Babel function

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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[edit]

The Babel function of a dictionary with normalized columns is a real-valued function that is defined as

where are the columns (atoms) of the dictionary .[1][2]

Special case[edit]

When p=1, the babel function is the mutual coherence.


  1. ^ Joel A. Tropp (2004). "Greed is good: Algorithmic results for sparse approximation". CiteSeerX: 
  2. ^ Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise

See also[edit]