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This work provides a theoretical analysis of linear spherical deconvolution methods in diffusion MRI, building off of a theoretical framework that was previously developed for model-free linear transforms of the Fourier 2-sphere. It is demonstrated that linear spherical deconvolution methods have an equivalent representation as model-free linear transform methods. This perspective is used to study...
We consider the problem of processing high angular resolution diffusion images described by orientation distribution functions (ODFs). Prior work showed that several processing operations, e.g., averaging, interpolation and filtering, can be reduced to averaging in the space of ODFs. However, this approach leads to anatomically erroneous results when the ODFs to be processed have very different orientations...
In Diffusion Magnetic Resonance Imaging, the diffusion process is commonly modeled by a symmetric 2nd order tensor. Since 2nd order tensors are not able to properly model crossing fibers, High Order Tensors (HOTs) can be considered in particular to model the Orientation Distribution Function. Applying a spatial transformation to such tensor fields requires an appropriate reorientation strategy to...
In Diffusion Magnetic Resonance Imaging (D-MRI), the 2nd order diffusion tensor has given rise to a widely used tool - Diffusion Tensor Imaging (DTI). However, it is known that DTI is limited to a single prominent diffusion direction and is inaccurate in regions of complex fiber structures such as crossings. Various other approaches have been introduced to recover such complex tissue micro-geometries,...
This paper describes a general and flexible Monte- Carlo simulation framework for diffusing spins that generates realistic synthetic data for diffusion magnetic resonance imaging. Similar systems in the literature consider only simple substrates and their authors do not consider convergence and parameter optimization. We show how to run Monte-Carlo simulations within complex irregular substrates....
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