New coherence and rip analysis for weak orthogonal matching pursuit

In this paper we define a new coherence index, named the global 2-coherence, of a given dictionary and study its relationship with the conventional mutual coherence and the restricted isometry constant. By exploring this relationship, we obtain more general results on sparse signal reconstruction using greedy algorithms in the compressive sensing (CS) framework. In particular, we obtain an improved bound over the best known results on the restricted isometry constant for successful recovery of sparse signals using orthogonal matching pursuit (OMP).