Estimating Spatially-Smoothed Fiber Orientation Distribution
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Diffusion-weighted magnetic resonance imaging (D-MRI) is an in-vivo and non-invasive imaging technology to probe anatomical architectures of biological samples. The anatomy of white matter fiber tracts in the brain can be revealed to help understanding of the connectivity patterns among different brain regions. In this paper, we propose a novel Nearest-neighbor Adaptive Regression Model (NARM) for adaptive estimation of the fiber orientation distribution (FOD) function based on D-MRI data, where spatial homogeneity is used to improve FOD estimation by incorporating neighborhood information. Specifically, we formulate the FOD estimation problem as a weighted linear regression problem, where the weights are chosen to account for spatial proximity and potential heterogeneity due to different fiber configurations. The weights are adaptively updated and a stopping rule based on nearest neighbor distance is designed to prevent over-smoothing. NARM is further extended to accommodate D-MRI data with multiple bvalues. Comprehensive simulation results demonstrate that NARM leads to satisfactory FOD reconstructions and performs better than voxel-wise estimation as well as competing smoothing methods. By applying NARM to real 3T D-MRI datasets, we demonstrate the effectiveness of NARM in recovering more realistic crossing fiber patterns and producing more coherent fiber tracking results, establishing the practical value of NARM for analyzing D-MRI data and providing reliable information on brain structural connectivity.
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