Learning a model of non-stationary nuisances with non-local correlations for object detection

Abstract

We tackle the problem of detecting faint objects in multivariate data corrupted by a strong and spatially correlated nuisance component in the low-sample regime. Standard covariance-based models often yield unstable or ill-conditioned estimators of the nuisance statistics, severely degrading detection performance. We propose a data-driven approach based on sparse precision matrix modeling, where the precision matrix is approximated through a pivoted sparse Cholesky factorization whose non-zeros coefficients are learned by maximum likelihood. This yields a low-complexity yet expressive statistical model of the nuisance. Building on this model, we derive a generalized likelihood ratio test for faint source detection enabling direct control of the false alarm rate. The approach is evaluated on an astrophysical application: the detection of exoplanets by high contrast imaging, where it achieves state-of-the-art performance.