Wavelet-based denoising using hidden Markov models

Hidden Markov models have been used in a wide variety of wavelet-based statistical signal processing applications. Typically, Gaussian mixture distributions are used to model the wavelet coefficients and the correlation between the magnitudes of the wavelet coefficients within each scale and/or across the scales is captured by a Markov tree imposed on the (hidden) states of the mixture. This paper investigates correlations directly among the wavelet coefficient amplitudes (sign x magnitude), instead of magnitudes alone. Our theoretical analysis shows that the coefficients display significant correlations in sign as well as magnitude, especially near strong edges. We propose a new wavelet-based HMM structure based on mixtures of one-sided exponential densities that exploits both sign and magnitude correlations. We also investigate the application of this for denoising the signals corrupted by additive white Gaussian noise. Using some examples with standard test signals, we show that our new method can achieve better mean squared error, and the resulting denoised signals are generally much smoother.