Wavelet-domain Hidden Markov Models Research Articles

Image denoising using a local contextual hidden Markov model in the wavelet domain

Wavelet domain hidden Markov models (HMMs) have been proposed and applied to image processing, e.g., image denoising. We develop a new HMM, called local contextual HMM (LCHMM), by introducing the Gaussian mixture field where wavelet coefficients are assumed to locally follow the Gaussian mixture distributions determined by their neighborhoods. The LCHMM can exploit both the local statistics and the intrascale dependencies of wavelet coefficients at a low computational complexity. We show that the LCHMM combined with the "cycle-spinning" technique can achieve state-of-the-art image denoising performance.

Improved hidden Markov models in the wavelet-domain

Wavelet-domain hidden Markov models (HMMs), in particular the hidden Markov tree (HMT) model, have been introduced and applied to signal and image processing, e.g., signal denoising. We develop a simple initialization scheme for the efficient HMT model training and then propose a new four-state HMT model called HMT-2. We find that the new initialization scheme fits the HMT-2 model well. Experimental results show that the performance of signal denoising using the HMT-2 model is often improved over the two-state HMT model developed by Crouse et al. (see ibid., vol.46, p.886-902, 1998).

Detection and classification of abnormal process situations using multidimensional wavelet domain hidden Markov trees

This paper addresses the detection of abnormal process situations during plant operation via an effective trending strategy. Wavelet-domain hidden Markov models (HMMs) are exploited as a powerful tool for statistical modeling and processing of wavelet coefficients. We focus on the multivariate problem as many variables contribute to the decision regarding process status. A simulation study illustrates the salient features of the proposed framework.

Wavelet-based statistical signal processing using hidden Markov models

Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real-world signals. We develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals. Wavelet-domain HMMs are designed with the intrinsic properties of the wavelet transform in mind and provide powerful, yet tractable, probabilistic signal models. Efficient expectation maximization algorithms are developed for fitting the HMMs to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of wavelet-domain HMMs, we develop novel algorithms for signal denoising, classification, and detection.