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.
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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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oai:ucacris:123456789-171992023-10-02T22:52:24Z Random sampling over locally compact abelian groups and inversion of the radon transform Porten, Erika Medina, Juan Miguel Morvidone, Marcela MUESTREO ANALISIS ARMÓNICO ABSTRACTO TRANSFORMACION DE RADON PROCESOS ALEATORIOS 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. 2023-09-28T10:28:42Z 2023-09-28T10:28:42Z 2023 Artículo Porten, E., Medina, J. M., Morvidone, M. Random sampling over locally compact abelian groups and inversion of the radon transform [en línea]. Applied and Computational Harmonic Analysis. 2023, 67. doi: 10.1016/j.acha.2023.101576 . Disponible en: https://repositorio.uca.edu.ar/handle/123456789/17199 1063-5203 (impreso) 1096-603X (online) https://repositorio.uca.edu.ar/handle/123456789/17199 10.1016/j.acha.2023.101576 eng Acceso restringido http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Elsevier Applied and Computational Harmonic Analysis. Vol. 67, 2023 |
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AR |
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Bibliográfico |
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biblioteca |
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| language |
eng |
| topic |
MUESTREO ANALISIS ARMÓNICO ABSTRACTO TRANSFORMACION DE RADON PROCESOS ALEATORIOS MUESTREO ANALISIS ARMÓNICO ABSTRACTO TRANSFORMACION DE RADON PROCESOS ALEATORIOS |
| spellingShingle |
MUESTREO ANALISIS ARMÓNICO ABSTRACTO TRANSFORMACION DE RADON PROCESOS ALEATORIOS MUESTREO ANALISIS ARMÓNICO ABSTRACTO TRANSFORMACION DE RADON PROCESOS ALEATORIOS Porten, Erika Medina, Juan Miguel Morvidone, Marcela Random sampling over locally compact abelian groups and inversion of the radon transform |
| description |
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. |
| format |
Artículo |
| topic_facet |
MUESTREO ANALISIS ARMÓNICO ABSTRACTO TRANSFORMACION DE RADON PROCESOS ALEATORIOS |
| author |
Porten, Erika Medina, Juan Miguel Morvidone, Marcela |
| author_facet |
Porten, Erika Medina, Juan Miguel Morvidone, Marcela |
| author_sort |
Porten, Erika |
| title |
Random sampling over locally compact abelian groups and inversion of the radon transform |
| title_short |
Random sampling over locally compact abelian groups and inversion of the radon transform |
| title_full |
Random sampling over locally compact abelian groups and inversion of the radon transform |
| title_fullStr |
Random sampling over locally compact abelian groups and inversion of the radon transform |
| title_full_unstemmed |
Random sampling over locally compact abelian groups and inversion of the radon transform |
| title_sort |
random sampling over locally compact abelian groups and inversion of the radon transform |
| publisher |
Elsevier |
| publishDate |
2023 |
| url |
https://repositorio.uca.edu.ar/handle/123456789/17199 |
| work_keys_str_mv |
AT portenerika randomsamplingoverlocallycompactabeliangroupsandinversionoftheradontransform AT medinajuanmiguel randomsamplingoverlocallycompactabeliangroupsandinversionoftheradontransform AT morvidonemarcela randomsamplingoverlocallycompactabeliangroupsandinversionoftheradontransform |
| _version_ |
1781879426522284032 |