Algorithm 1 Proposed view-aligned nonlocal low-rank tensor reconstruction method

Input: $\mathbf{Y}$, $\mathcal{C}$, $\mathcal{A}$; parameters $\rho ,s,\mathsf{\Omega },M,\mathcal{D},{\left\{{\mathbf{b}}_k\right\}}_{k=1}^K,{\tau }_{\mathrm{init}},T,\epsilon$.    Output: Reconstructed view-spectral tensor $\widehat{\mathcal{X}}$.   1:Obtain ${\mathcal{X}}_{\mathrm{GAP}}$ and initialize ${\mathcal{X}}^0={\mathcal{X}}_{\mathrm{GAP}}$, ${\mathcal{V}}^0={\mathcal{X}}^0$, ${\mathcal{U}}^0$ as a zero tensor, and ${\mathcal{X}}_{\mathrm{ref}}^0={\mathcal{X}}_{\mathrm{GAP}}$.   2:for $t=0,1,\dots ,T-1$ do   3:    Update ${\mathcal{X}}^{t+1}$ by the data-consistency solution in Equation (8).   4:    Form the prior input ${\mathcal{Z}}^{t+1}={\mathcal{X}}^{t+1}+{\mathcal{U}}^t$.   5:    Update the reference tensor ${\mathcal{X}}_{\mathrm{ref}}^{t+1}$ using Equation (10).   6:    for each reference patch center ${\mathbf{p}}_i$ do   7:        Estimate ${\tilde{d}}_i^{t+1}$ by minimizing $J_i^{t+1}\left(d\right)$ over $\mathcal{D}$ using Equations (11) and (12).   8:        Construct the view-aligned nonlocal tensor group ${\mathcal{G}}_i^{t+1}={\mathcal{Q}}_i({\mathcal{Z}}^{t+1};{\mathcal{X}}_{\mathrm{ref}}^{t+1})$.   9:        Compute the CP low-rank approximation ${\mathcal{D}}_{\mathrm{CP}}\left({\mathcal{G}}_i^{t+1}\right)$. 10:    end for 11:    Aggregate all restored groups to obtain ${\mathcal{V}}^{t+1}$ using Equation (18). 12:    Update ${\mathcal{U}}^{t+1}$ using Equation (19). 13:    if $\parallel {\mathcal{X}}^{t+1}-{\mathcal{X}}^t{\parallel }_F/max(\parallel {\mathcal{X}}^t{\parallel }_F,\epsilon )<\epsilon$ then 14:        break 15:    end if 16:end for 17:Set $\widehat{\mathcal{X}}={\mathcal{X}}^{t+1}$.