Iterative solution for the inverse filter

The inversion of the cross-product matrix ${\bf A}$ is a computationally challenging task. We use an iterative solution to estimate the inverse of ${\bf A}$. This solves a huge set of simultaneous equations without the need to write down the matrix of coefficients. The iterative technique is based on the conjugate gradient method, which produces a good result at a reasonable cost. Experience has shown that a satisfactory solution for equation (11) can be achieved in less than 10 iterations, where each iteration involves the application of the adjoint followed by the forward operator. In every iteration, a total of 2n AMO operations are performed in order to project each trace to all the other traces in the selected input. Note that both the forward and transpose operations are AMO transformations. The cost of each operation is very cheap giving the narrow aperture of AMO.