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 double-struck L 2-valued mappings u: X → double-struck L 2(double-struck S 2), with X being a subset of ℝ 3 and double-struck L 2(double-struck S 2 being the set of squared-integrable functions supported on the unit sphere double-struck 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.

Function-valued mappings, total variation and compressed sensing for diffusion MRI / O. Michailovich, D. La Torre, E.R. Vrscay - In: Image analysis and recognition : 9th international conference, ICIAR 2012 : Proceedings. Part 2 / [a cura di] A. Campilho, M. Kamel. - [s.l] : Springer, 2012. - ISBN 978-3-642-31297-7. - pp. 286-295 (( Intervento presentato al 9. convegno ICIAR 2012 tenutosi a Aveiro nel 2012 [10.1007/978-3-642-31298-4_34].

Function-valued mappings, total variation and compressed sensing for diffusion MRI

D. La Torre
Secondo
;
2012

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 double-struck L 2-valued mappings u: X → double-struck L 2(double-struck S 2), with X being a subset of ℝ 3 and double-struck L 2(double-struck S 2 being the set of squared-integrable functions supported on the unit sphere double-struck 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.
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/190486
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