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Biostatistics Advance Access published online on April 11, 2007
Biostatistics, doi:10.1093/biostatistics/kxm005
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Bayesian regularization of diffusion tensor images

Jesper Frandsen

Department of Neuroradiology, Centre for Functionally Integrative Neuroscience, Århus University Hospital, Århus, Denmark

Asger Hobolth

Bioinformatics Research Center, Aarhus University, Århus, Denmark

Leif Østergaard and Peter Vestergaard-Poulsen

Department of Neuroradiology, Centre for Functionally Integrative Neuroscience, Århus University Hospital, Århus, Denmark

Eva B. Vedel Jensen*

The T.N. Thiele Centre of Applied Mathematics in Natural Science Department of Mathematical Sciences, Aarhus University Ny Munkegade, DK-8000, Århus C, Denmark eva{at}imf.au.dk

* To whom correspondence should be addressed.

Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fiber bundles in the human brain. Using DTI, the local fiber orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the 3-dimensional (3D) fiber bundles. In this paper, we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing the available 3D information of fiber orientation. The use of the procedure is exemplified on synthetic and in vivo data.

Keywords: Bayesian regularization; Diffusion tensor imaging; Fiber tracking; Markov chain Monte Carlo; Prior model; Rice distributions; Tensors

{dagger} We say that S~R(a,{sigma}2) if S has the same distribution as Formula , where X and Y are independent random variables, X~N(acos{varphi},{sigma}2), and Y~N(asin{varphi},{sigma}2). In the density of S, a modified Bessel function of the first kind and zero order appears.

Received March 31, 2006; revised September 22, 2006; revised November 24, 2006; revised January 12, 2007; accepted for publication February 7, 2007.


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