A note on guaranteed sparse recovery via l1-minimization

It is proved that every s-sparse vector X is an element of C-N can be recovered from the measurement vector y = Ax is an element of C-m via l(1)-minimization as soon as the 2s-th restricted isometry constant of the matrix A is smaller than 3/(4+root 6) approximate to 0.4652, or smaller than 47(6+root 6) approximate to 0.4734 for large values of s. (C) 2009 Elsevier Inc. All rights reserved.