Random sampling over locally compact abelian groups and inversion of the radon transform
Abstract: We consider the problem of reconstructing a measurable function over a Locally Compact Abelian group G from random measurements. The results presented herein are partially inspired by the concept of alias-free sampling. Here, the sampling and interpolation operation is modelled as an ap...
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| Autores principales: | , , |
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| Formato: | Artículo |
| Lenguaje: | Inglés |
| Publicado: |
Elsevier
2023
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| Materias: | |
| Acceso en línea: | https://repositorio.uca.edu.ar/handle/123456789/17199 |
| Aporte de: |
| Sumario: | Abstract:
We consider the problem of reconstructing a measurable function over a Locally Compact Abelian
group G from random measurements. The results presented herein are partially inspired by the concept
of alias-free sampling. Here, the sampling and interpolation operation is modelled as an approximate
convolution operator with respect to a stochastic integral defined with an appropriately chosen random
measure. In particular, this includes the case where the random sampling points are chosen accordingly
to a Poisson random point process. We provide sufficient conditions that guarantee an approximate
reconstruction through a sampling process that is similar to alias-free random sampling. These results
are applied to the problem of approximating the inverse Radon transform of a function. |
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