Weak RIP and Its Application to Compressed Sensing

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 × n random matrix A satisfies the isotropy property: E ( A{k}A ? {k} ) = I for every row vector A{k} of A, A ≡ A √ m always obeys the weak RIP with high probability and it is applicable to the CS theory.