The Babel function (also known as cumulative coherence) measures the maximum total coherence between a fixed atom and a collection of other atoms in a dictionary.
The Babel function was conceived of in the context of signals for which there exists a sparse representation consisting of atoms or columns of a redundant dictionary matrix, A.
with normalized columns is a real-valued function that is defined as where
[1][2] When p=1, the Babel function is the mutual coherence.
Li and Lin have used the Babel function to aid in creating effective dictionaries for machine learning applications.