The mutual coherence of A is then defined as[1][2] A lower bound is[3] A deterministic matrix with the mutual coherence almost meeting the lower bound can be constructed by Weil's theorem.
[4] This concept was reintroduced by David Donoho and Michael Elad in the context of sparse representations.
[6] The mutual coherence has since been used extensively in the field of sparse representations of signals.
In particular, it is used as a measure of the ability of suboptimal algorithms such as matching pursuit and basis pursuit to correctly identify the true representation of a sparse signal.
The Babel function for two columns is exactly the Mutual coherence, but it also extends the coherence relationship concept in a way that is useful and relevant for any number of columns in the sparse representation matrix as well.