| Paper: | SPTM-L1.4 | ||
| Session: | Bayesian Approaches and Particle Filters | ||
| Time: | Tuesday, May 16, 11:30 - 11:50 | ||
| Presentation: | Lecture | ||
| Topic: | Signal Processing Theory and Methods: Detection, Estimation, Classification Theory and Applications | ||
| Title: | Unsupervised Signal Restoration in Partially Observed Markov Chains | ||
| Authors: | Boujemaa Ait-el-Fquih, François Desbouvries, INT, France | ||
| Abstract: | An important problem in signal processing consists in estimating an unobservable process $x = \{ x_n \}_{n \in \NN}$ from an observed process $y = \{ y_n \}_{n \in \NN}$. In Linear Gaussian Hidden Markov Chains (LGHMC), recursive solutions are given by Kalman-like Bayesian restoration algorithms. In this paper, we consider the more general framework of Linear Gaussian Triplet Markov Chains (LGTMC), i.e. of models in which the triplet $(x,r,y)$ (where ${\bf r} = \{ r_n \}_{n \in \NN}$ is some additional process) is Markovian and Gaussian. We address unsupervised restoration in LGTMC by extending to LGTMC the EM parameter estimation algorithm which was already developed in classical state-space models. | ||
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