Similarly to the data-space filter, computing the model-space inverse reduces to estimating an inverse for a cross-product matrix . This inverse acts as a filter for the model space. Each element of measures the correlation between a model element and another model element . The computation of each element requires the evaluation of an inner product in the data space. Since that the data-space is irregularly sampled, the computation must be carried numerically.
The size of is the square of the size of the model. Given that the adjoint operator, , is AMO-Stacking then the size of the model is generally much smaller than the data. This leads to a more affordable computation of compared to the costs of computing the data-space filter.