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This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk–Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance...
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...
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