Abstract

We consider inverse scattering problems for the wave equation in the time domain: find the shape of a Dirichlet scattering object from time domain measurements of scattered waves. For this time domain inverse problem, we introduce sampling methods, a well-known family of techniques for corresponding frequency domain inverse scattering problems.

The problem setting and the time domain algorithm incorporate two basic features: The data consists of measurement of causal waves, and the inversion algorithm directly works on the time domain data without using a Fourier transformation.

Time-domain sampling methods naturally incorporate a continuum of frequencies in the inversion algorithm. Consequently, they induce the potential to improve the reconstruction quality when compared to methods working at one single frequency.