A globally accelerated numerical method for optical tomography with continuous wave source

TL;DR

This paper introduces a new globally convergent numerical method for optical tomography with a continuous wave source, improving inverse problem solutions in medical and battlefield imaging by effectively approximating the tail function.

Contribution

The paper presents a novel numerical approach with proven global convergence for inverse elliptic problems involving moving point sources, enhancing imaging techniques.

Findings

Method converges globally with proper tail function approximation

Numerical experiments verify convergence and effectiveness

Applicable to medical imaging and electrical impedance tomography

Abstract

A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured as the data for the inverse problem. A rigorous convergence analysis shows that this method converges globally, provided that the so-called tail function is approximated well. This approximation is verified in numerical experiments, so as the global convergence. Applications to medical imaging, imaging of targets on battlefields and to electrical impedance tomography are discussed.