Spline Estimation of Integral Curves from Noisy Vector Field Data

• Activity Number: 477
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guanqun Cao*+ and Lyudmila Sakhanenko and Lijian Yang and Owen Carmichael
• Companies: Auburn University and Michigan State University and Michigan State University and University of California at Davis
• Keywords: B-spline ; confidence ellipses ; diffusion tensor imaging ; integral curves ; vector fields

Abstract

In Diffusion Tensor Imaging, a brain imaging technique, neuroscientists study the location of neural fibers. They are modeled by integral curves, those are not observed directly. Instead, for example a two-dimensional vector field is observed on a regular grid perturbed by additive random noise. The object of interest is an estimator of an integral curve driven by the vector field starting at a fixed location. We construct a B-spline estimator of the vector field and a plug-in estimator of the integral curve. We show that the properly normalized difference between our estimated curve and the true curve as a stochastic process converges to a centered Gaussian process. We perform theoretical and simulation comparison study for our estimator versus an estimator constructed in Koltchinskii, Sakhanenko and Cai (2007). As an alternative approach, our estimator has no asymptotic bias and the corresponding confidence ellipses can be computed faster than those studied in Koltchinskii et al. (2007).