WAVELET-BASED SIGNAL PROCESSING USING HIDDEN MARKOV MODELS


Matthew S. Crouse, Robert D. Nowak and Richard G. Baraniuk

Department of Electrical and Computer Engineering
Rice University
Houston, TX  77005-1892
Email:   mcrouse@rice.edu, richb@rice.edu

Department of Electrical Engineering
Michigan State University
East Lansing, MI  48824-1226
Email:    rnowak@egr.msu.edu

Submitted to IEEE Transactions on Signal Processing, January 1997
(Special Issue on Wavelets and Filterbanks)


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.  In this paper, we develop a new framework
for statistical signal processing based on wavelet-domain hidden
Markov models (HMMs).  The framework enables us to concisely model the
statistical dependencies and nonGaussian statistics encountered with
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.