1：Experimental Design and Method Selection:

The study introduces SHARD, a data-driven representation using spherical harmonics and radial decomposition via singular value decomposition (SVD) to create an orthonormal basis. It compares SHARD with alternative bases like spherical Bessel functions and SHORE.

2：Sample Selection and Data Sources:

Two datasets from healthy subjects were used: Dataset 1 with 11 shells (b=0 to 10,000 s/mm2) and Dataset 2 with 5 shells (b=0, 600, 1400, 2600, 4000 s/mm2), acquired on a 3T Philips Achieva TX system.

3：List of Experimental Equipment and Materials:

A 3T Philips Achieva TX MRI system with a 32-channel head coil, echo planar imaging (EPI) sequences, and software for preprocessing (e.g., denoising, motion correction).

4：Experimental Procedures and Operational Workflow:

Data preprocessing included denoising, Gibbs-ringing removal, motion and distortion correction. SH coefficients were computed per shell, followed by SVD to derive the SHARD basis. Comparisons were made using root-mean-squared error (RMSE) and cross-validation. Outlier rejection was simulated by setting random samples to zero.

5：Data Analysis Methods:

RMSE was used to evaluate fitting accuracy. Leave-one-out cross-validation selected optimal basis rank. Robust regression with Soft-L1 and Cauchy loss functions was applied for outlier rejection, with ROC curves for performance assessment.