Weak RIP and Its Application to Compressed Sensing
Hiroshi Inoue *
Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan.
*Author to whom correspondence should be addressed.
Abstract
The first purpose of this paper is to give a sufficient condition under which A obeys the weak RIP and to evaluate the solution of CS using this result. The second is to show that when an m x n random matrix A satisfies the isotropy property: 
for every row vector A{k} of A, 
always obeys the weak RIP with high probability and it is applicable to the CS theory.
Keywords: Compressed sensing, Isotropy property, Restricted isometry constants, Restricted isometry property, Sparse approximation, Sparse signal recovery, Weak restricted isometry property.