Algorithm 1 The Optimization Strategy of FORNI+
Input: Diffusion signals: ${\{{\mathit{y}}_m\}}_{m=1}^M$; maximum number of iterations: tmax; the initialization of FOs: ${\{{\mathrm{\Omega }}_m^0\}}_{m=1}^M$; the iteration number starts from t = 1;
Output: FOs: ${\{{\mathrm{\Omega }}_m\}}_{m=1}^M$; mixture fractions of FOs: ${\{{\mathcal{H}}_m\}}_{m=1}^M$; weights of similarity between neighboring FOs: ℬ; mixture fractions of dictionary atoms: ${\{{\mathit{f}}_m\}}_{m=1}^M$
1:	Initialize FOs: ${\{{\mathrm{\Omega }}_m\}}_{m=1}^M≔{\{{\mathrm{\Omega }}_m^0\}}_{m=1}^M$
2:	while t ≤ tmax do
3:	Fix ${\{{\mathrm{\Omega }}_m\}}_{m=1}^M$, ${\{{\mathcal{H}}_m\}}_{m=1}^M$, and ℬ, and solve for ${\{{\mathit{f}}_m\}}_{m=1}^M$ using Eq. (9)
4:	Apply Eq. (5) to compute ${\{{\mathcal{H}}_m\}}_{m=1}^M$ and reinitialize ${\{{\mathrm{\Omega }}_m\}}_{m=1}^M$ using ${\{{\mathit{f}}_m\}}_{m=1}^M$
5:	Fix ${\{{\mathit{f}}_m\}}_{m=1}^M$, ${\{{\mathcal{H}}_m\}}_{m=1}^M$, and ${\{{\mathrm{\Omega }}_m\}}_{m=1}^M$, and solve for ℬ using Eq. (12)
6:	Fix ${\{{\mathit{f}}_m\}}_{m=1}^M$, ${\{{\mathcal{H}}_m\}}_{m=1}^M$, and ℬ, and solve for ${\{{\mathrm{\Omega }}_m\}}_{m=1}^M$ using Eq. (13)
7:	t ≔ t + 1 until convergence
8:	end while
9:	return ${\{{\mathrm{\Omega }}_m\}}_{m=1}^M$, ${\{{\mathcal{H}}_m\}}_{m=1}^M$, ℬ, and ${\{{\mathit{f}}_m\}}_{m=1}^M$