In this work, we examine an inverse boundary value problem for a nonlinear wave equation in the plane, focusing on the recovery of an unknown potential. We present a fast, non-iterative numerical reconstruction method, based on higher-order linearization, that yields the Radon transform of the potential; this can then be inverted using standard X-ray tomography techniques to determine the potential. We also introduce a spectral regularization procedure to stabilize the numerical differentiation step required in the reconstruction. Numerical examples demonstrate the feasibility and accuracy of the approach.

The poster is based on joint work with Markus Harju and Teemu Tyni.