REDUNDANCY IN GAUSSIAN RANDOM FIELDS
| hal.structure.identifier | CB - Centre Borelli - UMR 9010 [CB] | |
| dc.contributor.author | DE BORTOLI, Valentin | |
| hal.structure.identifier | CB - Centre Borelli - UMR 9010 [CB] | |
| dc.contributor.author | DESOLNEUX, Agnès | |
| hal.structure.identifier | Institut Denis Poisson [IDP] | |
| dc.contributor.author | GALERNE, Bruno | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LECLAIRE, Arthur | |
| dc.date.accessioned | 2024-04-04T03:04:05Z | |
| dc.date.available | 2024-04-04T03:04:05Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 1292-8100 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193118 | |
| dc.description.abstractEn | We introduce and study a notion of spatial redundancy in Gaussian random fields. we define similarity functions with some properties and give insight about their statistical properties in the context of image processing. We compute these similarity functions on local windows in random fields defined over discrete or continuous domains. We give explicit asymptotic Gaussian expressions for the distribution of similarity function random variables when computed over Gaussian random fields and illustrate the weaknesses of such Gaussian approximations by showing that the approximated probability of rare events is not precise enough, even for large windows. In the special case of the squared L 2 norm, non-asymptotic expressions are derived in both discrete and continuous periodic settings. A fast and accurate approximation is introduced using eigenvalues projection and moment methods. | |
| dc.language.iso | en | |
| dc.publisher | EDP Sciences | |
| dc.subject.en | Random fields | |
| dc.subject.en | spatial redundancy | |
| dc.subject.en | central limit theorem | |
| dc.subject.en | law of large numbers | |
| dc.subject.en | eigenvalues approximation | |
| dc.subject.en | moment methods | |
| dc.title.en | REDUNDANCY IN GAUSSIAN RANDOM FIELDS | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1051/ps/2020010 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Statistiques [math.ST] | |
| bordeaux.journal | ESAIM: Probability and Statistics | |
| bordeaux.page | pp. 627-660 | |
| bordeaux.volume | Vol. 24 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01931737 | |
| hal.version | 2 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01931737v2 | |
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