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.