Image Denoising with Nonparametric Hidden Markov Trees

We develop a hierarchical, nonparametric statistical model for wavelet representations of natural images. Extending previous work on Gaussian scale mixtures, wavelet coefficients are marginally distributed according to infinite, Dirichlet process mixtures. A hidden Markov tree is then used to couple the mixture assignments at neighboring nodes. Via a Monte Carlo learning algorithm, the resulting hierarchical Dirichlet process hidden Markov tree (HDP-HMT) model automatically adapts to the complexity of different images and wavelet bases. Image denoising results demonstrate the effectiveness of this learning process.