Algorithm 1.

FORNI

Input: Diffusion weighted signals ${\{S_m({\mathit{q}}_1),\dots ,S_m({\mathit{q}}_K)\}}_{m=1}^M$; baseline signals ${\{S_{0m}\}}_{m=1}^M$ without diffusion weighting; diffusion gradients {q1, …, qK}; size of parallel processing: Np; the tensor basis ${\{{\mathbf{D}}_i\}}_{i=1}^N$ and their PEVs ${\{{\mathit{v}}_i\}}_{i=1}^N$; maximum number of iterations tmax; the initialization of FOs ${\{{\mathcal{W}}_m^0\}}_{m=1}^M$ computed from Landman et al. (2012); the iteration number starts from t = 1;
Output: Mixture fractions ${\{{\mathit{f}}_m\}}_{m=1}^M$ and FOs ${\{{\mathcal{W}}_m\}}_{m=1}^M$
1:	Compute the attenuation matrix G: $G_{ki}=e^{-{\mathit{q}}_k^T{\mathbf{D}}_i{\mathit{q}}_k}$
2:	Compute ${\{{\mathit{y}}_m\}}_{m=1}^M:{\mathit{y}}_m={(S_m({\mathit{q}}_1)/S_{0m},\dots ,S_m({\mathit{q}}_K)/S_{0m})}^T$: ym = (Sm(q1)/S0m, …, Sm(qK)/S0m)T
3:	Initialize FOs: ${\{{\mathcal{W}}_m\}}_{m=1}^M:={\{{\mathcal{W}}_m^0\}}_{m=1}^M$
4:	while t ≤ tmax do
5:	for $a=0:\lceil \frac{M}{N_{\mathrm{p}}}-1\rceil$ do
6:	parfor b = 1 : min(Np, M − aNp) do
7:	m := aNp + b
8:	for all basis directions vi do
9:	$R_m(i):={\displaystyle \sum _{n\in {\mathcal{N}}_m}}{w}_{m,n}\underset{j=1,\dots ,W_n}{max}\mid {\mathit{v}}_i·{\mathit{w}}_{n,j}\mid$
10:	end for
11:	${\{{\mathit{u}}_{m,p}\}}_{p=1}^{U_m}:=\{{\mathit{v}}_i\mid \forall i^{\prime }\ne i\text{and}arccos(\mid {\mathit{v}}_i·{\mathit{v}}_{i^{\prime }}\mid )\le \frac{\pi }{180°}{\theta }_R:R_m(i)\ge R_m(i^{\prime })\}$
12:	for i = 1 : N do
13:	$C_{m,i}:=\left(1-\alpha \underset{p=1,\dots ,U_m}{max}\mid {\mathit{v}}_i·{\mathit{u}}_{m,p}\mid \right)/\left(\underset{q=1,\dots ,N}{min}\left(1-\alpha \underset{p=1,\dots ,U_m}{max}\mid {\mathit{v}}_q·{\mathit{u}}_{m,p}\mid \right)\right)$
14:	end for
15:	Solve Eq. (17) to obtain ${\widehat{\mathit{f}}}_m^t$
16:	${\mathit{f}}_m:={\widehat{\mathit{f}}}_m^t/{\Vert {\widehat{\mathit{f}}}_m^t\Vert }_1$
17:	end parfor
18:	for b = 1 : min(Np, M − aNp) do
19:	m := aNp + b
20:	𝒲m := {vi|fm,i > fth, i = 1, …, N}
21:	end for
22:	end for
23:	t := t + 1 until convergence
24:	end while
25:	return ${\{{\mathit{f}}_m\}}_{m=1}^M$ nd ${\{{\mathcal{W}}_m\}}_{m=1}^M$