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

In this work, we introduce a hidden Markov field model for wavelet image coefficients within a subband 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 the underlying hidden Markov process. Our model is inspired by the recent Estimation-Quantization (EQ) image coder and its excellent performance in compression. To reduce the computational complexity we apply a novel factor graph framework to combine two 1-D hidden Markov chain models to approximate a hidden Markov Random field (HMRF) 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 an 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.