Unsupervised signal restoration in partially observed Markov Chains

Boujemaa Ait El Fquih; François Desbouvries

Unsupervised signal restoration in partially observed Markov Chains

Boujemaa Ait El Fquih^*, François Desbouvries

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

An important problem in signal processing consists in estimating an unobservable process x = {x_n}_nεIN from an observed process y = {y_n}_nεIN. 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 r = {r_n}_nεIN 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.

Original language	English (US)
Title of host publication	2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings
Volume	3
State	Published - 2006
Externally published	Yes
Event	2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 - Toulouse, France Duration: May 14 2006 → May 19 2006

Other

Other	2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006
Country/Territory	France
City	Toulouse
Period	05/14/06 → 05/19/06

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering

Cite this

@inproceedings{7eacd94afdc949309e2a069462d48043,

title = "Unsupervised signal restoration in partially observed Markov Chains",

abstract = "An important problem in signal processing consists in estimating an unobservable process x = {xn}nεIN from an observed process y = {yn}nεIN. 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 r = {rn}nεIN 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.",

author = "{El Fquih}, {Boujemaa Ait} and Fran{\c c}ois Desbouvries",

year = "2006",

language = "English (US)",

isbn = "142440469X",

volume = "3",

booktitle = "2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings",

note = "2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 ; Conference date: 14-05-2006 Through 19-05-2006",

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TY - GEN

T1 - Unsupervised signal restoration in partially observed Markov Chains

AU - El Fquih, Boujemaa Ait

AU - Desbouvries, François

PY - 2006

Y1 - 2006

N2 - An important problem in signal processing consists in estimating an unobservable process x = {xn}nεIN from an observed process y = {yn}nεIN. 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 r = {rn}nεIN 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.

AB - An important problem in signal processing consists in estimating an unobservable process x = {xn}nεIN from an observed process y = {yn}nεIN. 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 r = {rn}nεIN 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.

UR - http://www.scopus.com/inward/record.url?scp=33947624697&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33947624697

SN - 142440469X

SN - 9781424404698

VL - 3

BT - 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings

T2 - 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006

Y2 - 14 May 2006 through 19 May 2006

ER -

Unsupervised signal restoration in partially observed Markov Chains

Abstract

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ASJC Scopus subject areas

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