Quasi-Newton Approach for an Atmospheric Tomography Problem
This work addresses the computational challenge of atmospheric tomography for GPS applications, but the results are incremental as it applies existing optimization techniques to a specific problem without quantitative SOTA comparisons.
The authors apply quasi-Newton methods with smoothed total variation regularization to solve the GPS atmospheric tomography problem, finding that the limited memory BFGS algorithm with trust region effectively obtains a reasonably optimum solution.
This work studies the usage of well-known smoothed total variation regularization for solving an atmospheric tomography problem named as {\em GPS-tomography} in some quasi-Newton methods. That is we solve an unconstrained, convex, smooth minimization problem associated with a general type Tikhonov functional containing smoothed type total variation penalty term by quasi-Newton methods. As a result of the conducted experiments, it is concluded that limited memory BFGS algorithm with trust region is the effective algorithm in terms obtaining a reasonably optimum solution.