Stochastic wavelet-based image modeling using factor graphs and its application to denoising

In this work, we introduce an efficient hidden Markov field model for wavelet image coefficients and apply it to the image denoising problem. Specifically, we propose to model wavelet image coefficients within subbands as Gaussian random variables with parameters determined by underlying hidden Markov-type process. Our model is inspired by the recent estimation-quantization image coder. To reduce the computational complexity we apply the novel factor graph framework to combine two 1-D chain models to approximate a hidden Markov field (HMF) model. We then apply the proposed models for wavelet image coefficients to perform an approximate minimum mean square error (MMSE) estimation procedure to restore an image corrupted by additive white Gaussian noise. Our results are among the state-of-the-art in the field and they indicate the promise of the proposed modeling techniques.