Modèles et algorithmes pour la modélisation parcimonieuse de signaux de grande dimension

Boris Mailhé 1
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : This thesis provides fast algorithms for sparse representations. Sparse representations consist in modelling the signal as a linear combination of a few atoms chosen among a redundant (more atoms than the signal dimension) dictionary. How to decompose a given signal over a given dictionary? This problem is NP-Complete. Existing suboptimal algorithms are either to slow to be applied on large signals or compute coarse approximations. We propose a new algorithm, LocOMP, that is both scalable and achieves good approximation quality. LocOMP only works with local dictionaries: the support of an atom is much shorter than the signal length. How to learn a dictionary on which a given class of signals can be decomposed? This problem is even more difficult: its resolution usually involves several sparse decompositions. We propose to improve the Olshausen-Field algorithm. It optimizes the dictionary via fixed step gradient descent. We show how to compute the optimal step. This makes the algorithm converge faster towards a better dictionary. These algorithms were applied to the study of atrial fibrillation. Atrial fibrillation is a common heart arrhythmia: the atria start vibrating instead of beating. One would like to observe I in the patient's ECG but the ECG is a mixture of fibrillation and ventricular activity. Our separation method is based on the learning of one dictionary for the fibrillation and one for the ventricular activity, both of them learnt on the patient's ECG.
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Contributor : Boris Mailhé <>
Submitted on : Monday, August 30, 2010 - 6:56:29 PM
Last modification on : Friday, November 16, 2018 - 1:23:17 AM
Document(s) archivé(s) le : Thursday, December 1, 2016 - 10:06:52 PM

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  • HAL Id : tel-00512559, version 1

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Boris Mailhé. Modèles et algorithmes pour la modélisation parcimonieuse de signaux de grande dimension. Traitement du signal et de l'image. Université Rennes 1, 2009. Français. ⟨tel-00512559⟩

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