Algorithm 1 ADMM for Subproblem (6).

1:Input: Blur kernel ${\mathbf{k}}_m$, blurred image gradient $\mathbf{y}$, $\tau =1.618$, $\rho =3$, $I_{max}=5$ and $ϵ=5\times {10}^{-6}$. 2:Initialize: ${\phi }_0^{\mathbf{x}}=0$, ${\beta }_1=0.03$ and $i=0$. 3:${\mathbf{x}}_{m,0}={\mathbf{x}}_m$. 4:while (not converged and $i\le I_{max}$) do 5:  Compute ${\mathbf{v}}_{i+1}$ according to (10). 6:  Compute ${\mathbf{x}}_{m,i+1}$ according to (13). 7:  Update Lagrangian multiplier and parameter: ${\phi }_{i+1}^{\mathbf{x}}={\phi }_i^{\mathbf{x}}-\tau {\beta }_1\left({\mathbf{v}}_{i+1}-{\mathbf{x}}_{m,i+1}\right)$ and ${\beta }_1\leftarrow \rho {\beta }_1$. 8:  Check convergence condition: ${∥{\mathbf{v}}_{i+1}-{\mathbf{x}}_{m,i+1}∥}_{\infty }<ϵ$ 9:end while 10:${\mathbf{x}}_{m+1}={\mathbf{x}}_{m,I_{max}}$.