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

New Coherence and RIP Analysis for Weak Orthogonal Matching Pursuit