Demystifying the Coherence Index in Compressive Sensing [Lecture Notes]

The existence and uniqueness conditions are a prerequisite to ensure the reliable reconstruction of sparse signals from reduced sets of measurements within the compressive sensing (CS) paradigm. However, despite their underpinning role in practical applications, the existing uniqueness relations are either computationally prohibitive to implement [the restricted isometry property (RIP)] or involve mathematical tools that are beyond the standard background of engineering graduates (the coherence index). This may introduce conceptual and computational obstacles in the development of engineering intuition, design of suboptimal practical solutions, and understanding of theoretical and practical limitations of the CS framework.