Stima di curve tridimensionali tramite wavelets, con un applicazione alla geometria dell arteria carotide interna
Wednesday 23rd December 2009
Functional Data Analysis is a branch of statistics which focuses on data which can be seen as the observed value of a functional random variable. Anyway, from a practical point of view every data is observed on a discrete grid and a measurement error is also present. Thus, a crucial step of the analysis consists of the reconstruction of the continuous functional data starting from the discrete observations. Choosing the functional basis for the reconstruction is essential in the process. In this thesis work a wavelets basis is used for the estimation of smooth functional data and their derivatives. Moreover, we extend wavelets based estimation techniques to the multidimensional case, in order to apply our method to 3D curves. Finally, we obtain an estimation of centreline and radius of the internal carotid artery (ICA) for the patients of the AneuRisk Project dataset.