A new version of the convexification method for a 1-D coefficient inverse problem with experimental data

TL;DR

This paper introduces an improved convexification method for a 1-D coefficient inverse problem that avoids using the tail function, ensuring global convergence and validated through numerical tests with experimental data.

Contribution

The paper presents a novel version of the convexification method that eliminates the tail function and proves its global convergence for the first time.

Findings

Successfully reconstructs coefficients from experimental data

Demonstrates global convergence of the method

Achieves accurate results with both simulated and experimental data

Abstract

A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function", which is a complement of a certain truncated integral with respect to the wave number. Globally strictly convex cost functional is constructed with the Carleman Weight Function. Global convergence of the gradient projection method to the correct solution is proved. Numerical tests are conducted for both computationally simulated and experimental data.