...''

In the present work, p indexes pixels in the classic spatial domain. However, the same formalism applies if other domains are considered, for example, the Fourier one.

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... unbiased

The expression ${\rm E}[a\vert b]$ indicates conditional expectation of a given b.

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...)

The entries of ${\vec{\Delta}}\Cb_{{\vec{\mathfrak S}}}$ are not independent. If ${\bf {C}}$ is a symmetric, positive definite matrix, then the same holds for its inverse  ${\bf {C}}^{-1}$. However, in general, this is not true for a matrix ${\bf {\mathcal C}}= {\bf {C}}+ {\vec{\Delta}}{\bf {C}}$ obtained perturbing ${\bf {C}}$ with an arbitrary matrix. This means that the entries of ${\vec{\Delta}}{\bf {C}}$ have to satisfy certain conditions. If ${\bf {\mathcal C}}$ is written in the form $[({\bf {Q}}+ {\vec{\Delta}}{\bf {Q}}) ({\bf {Q}}+ {\vec{\Delta}}{\bf {Q}})^{\rm T}]$, with ${\bf {Q}}= {\bf {C}}^{1/2}$ and ${\vec{\Delta}}Q$ a matrix of zero-mean random quantities, and then expanded expanded in Taylor series, one can find the same result as in Eq. (34) with ${\vec{\Delta}}{\bf {C}}= ({\vec{\Delta}}{\bf {Q}}) {\bf {Q}}^{\rm T} + {\bf {Q}}({\vec{\Delta}}{\bf {Q}})^{\rm T}$.

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