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: Porten, Erika, Medina, Juan Miguel, Morvidone, Marcela
Formato: Artículo
Lenguaje:Inglés
Publicado: Elsevier 2023
Materias:
MUESTREO
ANALISIS ARMÓNICO ABSTRACTO
TRANSFORMACION DE RADON
PROCESOS ALEATORIOS
Acceso en línea:https://repositorio.uca.edu.ar/handle/123456789/17199
Aporte de:
Repositorio Institucional de la Universidad Católica Argentina (UCA) de Universidad Católica Argentina
id I33-R139-123456789-17199
record_format dspace
spelling I33-R139-123456789-171992023-10-02T22:52:24Z 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
institution Universidad Católica Argentina
institution_str I-33
repository_str R-139
collection Repositorio Institucional de la Universidad Católica Argentina (UCA)
language Inglés
topic MUESTREO
ANALISIS ARMÓNICO ABSTRACTO
TRANSFORMACION DE RADON
PROCESOS ALEATORIOS
spellingShingle 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
topic_facet MUESTREO
ANALISIS ARMÓNICO ABSTRACTO
TRANSFORMACION DE RADON
PROCESOS ALEATORIOS
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
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
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