Projected Newton method for a system of Tikhonov-Morozov equations
For practitioners solving ill-posed inverse problems, this provides a theoretically grounded, efficient algorithm for automatic regularization parameter selection.
The authors derive a Newton-type method for solving the nonlinear system formed by Tikhonov regularization and Morozov's discrepancy principle, proving convergence with bounded step size. They reduce computational cost by projecting onto a low-dimensional Krylov subspace.
In this paper we derive a Newton type method to solve the non-linear system formed by combining the Tikhonov normal equations and Morozov's discrepancy principle. We prove that by placing a bound on the step size of the Newton iterations the method will always converge to the solution. By projecting the problem onto a low dimensional Krylov subspace and using the method to solve the projected non-linear system we show that we can reduce the computational cost of the method.