This system is solved using Levinson algorithm, since the matrix LTWL is Toeplitz. This property is independent of the weighting matrix W; it just needs to be diagonal. It is also true for any spatial sampling.
We get the field U(t0,p) by applying the inverse Fourier in the time direction. After having filtered the field U (for multiple removal, for instance), we come back to the time-offset domain with the modeling operator L. To do so, we transform the field U to the frequency domain, and for each frequency , we multiply it by the matrix L (depending on ):
Finally, applying an inverse Fourier transform and an inverse NMO correction brings us back to the original time-offset domain.