1. Effective Dictionary, Mutual Coherence, and Average Mutual Coherence

Let 1nR ×∈s be a signal of interest and consider compressive sampling of s by linear projection =y P s with m nR ×∈P and m n . Let n LR ×∈D with L n ≥ be a dictionary that sparsifies s: =s Dθ where θ is sparse or near sparse. By convention the 2-norm of each column of D is normalized to unity. The compressed measurement can be expressed as =y PDθ where the product matrix = PDD is called effective dictionary