R1magic (version 0.3.4)

mutualCoherence: Cumulative mutual coherence

Description

Generate vector of cumulative mutual coherence of a given matrix up to a given order. \ Mutual Cumulative Coherence of a Matrix A at order k is defined as \( M(A, k) = max_{p} max_{p \ne q, q \in \Omega } \sum_{q} | <a_{p}, a_{q}> | / ( |a_{p}| |a_{q}|)\)

Usage

mutualCoherence(A, k)

Value

Returns k-vector

Arguments

A

A matrix.

k

Integer value determines number of columns or the order of mutual coherence function to .

Author

Mehmet Suzen

References

Compressed sensing in diffuse optical tomography \ M. Suzen, A.Giannoula and T. Durduran, \ Opt. Express 18, 23676-23690 (2010) \ J. A. Tropp \ Greed is good: algorithmic results for sparse approximation, \IEEE Trans. Inf. Theory 50, 2231-2242 (2004)

Examples

set.seed(42)
B <- matrix(rnorm(100), 10, 10) # Gaussian Random Matrix
mutualCoherence(B, 3) # mutual coherence up to order k