VALIDATION AND COMPARISON OF ANALYTICAL Q-BALL IMAGING METHODS

Q-ball imaging (QBI), introduced by D. Tuch, reconstructs the diffusion orientation distribution function (ODF) of the underlying fiber population of a biological tissue. An analytical solution for QBI was recently proposed by several independent groups, using a spherical harmonic (SH) representation of the input signal. The methods differ primarily in the way SH are estimated. In this paper we validate these methods and compare them against Tuch´s numerical QBI on synthetic data, on a biological phantom and on a human brain dataset. We show that analytical QBI results in a speed-up factor of 15 over Tuch´s QBI, while providing results that are in strong agreement. We also show that at the cost of slightly reducing angular resolution, QBI with Laplace-Beltrami regularization provides the strongest robustness to noise and the most accurate detection of fiber crossings.