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REDUNDANCY IN GAUSSIAN RANDOM FIELDS

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01931737
Contributor : Agnès Desolneux Connect in order to contact the contributor
Submitted on : Thursday, November 22, 2018 - 10:01:00 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM
Long-term archiving on: : Saturday, February 23, 2019 - 4:16:00 PM

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  • HAL Id : hal-01931737, version 1

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Valentin de Bortoli, Agnès Desolneux, Bruno Galerne, Arthur Leclaire. REDUNDANCY IN GAUSSIAN RANDOM FIELDS. ESAIM: Probability and Statistics, EDP Sciences, 2020, Vol. 24, pp. 627-660. ⟨hal-01931737⟩

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