Image processing using template model and wavelet domain hidden Markov model

Abstract

Wavelet domain hidden Markov models (HMMs) have been proven to be useful tools for statistical signal and image processing. However, most of the improvements of wavelet domain HMMs only focus on how to impose an additional dependency structure on the original wavelet domain HMMs to capture the additional dependencies among wavelet coefficients. Besides this, existing methods do not fully consider the effects of noise in high frequency subbands of wavelet transforms. Some simple algorithms of wavelet domain HMMs, such as dividing the subband of wavelet coefficients into blocks, cannot be carried on smoothly in a noisy image. We give a more general framework to simplify wavelet domain HMM using templates. The new model enables us to concisely share the statistics in real-world noisy image using a more reasonable way and enables us to get a simple, local and reliable model using templates. Templates are constructed in the subband of scaling coefficients in order to reduce the effects of image noises and provide powerful yet tractable probabilistic image models. Before we process images using wavelet domain HMMs, the estimation of parameters for the HMMs must be obtained by the EM training algorithm that shares statistics according to the templates. Finally, to demonstrate the utility of new models, we give an example for image denoising using templates and wavelet-domain HMMs.