Signal denoising using wavelet packet hidden Markov model

The paper presents a new framework for signal denoising based on wavelet packet hidden Markov models (HMMs). The new framework enables us to model concisely the statistical dependencies and nonGaussian statistics encountered in real-world signals, and enables us to get a more reliable and local model using blocks. Wavelet packet HMMs are designed with the intrinsic properties of the wavelet transform and provide powerful yet tractable probabilistic signal models. We propose a novel wavelet domain HMM using blocks to strike a delicate balance between improving the 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 HMMs are used to modify the wavelet coefficients according to the rule of minimizing the mean squared error (MSE) of the signal. Then, a reverse wavelet transformation is utilized to modify the wavelet coefficients. Experimental results show that the block hidden Markov model (BHMM) is a powerful yet simple tool in signal denoising.