Shift-invariant denoising using wavelet-domain hidden Markov trees

Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint statistics of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training (using the EM algorithm, for example). We use an image structure not yet recognized by the HMT to show that the HMT parameters of real-world, grayscale images have a certain form. This leads to a description of the HMT model with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also observe that these nine meta-parameters are similar for many images. This leads to a universal HMT (uHMT) model for grayscale images. Algorithms using the uHMT require no training of any kind. While simple, a series of image estimation/denoising experiments show that the uHMT retains nearly all of the key structures modeled by the full HMT. Based on the uHMT model, we develop a shift-invariant wavelet denoising scheme that outperforms all algorithms in the current literature.