Abstract
In this short note, we present a probabilistic perspective on Schiffer's problem in inverse scattering theory, which asks whether one can uniquely determine the shape of an unknown obstacle by a single far-field measurement. It is a longstanding problem and has received considerable studies in the literature. We show that this conjecture holds true in more general settings in the probabilistic sense. Our new perspective has important implications from the practical viewpoint and also points an interesting direction of research for broader inverse problems.
| Original language | English |
|---|---|
| Pages (from-to) | 294-299 |
| Journal | Communications on Analysis and Computation |
| Volume | 2 |
| Issue number | 3 |
| Online published | Sept 2024 |
| DOIs | |
| Publication status | Published - Sept 2024 |
Funding
The research was supported by NSFC/RGC Joint Research Scheme, N CityU101/21, ANR/RGC Joint Research Scheme, A-CityU203/19, and the Hong Kong RGC General Research Funds (projects 11311122, 11304224, and 11300821).
Research Keywords
- Inverse scattering
- obstacle
- shape determination
- single far-field measurement
- probability
- almost surely
RGC Funding Information
- RGC-funded
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