In all experiments, we used the piecewise linear tight wavelet frame and set the level L to 2. The optimal X was chosen based on grid search.
Synthetic Data A synthetic dataset of a spiral was generated for quantitative evaluation. The parameters used for generating synthetic data simulation were consistent with the real data described next: b = 2000 s/mm2, 48 gradient directions, 64 x 64 x 16 voxels with resolution 2 x 2 x 2 mm3. Three levels of 32- channel noncentral Chi noise  was added: a = 5, 7.5, and 10, corresponding to SNR = 30, 20, 10 with respect to the white matter non-diffusion-weighted signal.
Real Data The real datasets were acquired using Siemens 3T TRIO MR scanner with the same gradient directions and b-value as the synthetic dataset. The imaging protocol is as follows: 128 x 96 imaging matrix, voxel size of 2 x 2 x 2 mm3, TE=97 ms, TR= 11,300 ms. Imaging acquisition was repeatedly performed on the same subject for eight times. We averaged the eight sets of DW images and removed the noncentral chi noise bias to obtain the ground truth for evaluation.