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- W2231882012 abstract "– De nombreux contextes applicatifs d'importance presupposent une connaissance partielle des parametres du modele d'observation issus de mesures realisees au prealable. Le modele d'observation est alors compose d'un signal d'interet, d'un signal interference partiellement connu et d'un bruit additif. Ce travail propose dans le cadre de l'acquisition comprimee, une etude asymptotique des performances d'estimation du vecteur parcimonieux des amplitudes pour les estimateurs parcimonieux exploitant par deflation la connaissance a priori du sous-espace interference. Sous ces hypotheses, nous proposons l'expression de la Borne de Cramer-Rao Moyennee (BCRM) dans un contexte asymptotique c'est-a-dire lorsque le nombre de mesures et le valeurs non-nulles d'amplitude croient avec un ratio asymptotiquement constant. L'expression qui en resulte est particulierement compacte en terme d'implementation et d'interpretation et est valable pour tout type de prior sur le vecteur d'amplitudes. Enfin, quelques simulations numeriques illustrent l'interet de la borne Bayesienne proposee au regard des estimateurs parcimonieux de l'etat de l'art. Abstract – Numbers of applicative contexts presuppose a partial knowledge of the observation model induced by post-processing acquisitions. The observation model is then composed of a signal of interest, a partially known interfering signal and an additive noise. Based on the compressed sensing theory, the presented work proposes an asymptotic performances analysis of the sparse amplitudes vector for sparse popular estimators straightforwardly extended in this article to exploitation of the a prior knowledge of the interfering subspace. With these assumptions, we propose closed-form expressions of the Expected Cramer-Rao Bound (ECRB) in an asymptotic regime, i.e. when the number of measurements and non-zero amplitude values increase with constant asymptotic ratio. The derived closed-form expressions are easily computable and easy to interpret. In addition, the proposed Bayesian lower is valid for any amplitudes vector priors. Finally, several numerical simulations illustrate the practical interest of the proposed Bayesian bound regarding the state-of-art sparse estimatiors." @default.
- W2231882012 created "2016-06-24" @default.
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- W2231882012 date "2015-09-01" @default.
- W2231882012 modified "2023-09-23" @default.
- W2231882012 title "Acquisition Comprimée intégrant une Connaissance Partielle du Modèle d'Observation: Analyse Asymptotique" @default.
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