Bayesian Wavelet-Domain Image Modeling Using Hidden Markov Trees

Wavelet-domain hidden Markov models have proven to be useful tools. for statistical signal and image processing. The hidden Markov tree ( H M T ) model captures the key features of the joint statistics of the wavelet coeficients of real-world data. One potential drawback to the H M T framework is the need for computationally expensive iterative training (using the E M algorithm, fo r example). I n this paper, we propose two reduced-parameter H M T models that capture the general structure of a broad class of grayscale images. The image HMT (iHMT) model leverages the fact that f o r a large class of images the structure of the H M T is self-similar across scale. This allows us to reduce the complexity of the i H M T to just nine easily trained parameters (independent of the size of the image and the number of wavelet scales). I n the universal HMT (uHMT) we take a Bayesian approach and f ix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structures modeled by the full HMT. Based on these new models, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.