Neighbourhood space

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.

Definition and formulation

The Babel function of a dictionary $\mathit{A}$ with normalized columns is a real-valued function that is defined as

$\mu (p)={\max }_{\left|\lambda \right|=p}\{{\max }_{j\notin \lambda }\{\sum _{i\in \lambda }\left|{\mathit{a}}_i^{\mathit{T}}{\mathit{a}}_j\right|\}\}$

where ${\mathit{a}}_k$ are the columns (atoms) of the dictionary $\mathit{A}$

References

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