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Sampling methods for time domain inverse scattering problems

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Inverse Problems

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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