Volume 24, 2020
|Page(s)||627 - 660|
|Published online||04 November 2020|
Redundancy in Gaussian random fields
CMLA, ENS Paris Saclay, CNRS, Université Paris-Saclay,
2 CMLA, ENS Paris Saclay, CNRS, Université Paris-Saclay, 94235 Cachan, France.
3 Institut Denis Poisson, Université d’Orléans, Université de Tours, CNRS, France.
4 Univ. Bordeaux, IMB, Bordeaux INP, CNRS, UMR 5251, 33400 Talence, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 4 March 2020
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.
Mathematics Subject Classification: 60F05 / 60F15 / 60G15 / 60G60 / 62H15 / 62H35
Key words: Random fields / spatial redundancy / central limit theorem / law of large numbers / eigenvalues approximation, moment methods
© The authors. Published by EDP Sciences, SMAI 2020
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