Spatial Shrinkage Estimation of Diffusion Tensors on Diffusion-Weighted Imaging Data

Abstract

Diffusion tensor imaging (DTI), based on the diffusion-weighted imaging (DWI) data acquired from magnetic resonance experiments, has been widely used to analyze the physical structure of white-matter fibers in the human brain in vivo. The raw DWI data, however, carry noise; this contaminates the diffusion tensor (DT) estimates and introduces systematic bias into the induced eigenvalues. These bias components affect the effectiveness of fiber-tracking algorithms. In this article, we propose a two-stage spatial shrinkage estimation (SpSkE) procedure to accommodate the spatial information carried in DWI data in DT estimation and to reduce the bias components in the corresponding derived eigenvalues. To this end, in the framework of the heteroscedastic linear model, SpSkE incorporates L ₁-type penalization and the locally weighted least-square function. The theoretical properties of SpSkE are explored. The effectiveness of SpSkE is further illustrated by simulation and real-data examples. Supplementary materials for this article are available online.

KEY WORDS:

• Brain imaging
• Diffusion tensor imaging
• L ₁ penalty
• Locally weighted least squares

Acknowledgments

The authors thank the editor, the associate editor, and two referees for constructive comments and suggestions that led to significant improvements in the article; the authors also thank Richard J. Davidson and Andrew L. Alexander at the Waisman center, University of Wisconsin-Madison, for providing the DWI dataset. The research is supported in part by NUS Grant R-155-000-100-133, by the Natural Sciences and Engineering Research Council of Canada, and by a startup grant from the University of Waterloo.