Sufficient Conditions for CS-recovery

In this paper we define the k-restrictly norm constant rk(A) of a matrix A to be used in compressed

sensing and give better error estimations on recovering compressive signals with noise using the

matrix A~ _ A

rk(A) . Furthermore, we define the notion of k-restricted invertibility of A, which is

equivalent to that A~ _ A=rk(A) obeys the RIP of order k. And by using the Q. Mo and S. Li

idea and T. Cai and A. Zhang idea, we establish the sufficient condition for the restricted isometry

constant _~k (k _ s) of A~ under the assumption that A is k-restrictly invertible. In particular, if

~_s < 0:5 and ~_2s < 0:828, then an unknown compressive signal with noise can be recovered.