TNLM Reconstruction (TNLM-R) Algorithm:

Initialize: $f_i^{\left(0\right)}$ for i = 1, …, Np.
For k = 0, 1, …, do the following steps until convergence:
1.	Solve (P1) using CGLS with initial value $\left\{f_i^{(k-1)}\right\}$ to obtain $\left\{g_i^{\left(k\right)}\right\}$;
2.	Update weights $w_{f_i^{*},f_j^{*}}$ according to Eq. 7 using the image$\left\{g_i^{\left(k\right)}\right\}$;
3.	Compute images $\left\{f_i^{\left(k\right)}\right\}$ according to Eq. 6;
4.	Ensure image positiveness: $f_i^{\left(k\right)}=0,\mathrm{if}{f}_i^{\left(k\right)}<0.$