Therefore, the permutation of measurement matrix columns will not effect the mutual coherence value.
While the frames obtained with [30] exhibit the smallest mutual coherence, the values of average coherence computed by (15) are identical for all matrix constructions except for random Gaussian matrices.
The mutual coherence of is the maximum absolute value of the off-diagonal entry of, supposing the columns of are normalized.
According to [28], if the mutual coherence (MC) that is the maximum value of pairwise correlation among the columns of A is small, the sparse signal can be recovered with high probability.
The key function in the theory of partially coherent light is the mutual coherence function Γ12 = Γ x1,τ2,τ), a complex quantity, which is the time averaged value of the cross correlation function of the light at the two aperture points x1 and x2 with a time delay τ (relating to a path difference to the point of observation of the interference fringes).
The reason is that we use GRMM as an initial value of our proposed algorithm; therefore, the designed matrix will have less mutual coherence and consequently better performance compared to its initial value, i.e., GRMM.
where |·| is the absolute value, μ(D) is often called the mutual coherence of the matrix D, and d i =Φ Ψ i denotes the i th column of D. The mutual coherence is known to be a sub-optimal metric to quantify CS matrices as compared to RIC.
The mutual coherence c(A) can be viewed as the largest off-diagonal value of AHA, i.e., the highest sidelobe (e.g., [12]).
In the above theorems, the role of the mutual coherence μ is crucial as the number of measurements needed to reconstruct x scales quadratically with its value.
The mutual coherence function is an observable quantity that can be related to the intensity of the field.
