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- W90999908 abstract "Being the only imaging modality capable of delineating the anatomical structure of the white matter, diffusion magnetic resonance imaging (dMRI) is currently believed to provide a long-awaited means for early diagnosis of various neurological conditions as well as for interrogating the brain connectivity. Despite substantial advances in practical use of dMRI, a solid mathematical platform for modelling and treating dMRI signals still seems to be missing. Accordingly, in this paper, we show how a Hilbert space of $mathbb{L}^2$-valued mappings $u: X to mathbb{L}^2({mathbb{S}^2})$, with X being a subset of ℝ3 and $mathbb{L}^2({mathbb{S}^2})$ being the set of squared-integrable functions supported on the unit sphere ${mathbb{S}^2}$, provides a natural setting for a specific example of dMRI, known as high-angular resolution diffusion imaging. The proposed formalism is also shown to provide a basis for image processing schemes such as total variation minimization. Finally, we discuss a way to amalgamate the proposed models with the tools of compressed sensing to achieve a close-to-perfect recovery of diffusion signals from a minimal number of their discrete measurements. The main outcomes of this paper are supported by a series of experimental results." @default.
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- W90999908 date "2012-01-01" @default.
- W90999908 modified "2023-09-25" @default.
- W90999908 title "Function-Valued Mappings, Total Variation and Compressed Sensing for diffusion MRI" @default.
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- W90999908 doi "https://doi.org/10.1007/978-3-642-31298-4_34" @default.
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