| Autor: |
Helin, Tapio, Lassas, Matti, Päivärinta, Lassi |
| Rok vydání: |
2014 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study an inverse acoustic scattering problem in half-space with a probabilistic impedance boundary value condition. The Robin coefficient (surface impedance) is assumed to be a Gaussian random function $\lambda = \lambda(x)$ with a pseudodifferential operator describing the covariance. We measure the amplitude of the backscattered field averaged over the frequency band and assume that the data is generated by a single realization of $\lambda$. Our main result is to show that under certain conditions the principal symbol of the covariance operator of $\lambda$ is uniquely determined. Most importantly, no approximations are needed and we can solve the full non-linear inverse problem. We concentrate on anisotropic models for the principal symbol, which leads to the analysis of a novel anisotropic spherical Radon transform and its invertibility. |
| Databáze: |
arXiv |
| Externí odkaz: |
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