SOLVERS

Clement Kostov observed that in 2-D, even if the sampling in offset is irregular, the matrix L L^H is Toeplitz, as long as the sampling in ray parameter is uniform. For a Toeplitz matrix, an efficient means of solving the system, using Levinson recursion, exists with a cost proportional to the square of the length of the unknown vector.

In the migration case, because of the extra axis in the transform domain, the matrix is typically not Toeplitz. Though it is often block Toeplitz, and solution methods exist that take advantage of that form, we have elected to use a simple conjugate gradient scheme to solve the least-squares problem in these initial tests.