On the blurring of the Funk-Radon transform in Q-Ball imaging

Abstract

One known issue in Q-Ball imaging is the blurring in the radial integral defining the Orientation Distribution Function of fiber bundles, due to the computation of the Funk-Radon Transform (FRT). Three novel techniques to overcome this problem are presented, all of them based upon different assumptions about the behavior of the attenuation signal outside the sphere densely sampled from HARDI data sets. A systematic study with synthetic data has been carried out to show that the FRT blurring is not as important as the error introduced by some unrealistic assumptions, and only one of the three techniques (the one with the less restrictive assumption) improves the accuracy of Q-Balls.

Fig. 1

Angular error in the recovering of two fiber bundles vs. the original angle between their directions, for the six configurations tested and for all estimators. The diffusion signals have not been contaminated with Rician noise.

Fig. 2

3–D plot of the orientation functions (ODF for Q–Balls based estimators and P(R₀r) for DOT), for b = 3500, N_g = 121 and an angle of 60°. Red axis represent local maxima of the estimators, and green axis the ground–truth directions.

Fig. 3

Angular error vs. the inverse of the PSNR, for N_g = 121, and different b values and crossing angles, for all estimators.