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Session S08 - Inverse Problems and Applications

Friday, July 23, 17:00 ~ 17:30 UTC-3

Inversion from a random sampling of the Radon transform in the context of LCA groups

Erika Porten

Universidad Nacional de San Martín , Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Based on the definition of the Fourier transform on a locally compact abelian group $G$, we consider the problem of reconstructing a measurable function over $G$ from a countable subset of random samples. The sampling is carried out according to a Poisson random point process. For the interpolation step, we propose an iterative procedure in which a resampling is performed at each iteration, and we present error estimates of the approximation obtained. We apply these results to the problem of approximating the inverse Radon transform of a function. Finally, we present numerical simulations that support the effectiveness of the method.

Joint work with Marcela Morvidone (Universidad de San Martin, Argentina) and Juan Miguel Medina (Universidad de Buenos Aires, Argentina).

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