Definition 1 (Restricted isometry and orthogonality). The S-restricted isometry constant δS of a matrix F ∈ Rn×m is the smallest quantity such that (1− δS)‖x‖2 ≤ ‖FTx‖2 ≤ (1 + δS)‖x‖2 for all T ⊆ [m] with |T | ≤ S and all x ∈ R|T |. The (S, S′)-restricted orthogonality constant θS,S′ of F is the smallest quantity such that |FTx · FT ′x′| ≤ θS,S′‖c‖‖c‖ for all disjoint T, T ′ ⊆ [m] with |T | ≤ S...
