| Initialize: |
| Given initial guess |$\bf {m}_{0}$|, the observed data |$\bf {d}$|, the maximum |
| number of iterations L, |$\bf {v}^{0}=\bf {u}_{0}=\rho _{0}=0$|, |
| parameters |$\alpha$|, |$\beta$|, |$\gamma$|, and |$\epsilon$|. |
| Iterate: for |$l=0,1, \cdots ,L-1$| |
| (1) L-BFGS step: |
| |$\bf {m}_{l+1}=\underset{\bf {m}}{\arg \min }\lbrace {\frac{1}{2}}\Vert {\bf {P}}A_{\omega }(\bf {m})^{-1}\bf {Q}-\bf {d}\Vert _{2}^{2}+{\frac{\rho _{l}}{2}\Vert {\bf {m}-\bf {v}^{l}+\bf {u}_{l}}\Vert _{2}^{2}}\rbrace$|; |
| (2) Denoising steps: |
| (a) |$\bf {v}_{1}=\mbox{TV}(\bf {m}_{l+1}-\bf {u}_{l},\sqrt{\frac{\alpha }{\rho _{l}}})$|; |
| (b) |$\bf {v}_{2}=\mbox{BM3D}(\bf {v}_{1}-\bf {u}_{l},\sqrt{\frac{\beta }{\rho _{l}}})$|; |
| (c) |$\bf {v}_{3}=\mbox{FFDNet}(\bf {v}_{2}-\bf {u}_{l},\sqrt{\frac{\gamma }{\rho _{l}}})$|. |
| (3) Update step: |
| Let |$\bf {v}^{l+1}=\bf {v}_{3}$|, |
| |$\rho _{l+1}=(l+1)(1+\epsilon )^{l+1}$|, |
| |$\bf {u}_{l+1}=\bf {u}_{l}+\rho _{l+1}(\bf {m}_{l+1}-\bf {v}^{l+1})$|; |
| Output: The inversion result is |${\bf {v}}^{L}$|. |
| Initialize: |
| Given initial guess |$\bf {m}_{0}$|, the observed data |$\bf {d}$|, the maximum |
| number of iterations L, |$\bf {v}^{0}=\bf {u}_{0}=\rho _{0}=0$|, |
| parameters |$\alpha$|, |$\beta$|, |$\gamma$|, and |$\epsilon$|. |
| Iterate: for |$l=0,1, \cdots ,L-1$| |
| (1) L-BFGS step: |
| |$\bf {m}_{l+1}=\underset{\bf {m}}{\arg \min }\lbrace {\frac{1}{2}}\Vert {\bf {P}}A_{\omega }(\bf {m})^{-1}\bf {Q}-\bf {d}\Vert _{2}^{2}+{\frac{\rho _{l}}{2}\Vert {\bf {m}-\bf {v}^{l}+\bf {u}_{l}}\Vert _{2}^{2}}\rbrace$|; |
| (2) Denoising steps: |
| (a) |$\bf {v}_{1}=\mbox{TV}(\bf {m}_{l+1}-\bf {u}_{l},\sqrt{\frac{\alpha }{\rho _{l}}})$|; |
| (b) |$\bf {v}_{2}=\mbox{BM3D}(\bf {v}_{1}-\bf {u}_{l},\sqrt{\frac{\beta }{\rho _{l}}})$|; |
| (c) |$\bf {v}_{3}=\mbox{FFDNet}(\bf {v}_{2}-\bf {u}_{l},\sqrt{\frac{\gamma }{\rho _{l}}})$|. |
| (3) Update step: |
| Let |$\bf {v}^{l+1}=\bf {v}_{3}$|, |
| |$\rho _{l+1}=(l+1)(1+\epsilon )^{l+1}$|, |
| |$\bf {u}_{l+1}=\bf {u}_{l}+\rho _{l+1}(\bf {m}_{l+1}-\bf {v}^{l+1})$|; |
| Output: The inversion result is |${\bf {v}}^{L}$|. |
| Initialize: |
