REDUNDANCY IN GAUSSIAN RANDOM FIELDS
Language
en
Article de revue
This item was published in
ESAIM: Probability and Statistics. 2020, vol. Vol. 24, p. pp. 627-660
EDP Sciences
English 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. ...Read more >
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.Read less <
English Keywords
Random fields
spatial redundancy
central limit theorem
law of large numbers
eigenvalues approximation
moment methods
Origin
Hal imported