HIDDEN MARKOV MODELS Statistical Models for Non-Stationary Processes Hidden Markov Models Training Hidden Markov Models Decoding of Signals Using Hidden Markov Models HMM-Based Estimation of Signals in Noise Signal and Noise Model Combination and Decomposition HMM-Based Wiener Filters Summary H idden Markov models (HMMs) are used for the statistical modelling of non-stationary signal processes such as speech signals, image sequences and time-varying noise. An HMM models the time variations (and/or the space variations) of the statistics of a random process with a Markovian chain of state-dependent stationary subprocesses. An HMM is essentially a Bayesian finite state process, with a Markovian prior for modelling. | 5 Advanced Digital Signal Processing and Noise Reduction Second Edition. Saeed V. Vaseghi Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-62692-9 Hardback 0-470-84162-1 Electronic HIDDEN MARKOV MODELS Statistical Models for Non-Stationary Processes Hidden Markov Models Training Hidden Markov Models Decoding of Signals Using Hidden Markov Models HMM-Based Estimation of Signals in Noise Signal and Noise Model Combination and Decomposition HMM-Based Wiener Filters Summary Hidden Markov models HMMs are used for the statistical modelling of non-stationary signal processes such as speech signals image sequences and time-varying noise. An HMM models the time variations and or the space variations of the statistics of a random process with a Markovian chain of state-dependent stationary subprocesses. An HMM is essentially a Bayesian finite state process with a Markovian prior for modelling the transitions between the states and a set of state probability density functions for modelling the random variations of the signal process within each state. This chapter begins with a brief introduction to continuous and finite state non-stationary models before concentrating on the theory and applications of hidden Markov models. We study the various HMM structures the Baum-Welch method for the maximum-likelihood training of the parameters of an HMM and the use of HMMs and the Viterbi decoding algorithm for the classification and decoding of an unlabelled observation signal sequence. Finally applications of the HMMs for the enhancement of noisy signals are considered. 144 Hidden Markov Models Figure Illustration of a two-layered model of a non-stationary process. Statistical Models for Non-Stationary Processes A non-stationary process can be defined as one whose statistical parameters vary over time. Most naturally generated signals such as audio signals image signals biomedical signals and seismic signals are non-stationary in that the .
