Even though the target-oriented Hessian has a smaller number of rows and columns in equation (9), its condition number could be high, making the solution of the non-stationary least-squares filtering problem in equation (5) unstable. One solution is adding a smoothing regularization operator to equation (5):

(11) |

A more sophisticated regularization scheme could involve applying an smoothing operator in the angle (or ray parameter) dimension Kuehl and Sacchi (2001); Prucha et al. (2000). More research need to be done regarding that subject, which is of extreme importance to obtain stable and meaningful results in real case scenarios.

5/3/2005