Iterative algorithms for total variation-like reconstructions in seismic tomography

TL;DR

This paper compares various total variation-like penalties and iterative algorithms for seismic tomography, introducing a new algorithm for constrained problems and analyzing their convergence speeds.

Contribution

It provides a comparative analysis of total variation-like penalties and introduces a novel algorithm with proven convergence for seismic tomography reconstruction.

Findings

Different penalties have varying convergence speeds.

The new algorithm outperforms existing methods in constrained settings.

Numerical comparisons demonstrate effectiveness of the proposed approach.

Abstract

A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, ...) is made in the context of global seismic tomography. Both penalized and constrained formulations of seismic recovery problems are treated. A number of simple iterative recovery algorithms applicable to these problems are described. The convergence speed of these algorithms is compared numerically in this setting. For the constrained formulation a new algorithm is proposed and its convergence is proven.