Sparse Support Recovery with $ell_{infty}$ Data Fidelity

Type
Publication
Proceedings of the third international Traveling Workshop on Interactions between Sparse models and Technology (iTWIST'16), arXiv:1609.04167

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.