Consistency of ℓ1 recovery from noisy deterministic measurements

In this paper a new result of recovery of sparse vectors from deterministic and noisy measurements by ℓ1 minimization is given. The sparse vector is randomly chosen and follows a generic p-sparse model introduced by Candès and Plan [1]. The main theorem ensures consistency of ℓ1 minimization with high probability. This first result is secondly extended to compressible vectors.