Diffusion magnetic resonance imaging (dMRI) enables in vivo investigation of white matter tracts, where the estimation of fiber orientations (FOs) is a crucial step. Dictionary-based methods have been developed to compute FOs with a lower number of dMRI acquisitions. To reduce the effect of noise that is inherent in dMRI acquisitions, spatial consistency of FOs between neighbor voxels has been incorporated into dictionary-based methods. Because many fiber tracts are tube- or sheet-shaped, voxels belonging to the same tract could share similar FO configurations even when they are not adjacent to each other. Therefore, it is possible to use nonlocal information to improve the performance of FO estimation. In this work, we propose an FO estimation algorithm, Fiber Orientation Reconstruction using Nonlocal and Local Information (FORNLI), which adds nonlocal information to guide FO computation. The diffusion signals are represented by a set of fixed prolate tensors. For each voxel, we compare its patch-based diffusion profile with those of the voxels in a search range, and its nonlocal reference voxels are determined as the k nearest neighbors in terms of diffusion profiles. Then, FOs are estimated by iteratively solving weighted l1-norm regularized least squares problems, where the weights are determined using local neighbor voxels and nonlocal reference voxels. These weights encourage FOs that are consistent with the local and nonlocal information. FORNLI was performed on simulated and real brain dMRI, which demonstrates the benefit of incorporating nonlocal information for FO estimation.
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