Application of the Finite Element Method in a Quantitative Imaging technique

TL;DR

This paper demonstrates the use of the Finite Element Method combined with a globally convergent approach to accurately reconstruct sound speed in small tumor-like inclusions from a single measurement in a hyperbolic equation.

Contribution

It introduces a novel combination of FEM with a globally convergent method for solving multidimensional coefficient inverse problems in imaging.

Findings

Successful quantitative reconstruction of sound speed in tumor-like inclusions.

Effective application of FEM in a hyperbolic inverse problem context.

Validation through numerical examples showing accurate results.

Abstract

We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic equation using data resulted from a single measurement. To solve our MCIP we use approximate globally convergent method and then apply FEM for the resulted equation. Our numerical examples show quantitative reconstruction of the sound speed in small tumor-like inclusions.