Quasi-Newton Approach for an Atmospheric Tomography Problem

TL;DR

This paper explores the application of quasi-Newton methods, specifically limited memory BFGS with trust region, to solve a convex atmospheric tomography problem using smoothed total variation regularization, demonstrating its effectiveness.

Contribution

It introduces a quasi-Newton approach with smoothed total variation regularization for atmospheric tomography, highlighting the effectiveness of limited memory BFGS with trust region.

Findings

Limited memory BFGS with trust region effectively solves the problem.

Smoothed total variation regularization improves solution quality.

Quasi-Newton methods are suitable for convex atmospheric tomography problems.

Abstract

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.