Weak RIP and Its Application to Compressed Sensing

The first purpose of this paper is to give a sufficient condition under whichAobeys the weak RIPand to evaluate the solution of CS using this result. The second is to show that when anm×nrandom matrixAsatisfies the isotropy property:E(A{k}A?{k})=Ifor every row vectorA{k}ofA, ̃A≡A√malways obeys the weak RIP with high probability and it is applicable to the CS theory.