Speaker
Description
We consider the inverse problem of recovering the shape of an object from measurements of how it scatters time-harmonic waves. To quantify the uncertainy, the problem is cast in a Bayesian framework and we discuss possible choices for the prior distribution for the shape. As prototype of time-harmonic scattering, we consider the Helmholtz equation to relate the shape to the measurements and obtain the likelihood, from which the Bayesian posterior is obtained. We study the well-posedness of the inverse problem as well as numerical methods to sample from the posterior. In doing this, we focus on the role of the frequency of the incoming wave excitation on the result of the inversion. This is rigorously quantified in our well-posedness results via frequency-explicit stability estimates for the posterior, and observed numerically via simulations for different frequencies. This is joint work with Safiere Kuijpers (University of Groningen).
