2016 • Conference Paper
Sparse Support Recovery with l∞ Data Fidelity
Authors:
Degraux, Kévin,
Peyré, Gabriel,
Fadili, Jalal,
Jacques, Laurent
Published in:
International Traveling Workshop on Interactions Between Sparse Models and Technology
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.