| Initialization:Pick initial guess |$\bf {u}_{0}$|, |$\bf {v}^{0}$|, parameters |$\rho$|, |$\alpha$|, |$\beta$|, and |$\gamma$|. |
| For |$k=0,1,\cdots ,K-1$| |
| (a) |$\bf {m}_{k+1}=\underset{\bf {m}}{\arg \min }\lbrace \frac{1}{2}\Vert \mathcal {F}(\bf {m})-\bf {d}\Vert _{2}^{2}+ {\frac{\rho }{2}\Vert {\bf {m}-\bf {v}^{k}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace ;$| |
| (b) |$\bf {v}_{1}=\underset{\bf {v}}{\arg \min }\lbrace \alpha \Vert \bf {v}\Vert _{TV}+{\frac{\rho }{2}\Vert {\bf {v}-\bf {m}_{k+1}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (c) |$\bf {v}_{2}=\underset{\bf {v}}{\arg \min }\lbrace \beta \Phi (\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{1}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (d) |$\bf {v}_{3}=\underset{\bf {v}}{\arg \min }\lbrace \gamma \mathcal {D}(\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{2}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (e) Let |$\bf {v}^{k+1}=\bf {v}_{3}$|, |$\bf {u}_{k+1}=\bf {u}_{k}+\rho (\bf {m}_{k+1}-\bf {v}^{k+1})$|; |
| End For |
| Output result|$\bf {m}_{K}$|. |
| Initialization:Pick initial guess |$\bf {u}_{0}$|, |$\bf {v}^{0}$|, parameters |$\rho$|, |$\alpha$|, |$\beta$|, and |$\gamma$|. |
| For |$k=0,1,\cdots ,K-1$| |
| (a) |$\bf {m}_{k+1}=\underset{\bf {m}}{\arg \min }\lbrace \frac{1}{2}\Vert \mathcal {F}(\bf {m})-\bf {d}\Vert _{2}^{2}+ {\frac{\rho }{2}\Vert {\bf {m}-\bf {v}^{k}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace ;$| |
| (b) |$\bf {v}_{1}=\underset{\bf {v}}{\arg \min }\lbrace \alpha \Vert \bf {v}\Vert _{TV}+{\frac{\rho }{2}\Vert {\bf {v}-\bf {m}_{k+1}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (c) |$\bf {v}_{2}=\underset{\bf {v}}{\arg \min }\lbrace \beta \Phi (\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{1}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (d) |$\bf {v}_{3}=\underset{\bf {v}}{\arg \min }\lbrace \gamma \mathcal {D}(\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{2}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (e) Let |$\bf {v}^{k+1}=\bf {v}_{3}$|, |$\bf {u}_{k+1}=\bf {u}_{k}+\rho (\bf {m}_{k+1}-\bf {v}^{k+1})$|; |
| End For |
| Output result|$\bf {m}_{K}$|. |
| Initialization:Pick initial guess |$\bf {u}_{0}$|, |$\bf {v}^{0}$|, parameters |$\rho$|, |$\alpha$|, |$\beta$|, and |$\gamma$|. |
| For |$k=0,1,\cdots ,K-1$| |
| (a) |$\bf {m}_{k+1}=\underset{\bf {m}}{\arg \min }\lbrace \frac{1}{2}\Vert \mathcal {F}(\bf {m})-\bf {d}\Vert _{2}^{2}+ {\frac{\rho }{2}\Vert {\bf {m}-\bf {v}^{k}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace ;$| |
| (b) |$\bf {v}_{1}=\underset{\bf {v}}{\arg \min }\lbrace \alpha \Vert \bf {v}\Vert _{TV}+{\frac{\rho }{2}\Vert {\bf {v}-\bf {m}_{k+1}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (c) |$\bf {v}_{2}=\underset{\bf {v}}{\arg \min }\lbrace \beta \Phi (\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{1}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (d) |$\bf {v}_{3}=\underset{\bf {v}}{\arg \min }\lbrace \gamma \mathcal {D}(\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{2}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (e) Let |$\bf {v}^{k+1}=\bf {v}_{3}$|, |$\bf {u}_{k+1}=\bf {u}_{k}+\rho (\bf {m}_{k+1}-\bf {v}^{k+1})$|; |
| End For |
| Output result|$\bf {m}_{K}$|. |
| Initialization:Pick initial guess |$\bf {u}_{0}$|, |$\bf {v}^{0}$|, parameters |$\rho$|, |$\alpha$|, |$\beta$|, and |$\gamma$|. |
| For |$k=0,1,\cdots ,K-1$| |
| (a) |$\bf {m}_{k+1}=\underset{\bf {m}}{\arg \min }\lbrace \frac{1}{2}\Vert \mathcal {F}(\bf {m})-\bf {d}\Vert _{2}^{2}+ {\frac{\rho }{2}\Vert {\bf {m}-\bf {v}^{k}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace ;$| |
| (b) |$\bf {v}_{1}=\underset{\bf {v}}{\arg \min }\lbrace \alpha \Vert \bf {v}\Vert _{TV}+{\frac{\rho }{2}\Vert {\bf {v}-\bf {m}_{k+1}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (c) |$\bf {v}_{2}=\underset{\bf {v}}{\arg \min }\lbrace \beta \Phi (\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{1}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (d) |$\bf {v}_{3}=\underset{\bf {v}}{\arg \min }\lbrace \gamma \mathcal {D}(\bf {v})+{\frac{\rho }{2}\Vert {\bf {v}-{\bf {v}_{2}}+\bf {u}_{k}}\Vert _{2}^{2}}\rbrace$|; |
| (e) Let |$\bf {v}^{k+1}=\bf {v}_{3}$|, |$\bf {u}_{k+1}=\bf {u}_{k}+\rho (\bf {m}_{k+1}-\bf {v}^{k+1})$|; |
| End For |
| Output result|$\bf {m}_{K}$|. |
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