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

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.