| Given initial guess |$\bf {m}_{0}$|, the observed data |$\bf {d}$|, the maximum |
| number of iterations L, |$\bf {v}^{0}=\bf {u}_{0}=\rho _{0}=0$|, |
| parameters |$\alpha$|, |$\beta$|, |$\gamma$|, and |$\epsilon$|. |
| Iterate: for |$l=0,1, \cdots ,L-1$| |
| (1) L-BFGS step: |
| |$\bf {m}_{l+1}=\underset{\bf {m}}{\arg \min }\lbrace {\frac{1}{2}}\Vert {\bf {P}}A_{\omega }(\bf {m})^{-1}\bf {Q}-\bf {d}\Vert _{2}^{2}+{\frac{\rho _{l}}{2}\Vert {\bf {m}-\bf {v}^{l}+\bf {u}_{l}}\Vert _{2}^{2}}\rbrace$|; |
| (2) Denoising steps: |
| (a) |$\bf {v}_{1}=\mbox{TV}(\bf {m}_{l+1}-\bf {u}_{l},\sqrt{\frac{\alpha }{\rho _{l}}})$|; |
| (b) |$\bf {v}_{2}=\mbox{BM3D}(\bf {v}_{1}-\bf {u}_{l},\sqrt{\frac{\beta }{\rho _{l}}})$|; |
| (c) |$\bf {v}_{3}=\mbox{FFDNet}(\bf {v}_{2}-\bf {u}_{l},\sqrt{\frac{\gamma }{\rho _{l}}})$|. |
| (3) Update step: |
| Let |$\bf {v}^{l+1}=\bf {v}_{3}$|, |
| |$\rho _{l+1}=(l+1)(1+\epsilon )^{l+1}$|, |
| |$\bf {u}_{l+1}=\bf {u}_{l}+\rho _{l+1}(\bf {m}_{l+1}-\bf {v}^{l+1})$|; |
| Output: The inversion result is |${\bf {v}}^{L}$|. |
| Initialize: |
| Given initial guess |$\bf {m}_{0}$|, the observed data |$\bf {d}$|, the maximum |
| number of iterations L, |$\bf {v}^{0}=\bf {u}_{0}=\rho _{0}=0$|, |
| parameters |$\alpha$|, |$\beta$|, |$\gamma$|, and |$\epsilon$|. |
| Iterate: for |$l=0,1, \cdots ,L-1$| |
| (1) L-BFGS step: |
| |$\bf {m}_{l+1}=\underset{\bf {m}}{\arg \min }\lbrace {\frac{1}{2}}\Vert {\bf {P}}A_{\omega }(\bf {m})^{-1}\bf {Q}-\bf {d}\Vert _{2}^{2}+{\frac{\rho _{l}}{2}\Vert {\bf {m}-\bf {v}^{l}+\bf {u}_{l}}\Vert _{2}^{2}}\rbrace$|; |
| (2) Denoising steps: |
| (a) |$\bf {v}_{1}=\mbox{TV}(\bf {m}_{l+1}-\bf {u}_{l},\sqrt{\frac{\alpha }{\rho _{l}}})$|; |
| (b) |$\bf {v}_{2}=\mbox{BM3D}(\bf {v}_{1}-\bf {u}_{l},\sqrt{\frac{\beta }{\rho _{l}}})$|; |
| (c) |$\bf {v}_{3}=\mbox{FFDNet}(\bf {v}_{2}-\bf {u}_{l},\sqrt{\frac{\gamma }{\rho _{l}}})$|. |
| (3) Update step: |
| Let |$\bf {v}^{l+1}=\bf {v}_{3}$|, |
| |$\rho _{l+1}=(l+1)(1+\epsilon )^{l+1}$|, |
| |$\bf {u}_{l+1}=\bf {u}_{l}+\rho _{l+1}(\bf {m}_{l+1}-\bf {v}^{l+1})$|; |
| Output: The inversion result is |${\bf {v}}^{L}$|. |
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