Algorithm 1 Proposed Weighted Nuclear Norm and Multi-Norm RPCA Algorithm

Input: merging matrix $\mathbf{D}$, tolerance $\epsilon$, Maximum Convergence Number $\mathsf{\Omega }$, parameters $\lambda$, $\eta$

Output: low rank matrix $\mathbf{A}$, sparse matrix $\mathbf{E}$, structure matrix $\mathbf{G}$, number of iterations $\tau$.

1:Initialize parameter $\rho$,$\mu$, $\mathbf{A}=0$, $\mathbf{E}=0$, $\mathbf{G}=0$, $\mathbf{Y}$. 2:while not converged do 3: Randomly choose direction to iterate A, E and G; 4: When solve ${\mathbf{A}}_{k+1}=arg\underset{\mathbf{A}}{min}L(\mathbf{A},{\mathbf{E}}_k,{\mathbf{Y}}_k,{\mu }_k)$:; 5: $(\mathbf{U},\mathbf{S},\mathbf{V})=svd(\mathbf{D}-{\mathbf{E}}_k+{{\mu }_k}^{-1}{\mathbf{Y}}_k)$.; 6: ${\mathbf{A}}_{k+1}=U{S}_{w/\mu }\left(\mathbf{S}\right){\mathbf{V}}^T$; 7: When solve ${\mathbf{E}}_{k+1}=arg\underset{\mathbf{E}}{min}L({\mathbf{A}}_{k+1},\mathbf{E},{\mathbf{Y}}_k,{\mu }_k)$: 8: ${\mathbf{E}}_{k+1}=S_{\lambda /\mu }(\mathbf{D}-\mathbf{A}+1/\mu \mathbf{Y})$; 9: When solve ${\mathbf{G}}_{k+1}=arg\underset{\mathbf{E}}{min}L({\mathbf{A}}_{k+1},{\mathbf{E}}_{k+1},\mathbf{G},{\mathbf{Y}}_k,{\mu }_k)$: 10: ${\mathbf{G}}_{k+1}={}_{\eta /\mu }(\mathbf{D}-{\mathbf{A}}_{k+1}-{\mathbf{E}}_{k+1}+{\mu }^{-1}\mathbf{Y})$; 11: Update ${\mathbf{Y}}_{k+1}={\mathbf{Y}}_k+{\mu }_k(\mathbf{D}-{\mathbf{A}}_{k+1}-{\mathbf{E}}_{k+1})$; 12: Update ${\mu }_k$ to ${\mu }_{k+1}$; 13: $k\to k+1$. 14: end while 15: return $A_k,E_k,G_k$