title: A reproducing kernel hilbert space approach for q-ball imaging.
abstract: 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.
authors: Department of Computer Science, University of Leipzig,Germany. enrico.kaden@gmail.com
authors: Enrico
authors: E
authors: Kaden
authors: Frithjof
authors: F
authors: Kruggel