Séparation de sources. Principes et algorithmes - Gretsi

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Problème ACI Indépendance Sources parcimonieuses Exploiter des a priori (4/4) Sources dont les échantillons sont presque toujours nuls Parcimonie dans un espace de représentation adapté Cas de mélange linéaire : x = As ⇒ T (x) = T (As) = AT (s) Voir les cours de Stark et Daudet s1 = 0 ⇒ x = a2s2 s2 = 0 ⇒ x = a1s1 où ai = colonne i de A P.Comon & C.Jutten, Peyresq July 2011 BSS I.Le problème et les principes de résolution 36
Problème ACI Indépendance Cas de mélanges linéaires Séparation de mélanges bruités Les observations sont : x(t) = As(t) + n(t), où n est un bruit additif, indépendant de s. La présence de bruit entraîne généralement une erreur sur l’estimation de A ou de son inverse. Si on suppose que B est parfaitement estimée, soit B = A −1 , alors: y(t) = Bx(t) = s(t) + Bn(t) La séparation idéale conduit évidemment au meilleur SIR, mais pas forcément au meilleur SNR Pour des détails voir Chapitres 1 (1.4) et 4 (4.7) dans [CJ10] P.Comon & C.Jutten, Peyresq July 2011 BSS I.Le problème et les principes de résolution 37
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Principle Algebraic tools Statistic
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Introduction Colored Nonstationary
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Identifiability Identifiability ICA
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Lemma Problem Algorithms Biblio SCA
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Introduction NMF NTF Titre sous-sec
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Bibliography XI. Bibliography I II
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[BCMT10] J. Brachat, P. Comon, B. M
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[Com95] P. Comon. Supervised classi
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[F´88] L. Féty. Méthodes de trai
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[LISC11] R. Llinares, J. Igual, A.
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[PAB + 02] M. Plumbley, S.A. Abdall
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[TF07] T. Tanaka and S. Fiori. Leas
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Séparation de sources. Principes et algorithmes - Gretsi

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