WAVELET-BASED STATISTICAL SIGNAL-PROCESSING USING HIDDEN MARKOV-MODELS

Wavelet-based statistical signal processing techniques such as denoisi ng and detection typically model the wavelet coefficients as independe nt or jointly Gaussian. These models are unrealistic for many real-wor ld signals. In this paper, we develop a nerv framework for statistical signal processing based on wavelet-domain hidden Markov models (HMM's ) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals, Wavelet-domain HMM's are designed with the intrinsic properties of the wavelet transform in mi nd and provide powerful, vet tractable, probabilistic signal models, E fficient expectation maximization algorithms are developed for fitting the HMM's to observational signal data, The new framework is suitable for a wide range of applications, including signal estimation, detect ion, classification, prediction, and even synthesis, To demonstrate ti le utility of wavelet-domain HMM's, we develop novel algorithms for si gnal denoising, classification, and detection.