Robust ODF smoothing for accurate estimation of fiber orientation

Q-ball imaging was presented as a model free, linear and multimodal diffusion sensitive approach to reconstruct diffusion orientation distribution function (ODF) using diffusion weighted MRI data. The ODFs are widely used to estimate the fiber orientations. However, the smoothness constraint was proposed to achieve a balance between the angular resolution and noise stability for ODF constructs. Different regularization methods were proposed for this purpose. However, these methods are not robust and quite sensitive to the global regularization parameter. Although, numerical methods such as L-curve test are used to define a globally appropriate regularization parameter, it cannot serve as a universal value suitable for all regions of interest. This may result in over smoothing and potentially end up in neglecting an existing fiber population. In this paper, we propose to include an interpolation step prior to the spherical harmonic decomposition. This interpolation based approach is based on Delaunay triangulation provides a reliable, robust and accurate smoothing approach. This method is easy to implement and does not require other numerical methods to define the required parameters. Also, the fiber orientations estimated using this approach are more accurate compared to other common approaches.