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Wen-Liang Hwang

2012-05-25
15:00:00 - 16:40:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

From the perspective of the Bayesian approach, the denoising problem is essentially a prior probability estimation task. We propose an adaptive approach that constructs a Bayesian network from the wavelet coefficients of a single image and utilize the maximum-a- posterior (MAP) estimator to derive the denoised wavelet coefficients. Constructing a graphical model usually requires a large number of training images. However, we demonstrate that by using certain wavelet properties, namely, inter-scale data dependency, intra-scale data clustering, and sparsity of the wavelet representation, a robust Bayesian network for modeling high-order Markov Random Fields can be constructed from one image to resolve the denoising problem. We show that if the network is a spanning tree, the standard belief propagation algorithm can perform MAP estimation efficiently. Our experiment results demonstrate that, in terms of the peak-signal-to-noise-ratio (PSNR) performance, the proposed approach outperforms state-of-art algorithms on several images with various amounts of white Gaussian noise.