Convergent algorithm based on Carleman estimates for coefficient inverse problems

We are interested in an inverse problem for the wave equation. More precisely, it consists in the determination of an unknown time-independent coefficient from a single measurement of the Neumann derivative of the solution on a part of the boundary. While its uniqueness and stability properties are already well known, we propose an original reconstruction algorithm and prove its global convergence thanks to Carleman estimates for the wave operator. The numerical implementation of this strategy presents some challenges that we propose to address in this talk. Several numerical examples will illustrate the efficiency of the algorithm.