Redundancy in Gaussian random fields
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 627-660.

In this paper, we introduce a notion of spatial redundancy in Gaussian random fields. This study is motivated by applications of the a contrario method in image processing. We define similarity functions on local windows in random fields over discrete or continuous domains. We derive explicit Gaussian asymptotics for the distribution of similarity functions when computed on Gaussian random fields. Moreover, for the special case of the squared L2 norm, we give non-asymptotic expressions in both discrete and continuous periodic settings. Finally, we present fast and accurate approximations of these non-asymptotic expressions using moment methods and matrix projections.

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DOI : 10.1051/ps/2020010
Classification : 60F05, 60F15, 60G15, 60G60, 62H15, 62H35
Mots-clés : Random fields, spatial redundancy, central limit theorem, law of large numbers, eigenvalues approximation, moment methods 
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     author = {De Bortoli, Valentin and Desolneux, Agn\`es and Galerne, Bruno and Leclaire, Arthur},
     title = {Redundancy in {Gaussian} random fields},
     journal = {ESAIM: Probability and Statistics},
     pages = {627--660},
     publisher = {EDP-Sciences},
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     mrnumber = {4170178},
     zbl = {1455.60037},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2020010/}
}
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De Bortoli, Valentin; Desolneux, Agnès; Galerne, Bruno; Leclaire, Arthur. Redundancy in Gaussian random fields. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 627-660. doi : 10.1051/ps/2020010. http://www.numdam.org/articles/10.1051/ps/2020010/

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