**TITLE**

Image Denoising by Wavelet Bayesian Network based on MAP Estimation

**PDF**

**ABSTRACT**

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).

**KEYWORDS**

Denoising, Bayesian network, Wavelet coefficients, MAP, bivariate and multivariate

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**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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