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Abstract:
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Diffusion Tensor Imaging (DTI) is an MRI-based neuroimaging technique used to measuring diffusion process of water molecules in the brain. DTI scan produces 3-by-3 positive definite matrix for each voxel. A common approach is to reduce the matrix to a scalar (determinant, etc) for univariate spatial analysis. However, the information is lost in this dimension reduction. To make full use of the matrix-valued data, we propose a spatial Wishart process which considers has marginal Wishart distributions and captures spatial dependence between nearby matrices. For an efficient implementation of this model, we Cholesky decompose each diffusion tensor and apply spatial modeling with spatially varying coefficient processes. We demonstrate improved performance compared with univariate spatial model for both simulated and real DTI data.
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