Approche inverse pour la reconstruction des environnements circumstellaires en polarim?trie avec l?instrument d?imagerie directe ESO/VLT SPHERE IRDIS.

Circumstellars environments observation is a key for the comprehension of planet formation. If the very large telescopes allow the resolution of these environments, their observation is difficult due to the high contrast between the environment and their host stars. In fact the host stars are 1000 to 10 000 times brighter than the environment, even 10 000 000 times brighter for exoplanets. When images of these circumstellar environnements are acquired in direct imaging, the signal of the environnements mixed to star light residuals. Yet, the light of the environment is partially linearly polarized while the light od the star is unpolarized. The instrument Infrared Dual-band Imaging and Spectroscopy (IRDIS) of the European Southern Observatory?s (ESO) Spectro-Polarimeter High-contrast Expolanet REsearch (SPHERE) instrument, installed at one of the four Very Large Telescopes (VLT) in Atacama in Chile, acquires datasets where the polarization is modulated according to a known angles cycle. It is then possible, by combinations of the data, to extract the polarized signal of the environment from the unpolarized residual light of the stars and unpolarized light of the disks. The stat-of-the-art methods to extract such signal do not take optimally into account the photon noise statistics of the data, which dominate the signal of interest, nor the read out noise of the detector. Moreover, if any image from a rotation cycle is missing, the rest of the cycle is not used. Finally, any centering and rotation of the data or deconvolution by the PSF is generally performed in separated steps from the data reduction. The bad pixels and dead pixels are interpolated before the processing. The consequence of such approach is that the propagation of the errors in the data is not controlled.The ? inverse problem ? methods allow such processing while controlling the error propagation in the reconstructions. These approaches have never been developed, so far, for high contrast direct imaging in polarimetry. My goal in this thesis is to optimally reconstruct, from the polarimetric data of the instrument ESO/VLT-SPHERE IRDIS, maps of the circumstellar environments polarized light, the ascociated polarization angles and the unpolarized star light residuals and circumstellar environments light. First, I develop a nonlinear physical model of the data, pixelwise independent, parametric in these quantities of interest, or linear with respect to the Stokes parameters, from which they can be estimated. Throughout this thesis, I complete the model by adding centering, rotations and convolutions, making it pixelwise dependent. The parameters are then estimated by the minimization of an objective function, derived from the co-log-likelyhood of the data, under some constraint, such as positivity constraint or epigraphical constraint, and regularizations as smooth and non-smooth Total Variation and the Shatten norm on the Hessian. This methods are all applied on simulated datasets, created to reproduce typical astrophysical datasets obtained in circumstellar environment polarimetrical direct imaging. Depending of the properties of the functions considered in the objective function, the research of its minimum is done with different algorithms as the Variable Metric Limited Memory and Bound algorithm, Forward-Backward with backtracking and the preconditioned primal-dual Condat-Vu algorithm with backtracking. I also use the Stein Unbiased Risk Estimator to auto-tune the weights of the regularization. In the results, I show that the use of a complete direct model of the data, taking in account the recentering, the rotations and the convolution and the estimation of its parameters from a constraint problem, taking in account the measure precision and the missing data reduces the error on the estimation maps in such astrophysics context.