Analytical Q-Ball Imaging with Optimal Regularization
Résumé
Diffusion MRI is a unique noninvasive imaging technique capable of quantifying and visualizing the angular distribution and the anisotropy of the white matter fibers. Several approaches such as diffusion tensor imaging, q-ball imaging (QBI), spherical deconvolution and many others high angular resolution diffusion imaging (HARDI) have been proposed to describe the angular distribution of the white matter fibers within a voxel. The analytical QBI technique [1] uses a predetermined regularization parameter [2] (λ = 0.006), which has been well adopted in many clinical studies. Although there are well-known strategies, e.g., the generalized cross-validation (GCV) [3-5] or the L-curve [6], for selecting the optimal regularization parameter λ, the predetermined regularization parameter was adopted for reasons related to practical and computational efficiency based on L-curve simulations [2]. Here, we incorporate the GCV technique into the analytical qball formalism. We compare and contrast the fixed λ-regularization parameter ("Fixed λ") and the automatic GCV-selected optimal λ-regularization ("GCV-based λ"), for estimating diffusion MRI data. We also discuss the potential consequences of our work on quantitative HARDI anisotropy measures and tractography studies.