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 mutual coherence and the restricted isometry constant. By exploring this relationship, we obtain more g
eneral 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).
Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the global 2-coh
erence , which provides a bridge between the well known mutual coherence and the restricted isometry constant, the performance of orthogonal matching pursuit with thresholding is analyzed and more general results for sparse signal reconstruction are obtained. It is also shown that given the same assumption on the coherence index and the restricted isometry constant as required for orthogonal matching pursuit, the thresholding variation gives exactly the same reconstruction performance with significantly less complexity.
