Algorithm 2 ADMM for problem (7).

1:Let ${\mathbf{u}}^0\in {\mathbb{R}}^n$, ${\mathbf{w}}_1^0=D_{\theta }{\mathbf{u}}^0$, ${\mathbf{w}}_2^0=D_{{\theta }^{\perp }}{\mathbf{u}}^0$, ${\mu }^0=0$, ${\mathbf{z}}^0=0$, $\lambda ,\rho \in (0,+\infty )$, ${\alpha }_0,{\alpha }_1\in (0,1)$  2:Compute matrices $\mathsf{\Delta }$, $\mathsf{\Gamma }$, $\mathsf{\Psi }$, ${\mathsf{\Xi }}^{-1}$, and $\mathsf{{\rm Y}}$ as specified in Section 4.1  3:Let $k=0$, ${\mathbf{u}}^1={\mathbf{u}}^0$, ${\mathbf{w}}^1={\mathbf{w}}^0$, $stop=false$, $tol\in (0,1)$, $k_{max}\in \mathbb{N}$  4:while $\mathrm{not}stop\mathrm{and}k\le k_{max}$ do  5: Compute ${\mathbf{z}}^{k+1}$ by solving the four subproblems (27)–(30)  6: Compute ${\mu }^{k+1}$ as in (16)  7: $k=k+1$  8: Compute ${\mathbf{u}}^{k+1}$, ${\mathbf{w}}_1^{k+1}$ and ${\mathbf{w}}_2^{k+1}$ by (25) and (26)  9: Set $stop=\left(\parallel {\mathbf{u}}^{k+1}-{\mathbf{u}}^k\parallel <tol\parallel {\mathbf{u}}^k\parallel \right)$ 10:end while