Wavelet smoothing for curves in more than onedimension
Davide Pigoli, Laura Maria Sangalli · Virtual Community of Pathological Anatomy (University of Castilla La Mancha) · 2010
The estimation of smooth functions from their noisy and discrete observation is the first step in Functional Data Analysis. The choice of the basis functions is crucial in the process, since its properties influence the subsequent analysis. Wavelets offer functional basis systems with the property of localization both in space and frequency. We developed a procedure to use wavelet bases for the estimation of curves in more than one dimension, with a particular focus on the possibility of obtaining also estimates of curves derivatives from wavelet expansion. This method is tested on the estimation of centreline and radius of the Internal Carotid Artery (ICA) for patients suspected to be affected by cerebral aneurism