoretical, IEEE Signal Process. Mag., 30(1):106–128.
[13. Chatterjee P and Milanfar P (2012) Patchbased near-optimal image denoising, IEEE Trans. Image Process., 21(4):1635–1649.
. Chatterjee P and Milanfar P (2008), A generalization of non-local means via kernel regression in Proc of SPIE conf. on Computational Imaging.
. Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2009) Non-local sparse models for image restoration, in Proc. 12th IEEE Int. Conf. Comput. Vision, Kyoto, Japan, 2272– 2279.
. Portilla J, Strela V, Wainwright M.J, Simoncelli E.P (2003) Image denoising using scale mixtures of Gaussians in the wavelet domain, IEEE Trans. Image Process., 12(11) : 1338–1351.
. Ho J and Hwang W-L (2013) Wavelet Bayesian network image denoising, IEEE Trans. Image Process., 22(4): 1277-1290.
. Sadreazami H, Omair Ahmad M, Swamy M.N.S (2015), “A robust multiplicative watermark detector for color images in sparse domain, IEEE Transactions on Circuits and Systems II: Express Briefs, 62(12):1159-1163.
. Sadreazami H, Omair Ahmad M, Swamy M.N.S (2016) Color image denoising using multivariate cauchy PDF in the contourlet domain, In proc. of IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), 1- 4.
Cite this paper
Bhanumathi V., Lavanya S.. (2017) Image Denoising by Wavelet Bayesian Network based on MAP Estimation. International Journal of Mathematical and Computational Methods, 2, 265-272
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