This article may be too technical for most readers to understand.(May 2021)
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.
Definition and formulationEdit
The Babel function of a dictionary with normalized columns is a real-valued function that is defined as
When p=1, the babel function is the mutual coherence.
- Joel A. Tropp (2004). "Greed is good: Algorithmic results for sparse approximation" (PDF). IEEE Trans. Inform. Theory. 50 (10): 2231–2242. CiteSeerX 10.1.1.84.5256. doi:10.1109/TIT.2004.834793. S2CID 675692.
- Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
- Huan Li and Zhouchen Lin. "Construction of Incoherent Dictionaries via Direct Babel Function Minimization" (PDF).