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A Reproducing Kernel Hilbert Space Approach for Q-Ball Imaging

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2 Author(s)
Enrico Kaden ; Department of Computer Science, University of Leipzig, Leipzig, Germany ; Frithjof Kruggel

Diffusion magnetic resonance (MR) imaging has enabled us to reveal the white matter geometry in the living human brain. The Q-ball technique is widely used nowadays to recover the orientational heterogeneity of the intra-voxel fiber architecture. This article proposes to employ the Funk-Radon transform in a Hilbert space with a reproducing kernel derived from the spherical Laplace-Beltrami operator, thus generalizing previous approaches that assume a bandlimited diffusion signal. The function estimation problem is solved within a Tikhonov regularization framework, while a Gaussian process model allows for the selection of the smoothing parameter and the specification of confidence bands. Shortcomings of Q-ball imaging are discussed.

Published in:

IEEE Transactions on Medical Imaging  (Volume:30 ,  Issue: 11 )