Q‐space imaging based on Gaussian radial basis function with Laplace regularization

Abstract Purpose To introduce the diffusion signal characteristics presented by spherical harmonics (SH) basis into the q‐space imaging method based on Gaussian radial basis function (GRBF) to robustly reconstruct ensemble average diffusion propagator (EAP) in diffusion MRI (dMRI). Methods We introduced the Laplacian regularization of the signal into the dMRI imaging method based on GRBF, and derived the relevant indicators of microstructure imaging and the orientation distribution function (ODF) providing fiber bundle direction information based on EAP. In addition, this method is combined with a multi‐compartment model to calculate the diameter of fiber bundle axons. The evaluation of the results included qualitative comparisons and quantitative assessments of the signal fitting. Results The results show that the proposed method achieves the more significant accuracy improvement in reconstructing signal. Meanwhile, ODFs estimated by the proposed method show the sharper profiles and less spurious peaks, even under the sparse and noisy conditions. In the 36 sets of axon diameter estimation experiments, 34 and 30 sets of results showed that the proposed method reduced the mean and SD of axon diameter estimates, respectively. Moreover, compared with the current state‐of‐the‐art method, the mean and SD of axon diameter estimated by the proposed method are mostly lower, with 32 and 29 of 36 groups. Conclusion The proposed method outperforms the GRBF regarding signal fitting and the estimation of the EAP and ODF with multi‐shell sparse samples. Moreover, it shows the potential to recover important features of microstructures with less uncertainty by using proposed method together with multi‐compartment models.