Mathematics - Colloquium
Monday, December 10, 2012
3:00 PM-4:00 PM
ABSTRACT: The talk is related to the reconstruction of interfaces, for time-harmonic acoustic waves, using far-fields generated by incident plane waves corresponding to few directions of incidence but with many frequencies. We will report on the following three questions: uniqueness, stability and reconstruction. We divide our talk into two main parts.
1. The first part is related to the case when we use only one frequency. In this case, we have local uniqueness results for general shapes and only logarithmic stability estimates for small or moderate frequencies. This explains why we cannot always expect high quality reconstructions using such frequencies.
2. The second part is related to the case when we use many frequencies. In this case, we have a global uniqueness result. We also provide an asymptotic conditional Holder stability estimates at high frequencies. This explains why the small features of the interface are indeed encoded in the far-fields corresponding to high frequencies. Finally, we give a multifrequency reconstruction algorithm which shows how taking into account low as well as high frequency information on the far-fields provides good and stable reconstructions of the interfaces.
Suggested Audiences: College, Adult
Last Modified: December 5, 2012 at 9:50 AM