A monotonicity-based globalization of the level-set method for inclusion detection

TL;DR

This paper introduces a combined approach using the monotonicity and level-set methods to improve shape recovery in electrical conductivity inverse problems, reducing reliance on initial guesses and enhancing accuracy.

Contribution

It presents a novel integration of the monotonicity method with the level-set method for better shape detection in inverse problems.

Findings

Effective initial guess generation improves shape recovery.

Numerical results demonstrate the method's robustness.

Enhanced accuracy over traditional level-set approaches.

Abstract

We focus on a geometrical inverse problem that involves recovering discontinuities in electrical conductivity based on boundary measurements. This problem serves as a model to introduce a shape recovery technique that merges the monotonicity method with the level-set method. The level-set method, commonly used in shape optimization, often relies heavily on the accuracy of the initial guess. To overcome this challenge, we utilize the monotonicity method to generate a more precise initial guess, which is then used to initialize the level-set method. We provide numerical results to illustrate the effectiveness of this combined approach.