Sufficient Conditions for CS-recovery
Journal of Advances in Mathematics and Computer Science · pp. 184–198 · Published 23 Oct 2013
10.9734/BJMCS/2014/6171Abstract
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.
Cited by 1
Hiroshi Inoue · Applied and Computational Harmonic Analysis · 2014
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