Signal denoising using wavelet and block hidden Markov model

In this paper, we propose a novel wavelet domain HMM using block 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 the 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, the reverse wavelet transformation is utilized to modify wavelet coefficients. Finally, experimental results are given. The results show that the block hidden Markov model (BHMM) is a powerful yet simple tool in signal denoising.