If we change sides in equation equ9 and rewrite it in the more standard form:
To estimate an approximate inverse for we apply the same normalization techniques in computing its inner product entries, which are, AMO transformation from a given input geometry to another. This normalization makes the cross-product matrix unit-less. Therefore when approximating by its transpose we avoid the ambiguity of scaling this adjoint. Moreover, since is hermitian, then it is equal to its transpose.
We conclude that is itself a data covariance matrix. It represents an equalization filter that measures the interdependencies among the data elements and corrects the imaging operator for the effects of fold variations.