What Can We Hear From an Echo? Sampling Methods for Biharmonic Inverse Scattering

Inverse scattering problems ask us to recover an unknown object from the waves it scatters, with applications ranging from medical imaging to non-destructive testing. Such problems are nonlinear and ill-posed, and iterative methods typically need a good initial guess. Qualitative methods avoid this by reconstructing the scatterer through a simple, rigorously justified indicator function. In this talk, I consider biharmonic wave scattering by a penetrable obstacle, a model for flexural waves in thin plates. Although only the propagating part of the scattered field reaches the far field, a factorization of the far-field operator justifies sampling methods that recover the obstacle. Numerical examples show noise-robust reconstructions of non-convex and multiple scatterers. I will also discuss transmission eigenvalues, which can be recovered from the data and reveal the material properties of the scatterer.