One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations

摘要: The $\ell_1$-synthesis model and the $\ell_1$-analysis recover structured signals from their undersampled measurements. solution of former is a sparse sum dictionary atoms, that latter makes correlations with atoms. This paper addresses question: when can we trust these models to specific signals? We answer question condition both necessary sufficient guarantee recovery be unique exact and, in presence measurement noise, robust. one--for--all sense it applies models, constrained unconstrained formulations, robust cases. Furthermore, convex infinity--norm program introduced for numerically verifying condition. A comprehensive comparison related existing conditions are included.