Contextual Hidden Markov Models for Wavelet-domain Signal Processing
Crouse, Matthew; Baraniuk, Richard G.
Wavelet-domain hidden Markov models (HMMs) provide a powerful new approach for statistical modeling and processing of wavelet coefficients. In addition to characterizing the statistics of individual wavelet coefficients, HMMs capture some of the key interactions between wavelet coefficients. However, as HMMs model an increasing number of wavelet coefficient interactions, HMM-based signal processing becomes increasingly complicated. In this paper, we propose a new approach to HMMs based on the notion of context. By modeling wavelet coefficient inter-dependencies via contexts, we retain the approximation capabilities of HMMs, yet substantially reduce their complexity. To illustrate the power of this approach, we develop new algorithms for signal estimation and for efficient synthesis of nonGaussian, long-range-dependent network traffic.