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 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.
| Main Authors: | , , |
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| Format: | Artículo biblioteca |
| Language: | eng |
| Published: |
Elsevier
2023
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| Subjects: | MUESTREO, ANALISIS ARMÓNICO ABSTRACTO, TRANSFORMACION DE RADON, PROCESOS ALEATORIOS, |
| Online Access: | https://repositorio.uca.edu.ar/handle/123456789/17199 |
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