Algorithm 1: The proposed destriping model with Fast ADMM

Input: Degraded image $\mathbf{g}$ and related parameter ${\lambda }_1$, ${\lambda }_2$, ${\alpha }_1$, ${\alpha }_2$, and ${\alpha }_3$

1: Initialize: Set ${\mathbf{u}}^{\left(0\right)}={\mathbf{M}}_i^{\left(0\right)}={\mathbf{M}}_{ia}^{\left(0\right)}={\mathbf{Q}}_i^{\left(0\right)}={\mathbf{Q}}_{ia}^{\left(0\right)}=\mathbf{0}$ $(i=1,2,3)$, ${\eta }_i^{\left(0\right)}=1$, $\epsilon ={10}^{-4}$, $n_{max}=200$.

2: While: $\frac{{∥{\mathbf{u}}^{(k+1)}-{\mathbf{u}}^{\left(k\right)}∥}_2^2}{{∥{\mathbf{u}}^{\left(k\right)}∥}_2^2}<\epsilon$ and $n<n_{max}$

3: update $u^{(k+1)}$ by using Equation (13)

4: update ${\mathbf{M}}_1^{(k+1)}$, ${\mathbf{M}}_2^{(k+1)}$, and ${\mathbf{M}}_3^{(k+1)}$ by using Equations (17), (21) and (24)

5: update ${\mathbf{Q}}_1^{(k+1)}$, ${\mathbf{Q}}_2^{(k+1)}$, and ${\mathbf{Q}}_3^{(k+1)}$ by using Equations (25)–(27)

6: update $Z_i^{(k+1)}$ by using Equation (28)

7: if $Z_i^{(k+1)}<\mu Z_i^{\left(k\right)}$, $i=1,2,3$ then

8: update ${\eta }_i^{(k+1)}$, ${\mathbf{M}}_{ia}^{(k+1)}$ and ${\mathbf{Q}}_{ia}^{(k+1)}$ by using Equations (29)–(31)

9: else

10: ${\eta }_i^{(k+1)}=1$, ${\mathbf{M}}_{ia}^{(k+1)}={\mathbf{M}}_i^{(k+1)}$, ${\mathbf{Q}}_{ia}^{(k+1)}={\mathbf{Q}}_i^{(k+1)}$, $Z_i^{(k+1)}={\mu }^{-1}{Z}_i^{\left(k\right)}$, $i=1,2,3$

11: end if

12: $n=n+1$

13: End While

Output: Destriped image $\mathbf{u}$