Detection of a weak source: statistical models and methods. Application to exoplanets detection using direct imaging.

This thesis is concerned by extra-solar planets research using ground-based instruments that image a star and its very closeby environment. Such a research is extremely difficult due to the high light contrast ratio and the proximity between a potential exoplanet and its parent star. A fine qualitative and probabilistic description of the data and relevant inferential methods increase a posteriori the instruments performances. Hence, this thesis focuses on signal processing methods and on a more general statistical methodological issue. All studies are performed theoretically and practically. First, this thesis describes the data expected for the future SPHERE instrument of the Very Large Telescope, simulated from a detailed physical model. A simple probabilistic model of these data is used in particular to identify candidates. The inferences performances are also studied from a model that describes more realistically the noises that caracterize the images (correlated speckle noise, Poisson noise). The difference between the false alarm probabilities computed from the simple model and from the realistic model is emphasized. Then, the problem is adressed under the Bayesian paradigm. First, an original hypotheses test tool is introduced and studied: the posterior distribution of the likelihood ratio, denoted PLR. Its theoretical study especially shows that in a standard invariance framework the PLR is equal to a frequentist p-value. Further, a probabilistic model of the data is developped from the initial model and a probabilistic model of the light intensity of the exoplanet is proposed. They are finally used in the PLR and the Bayes factor.