Model-space preconditioning

This approach is based on a post-multiplication of the matrix $\bold L$ by a diagonal matrix ${\bf C^{-1}}$ where the sums of the elements from each column of $\bold L$ are along the diagonal of ${\bf C}$.The preconditioning operator introduces a new model $\bold x$ given by

$$\bold x = \bold C \bold m \EQNLABEL{mod-prec}$$ (56)

By the preconditioning transformation, we have recast the original inversion relation equ1 into

$$\bold d = \bold L \bold C^{-1} \bold x. \EQNLABEL{prec}$$ (57)

After solving for $\bold x$ we easily compute $\bold m = \bold C^{-1} \bold x$.

Given that each column of $\bold L$ corresponds to an output bin, $\bold C^{-1}$is normalization by the coverage after AMO.