Detection in the Presence of Speckle Using Multivariate Mixed Poisson Distributions
Lois de Poisson Mélangées Multivariées : Application À la Détection en Présence de Speckles
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This paper studied a family of multivariate mixed Poisson distributions that plays a central role in the statistic model associated to photocount vectors. Several estimation methods were studied for the estimation of the unknown parameters associated to these multivariate mixed Poisson distributions. An estimator was derived by considering spatial correlation between adjacent pixels of the image. This estimator performed very similarly when compared to another estimator neglecting the correlation between adjacent pixels of the image. Future investigations include the consideration of stronger prior information for the correlation parameters. This prior information might be obtained from specific data, e.g., coming from the wavefront sensor.
Résumé
L’article étudie l’estimation des paramètres de l’amplitude complexe du front d’onde à partir de mesures d’intensités faible-flux. La corrélation spatiale de l’amplitude complexe du front d’onde est modélisée au sein d’une clique de l’image observée. Le cas général où cette amplitude complexe est de moyenne non nulle est également considéré. Un estimateur classique des moments, ainsi qu’un estimateur des moindres carrés non-linéaires prenant en compte les corrélations spatiales sont proposés. Dans le cadre de la détection d’exo-planètes par imagerie directe, les performances de ces estimateurs et des détecteurs associés sont étudiées et comparées. Les résultats obtenus mettent en évidence la nécessité de disposer d’un a priori plus fort sur la corrélation spatiale du front d’onde afin d’améliorer les performances d’estimation et de détection.
Speckle, spatial correlation, multivariate mixed Poisson distribution, composite likelihood, method of moments, nonlinear least squares, exoplanet
Mots clés
Speckle, corrélation spatiale, lois de Poisson mélangées multivariées, vraisemblance composite, méthode de moments, moindres carrés non linéaires, détection d’exo-planètes.
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