Nonparametric regression bases image analysis

Pierre-André Cornillon (1, 2) , Nicolas Hengartner (3) , Eric Matzner-Løber (1, 2) , Benoit Thieurmel (4)

1 UR2 - Université de Rennes 2
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 LANL - Los Alamos National Laboratory
4 Greenwich Statistics

Multivariate nonparametric smoothers are adversely impacted by the sparseness of data in higher dimension, also known as the curse of dimensionality. Adaptive smoothers, that can exploit the underlying smoothness of the regression function, may partially mitigate this effect. We present an iterative procedure based on traditional kernel smoothers, thin plate spline smoothers or Duchon spline smoother that can be used when the number of covariates is important. However the method is limited to small sample sizes (n < 2,000) and we will propose some thoughts to circumvent that problem using, for example,pre-clustering of the data. Applications considered here are image denoising.

Mots clés: Image sequence denoising; Iterative bias reduction; Kernel smoother; Duchon splines

Domaines: Statistiques [math.ST]

Pierre-André Cornillon, Nicolas Hengartner, Eric Matzner-Løber, Benoit Thieurmel. Nonparametric regression bases image analysis. Akritas, Michael G.; Lahiri, S. N.; Politis, Dimitris N. Topics in Nonparametric Statistics Proceedings of the First Conference of the International Society for Nonparametric Statistics, Springer, pp.185-195, 2014, Springer Proceedings in Mathematics & Statistics, 978-1-4939-0569-0. ⟨10.1007/978-1-4939-0569-0_17⟩. ⟨hal-01143428⟩