Row scaling: model normalization

Since each row corresponds to a summation surface, we apply the row normalization to imaging operators implemented as (sum) pull operators. We solve the normalized system:

$$\bold m = \bold R^{-1} \bold F \bold d \EQNLABEL{equ-mod}$$ (3)

where the sum of the elements of each row is along the diagonal of ${\bf R}$.

The solution in equ-mod is equivalent to applying the imaging operator ${\bf F}$ followed by a diagonal transformation ${\bf R^{-1}}$. Therefore, we will refer to this normalization as model or image normalization. Since ${\bf R^{-1}}$has the inverse units of ${\bf F}$, the normalized image is unit-less.

Given that each row of ${\bf F}$ corresponds to an output bin, ${\bf R^{-1}}$ is therefore normalization by the coverage after imaging. We refer to this coverage as the imaging fold, e.g, AMO fold, DMO fold ... etc.