Signal denoising with hidden Markov models using hidden Markov trees as observation densities

Wavelet-domain hidden Markov models have been found successful in exploiting statistical dependencies between wavelet coefficients for signal denoising. However, these models typically deal with fixed-length sequences and are not suitable neither for very long nor for real-time signals. In this paper, we propose a novel denoising method based on a Markovian model for signals analyzed on a short-term basis. The architecture is composed of a hidden Markov model in which the observation probabilities are provided by hidden Markov trees. Long-term dependencies are captured in the external model which, in each internal state, deals with the local dynamics in the time-scale plane. Model-based denoising is carried out by an empirical Wiener filter applied to the sequence of frames in the wavelet domain. Experimental results with standard test signals show important reductions of the mean-squared errors.