Algorithm 2 DMFCNet-2

Require:  $X_{\mathrm{\Omega }}$: original incomplete image matrix; $\mathrm{\Omega }$: the position of the observed entries; non-negative parameters r, $\mu$ and $\lambda$. Ensure:  the restored matrix $X_{new}$.   1:Init: $X_0\in R^{m\times n}$: The matrix obtained by pre-filling $X_{\mathrm{\Omega }}$ using NNMF algorithm; $\mathrm{\Psi }\in {\{0,1\}}^{m\times n}:{\mathrm{\Psi }}_{ij}=\left\{\begin{array}{c}1,if(i,j)\in \mathrm{\Omega }\\ 0,if(i,j)\notin \mathrm{\Omega }\end{array}\right.$;   2:Compute$U_0\in R^{m\times r}$ and $V_0\in R^{n\times r}$ from $X_0$ using (12) and (13);   3:$U_1\leftarrow {\mathbb{C}}_U(X_0{V}_0,V_0,U_0)$;   4:$V_1\leftarrow {\mathbb{C}}_V({X_0}^T{U}_1,U_1,V_0)$;   5:${\widehat{X}}_1\leftarrow U_1{V_1}^T-\mu (X_0-U_1{V_1}^T)$;   6:${\tilde{X}}_1\leftarrow \mathrm{AutoEncoder}({\widehat{X}}_1)$;   7:$X_1\leftarrow (1-\mathrm{\Psi })\odot {\tilde{X}}_1+\frac{\mathrm{\Psi }\odot {\tilde{X}}_1+\lambda \mathrm{\Psi }\odot X_0}{1+\lambda }$;   8:$X_{new}\leftarrow (1-\mathrm{\Psi })\odot X_1+\mathrm{\Psi }\odot X_0$;   9:return$X_{new}$;