Varying Coefficient Tensor Models for Brain Imaging

Eilers, Paul H. C.; Heim, Susanne and Marx, Brian D. (2005): Varying Coefficient Tensor Models for Brain Imaging. Collaborative Research Center 386, Discussion Paper 436

Abstract

We revisit a multidimensional varying-coefficient model (VCM), by allowing regressor coefficients to vary smoothly in more than one dimension, thereby extending the VCM of Hastie and Tibshirani. The motivating example is 3-dimensional, involving a special type of nuclear magnetic resonance measurement technique that is being used to estimate the diffusion tensor at each point in the human brain. We aim to improve the current state of the art, which is to apply a multiple regression model for each voxel separately using information from six or more volume images. We present a model, based on P-spline tensor products, to introduce spatial smoothness of the estimated diffusion tensor. Since the regression design matrix is space-invariant, a 4-dimensional tensor product model results, allowing more efficient computation with penalized array regression.

• Item Type: Paper
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics
• Language: English