Abstract: This paper investigates non-uniform guarantees of \(ell_1\) minimization, subject to an \(ell_infty\) data fidelity constraint, to stably recover the support of a sparse vector when solving noisy linear inverse problems. Our main contribution consists in giving a sufficient condition, framed in terms of the notion of dual certificates, to ensure that a solution of the \(ell_1-ell_infty\) convex program has a support containing that of the original vector, when the noise level is sufficiently small.