SC²S Colloquium - February 16, 2012

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Date: February 16, 2012
Room: 02.07.023
Time: 15:00 am, s.t.

Vladimir Golkov: Kurtosis Estimation in Diffusion Spectrum Magnetic Resonance Imaging Using Non-Gaussian Noise Models

Diffusion tensor magnetic resonance imaging (DTI) is a non-invasive imaging method that allows for estimating the molecular self-diffusion of water molecules within the surrounding biological tissue, and for determination of the macroscopic orientation of the underlying microscopic cellular architecture. Because of the implicit assumption of a single-Gaussian diffusion model, DTI falls short in resolving fiber crossings adequately and in reflecting the non-Gaussian nature of diffusion in biological tissue in general. Due to these shortcomings, various alternative diffusion models and corresponding acquisition schemes have been proposed that reflect the histological tissue architecture more closely, one of which is the kurtosis model. The fast and robust estimation of kurtosis by means of constrained quadratic programming requires taking the logarithm of the initial data, together with the magnitude data processing of MR images (resulting in Rician instead of Gaussian noise), and both steps lead to a biased estimation of kurtosis. To resolve this bias, we propose to use the approach of a Bayesian or maximum likelihood estimator for kurtosis.