On the optimality of a L1/L1 solver for sparse signal recovery from sparsely corrupted compressive measurements

Laurent Jacques

This short note proves the ${\ell }_2-{\ell }_1$ instance optimality of a ${\ell }_1/{\ell }_1$ solver, i.e a variant of \emph{basis pursuit denoising} with a ${\ell }_1$ fidelity constraint, whe…