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Diffusion-weighted magnetic resonance imaging (DWI) and fiber tractographyare the only methods to measure the structure of the white matter in the livinghuman brain. The diffusion signal has been modelled as the combinedcontribution from many individual fascicles of nerve fibers passing througheach location in the white matter. Typically, this is done via basis pursuit,but estimation of the exact directions is limited due to discretization. Thedifficulties inherent in modeling DWI data are shared by many other problemsinvolving fitting non-parametric mixture models. Ekanadaham et al. proposed anapproach, continuous basis pursuit, to overcome discretization error in the1-dimensional case (e.g., spike-sorting). Here, we propose a more generalalgorithm that fits mixture models of any dimensionality withoutdiscretization. Our algorithm uses the principles of L2-boost, together withrefitting of the weights and pruning of the parameters. The addition of thesesteps to L2-boost both accelerates the algorithm and assures its accuracy. Werefer to the resulting algorithm as elastic basis pursuit, or EBP, since itexpands and contracts the active set of kernels as needed. We show that incontrast to existing approaches to fitting mixtures, our boosting framework (1)enables the selection of the optimal bias-variance tradeoff along the solutionpath, and (2) scales with high-dimensional problems. In simulations of DWI, wefind that EBP yields better parameter estimates than a non-negative leastsquares (NNLS) approach, or the standard model used in DWI, the tensor model,which serves as the basis for diffusion tensor imaging (DTI). We demonstratethe utility of the method in DWI data acquired in parts of the brain containingcrossings of multiple fascicles of nerve fibers.

Deconvolution of High-Dimensional Mixtures via Boosting, with Application to Diffusion-Weighted MRI of Human Brain