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 Candes and al. The main theorem ensures consistency of l1 minimization with high probability. This first result is secondly extended to compressible vectors. 
Charles Dossal and R\'emi Tesson
math.OC