Generalized Likelihood Ratio (GLR) : As parameters are unknown, we have to estimate them by maximum of likelihood under both hypothesis. Under H , we estimate the mean of the ₀ speckles and the covariance matrix, and under H , we estimate ₁ the mean of the speckles, the covariance matrix and the flux of the planet. We then compute the Likelihood Ratio which leads to the following statistic of test : When there is a planet, the determinant of the covariance matrix under H will be smaller than the one under H as the signature ₁ ₀ of the planet is not retrieved under H . Thus, the threshold will be ₀ superior when there is a planet. Neyman Pearson Test : In order to get the maximum theoretical performance, we build a Neyman Pearson test. It is the hypothesis test when all parameters are known. It leads to the following statistic of test : This statistic is thus a adapted filter applied on patches. Exoplanets detection by direct imaging using statistical learning Romain MAYER*, David MARY*, Élodie CHOQUET** * Lagrange (UCA, OCA,CNRS), Nice ** LAM, Marseille romain.mayer@oca.eu +33688448046 www.linkedin.com/in/ romain-mayer TOPIC AND CONTEXT OF THE PROJECT STATISTICAL LEARNING RESULTS ON 1D SIMULATIONS Modelisation : Each patch is modeled under both hypothesis : Under H (lack of planet) , a patch is composed from the ₀ mean of speckles μ and the noise ε, assumed Gaussian with covariance C. Under H , there is the signature of a potential planet : it is the ₁ PSF multiplied by the flux α . Objective : We build a new exoplanet detection algorithm based on statistical methods applied to spatial imagery data (from JWST and VLT/SPHERE). This field has already been explored through different methods, like the PACO¹ algorithm. The goal of our work is to compare and combine statistical learning approaches and machine learning methods, to set up an innovative hybrid method. Statistical method : We apply three hypothesis test by maximum of likelihood ratio on each pixel of an image considering the hypothesis whether there is a planet (H ) or not ₁ (H ). ₀ Patches construction: We use Angular Differential Imaging observations to get F frames over time centered on a studied star. Given the rotation of the earth, a potential planet will rotate around the star. We will consider patches (square of size K*K) centered on the studied pixel, Consequently each pixels and associated patches will rotate frame by frame. Using the projection of each patch on the frames, we get F patches per frame. We also note that patches will overlap each other over time. 1 2 F Projection of the first patch on frame 2 Projection of the first patch on frame F Simulation : In a first place, we simulate 1D-patches to test our methods. We want to compare three GLR methods (with more or less simplified assumptions) and the Neyman Pearson test. We thus implement: ● The Neyman Pearson test (dotted curves) ● The Global GLR (green curves) by not making the assumption of spatial independence between the patches ● The Spatial GLR (yellow curves) by making the assumption of spatial independence ● The Simplified GLR (blue curves) where we do not distinguish the two hypothesis. We distinguish a case without overlap and a case with strong overlap to see the impact it has on the performance of the methods ROC curves in case of no overlap ROC curves in case of strong overlap θ PSF of a planet Speckles RGLR= det( ^C0) det( ^C1) RNP=∑ f=1 F hf C −1(r f−μ) H0: r f=μ +ϵf 0 H 1: r f=μ +α∗PSF +ϵf 1 with ϵf i∼N(0,Ci) Results : We observe first that the Simplified GLR performance deteriorates when we increase the rate of overlap. Indeed, the mean of the speckles is not estimated under each hypothesis by this method. Thus the signature of a potential planet highly contaminate the estimation of μ when the overlap increases. The Global GLR is less efficient when there is no overlap as it leads to estimate a huge matrix of covariance. The Spatial GLR appears to be a good compromise as it assumes the