Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	Denoising and interior detection problems
Publication Date:	2020-11-02
Authors:	- Paulo Eduardo Oliveira - Nuno Picado
Abstract:	Let ℳ be a compact manifold of ℝ^d. The goal of this paper is to decide, based on a sample of points, whether the interior of ℳ is empty or not. We divide this work in two main parts. Firstly, under a dependent sample which may or may not contain some noise within, we characterize asymptotic properties of an interior detection test based on a suitable control of the dependence. Afterwards, we drop the dependence and consider a model where the points sampled from the manifold are mixed with some points sampled from a different measure (noisy observations). We study the behaviour with respect to the amount of noisy observations, introducing a methodology to identify true manifold points, characterizing convergence properties.
Institution:	DMUC 20-30
Online version:	http://www.mat.uc.pt...prints/eng_2020.html
Download:	Not available