Signal denoising using wavelets and block hidden Markov model

This paper presents a new framework for signal denoising based on wavelet-domain hidden Markov models (HMMs). The new framework enables us to concisely model the statistical dependencies and non-Gaussian statistics encountered in real-world signals, and enables us to get a more reliable and local model using blocks. Wavelet-domain HMMs are designed with the intrinsic properties of wavelet transform and provide powerful yet tractable probabilistic signal models. In this paper, we propose a novel wavelet domain HMM using blocks to strike a delicate balance between improving spatial adaptability of contextual HMM (CHMM) and modeling a more reliable HMM. Each wavelet coefficient is modeled as a Gaussian mixture model, and the dependencies among wavelet coefficients in each subband are described by a context structure, then the structure is modified by blocks which are connected areas in a scale conditioned on the same context. Before denoising a signal, efficient Expectation Maximization (EM) algorithms are developed for fitting the HMMs to observational signal data. Parameters of trained HMM are used to modify wavelet coefficients according to the rule of minimizing the mean squared error (MSE) of the signal. Then, reverse wavelet transformation is utilized to modified wavelet coefficients. Finally, experimental results are given. The results show that block hidden Markov model (BHMM) is a powerful yet simple tool in signal denoising.