# Low Tensor Rank Constrained Image Inpainting Using a Novel Arrangement Scheme
## 4 Experimental Results and Analyses
### Analyses of the Methods Exploiting Both Low Rankness and Sparsity
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Methods**} & \multicolumn{6}{c}{**PSNR (dB)/SSIM of Different Color Images Under Different Missing Patterns**} \\ \cline{4-9}  & & & **House** & **Peppers** & **Lens** & **Airplane** & **Baboon** & **B boats** \\  & & & **Random 50\%** & **Text** & **Lines** & **Random line** & **Blocks** & **Random 80\%** \\ \hline \multirow{8}{*}{**Other methods**} & 1 & STDC & 32.04/0.9300 & 33.61/0.9813 & 28.56/0.8995 & 23.49/0.7756 & 27.01/0.9293 & 21.88/0.7340 \\  & 2 & HALRTC & 32.07/0.9423 & 25.84/0.9496 & 13.43/0.8500 & 19.94/0.6334 & 28.04/0.9397 & 20.56/0.6858 \\  & 3 & FRCP & 26.41/0.8701 & NAN & 14.56/0.5242 & 10.025/10.954 & 18.71/0.5546 & 29.01/0.6947 \\  & 4 & TMac-TTKA & 23.18/0.8113 & 29.47/0.9681 & 29.95/0.9462 & 20.82/0.7521 & 28.04/0.9429 & 8.83/0.1229 \\  & 5 & SPCTV & 29.56/0.9133 & 23.38/0.9154 & 16.02/0.6107 & 18.85/0.6894 & 24.21/0.9144 & 20.98/0.7254 \\  & 6 & LRTV & 30.95/0.9382 & 36.98/0.9945 & 34.07/0.9724 & 26.82/0.9228 & 27.10/0.9319 & 21.62/0.7541 \\ \cline{2-9}  & 1 & TTLRTV & 33.02/0.9579 & 37.27/0.9945 & **34.94/0.9823** & 28.82/0.9561 & 29.46/0.9559 & 22.37/0.7487 \\ \cline{2-9}  & 2 & tSVDLRTV & 32.20/0.9550 & 37.49/0.9950 & 34.70/0.9818 & 28.03/0.9507 & 29.56/**0.9574** & 22.86/0.8021 \\  & 3 & UnfoldingLRTV & **35.610.9689** & **37.72/0.9952** & 34.87/0.9821 & **29.550/0.9639** & **29.59**/0.9556 & **25.430/0.8863** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PSNR (dB)/SSIM and SSIM of the nine methods. Figure 10: The PSNR curves of the inpainting results of the nine methods; the missing ratio ranges from 10% to 70% under a random missing pattern. The visual and numerical PSNR (dB)/SSIM comparisons of our methods for recovering the pepper image under 80% random missing patterns are shown in Figure 11. In the first row of Figure 11, the methods only exploit low-rank constraints. As shown in the color box, there are small blocky errors in the recovered image, these are caused by the QA scheme. This phenomenon can be solved by combining the constraints of low rank and sparsity (TV), as shown in the second row of Figure 11.  
All in all, due to the support of the QA scheme and the efficient TV prior, the low tensor rank-based methods (UnfoldingLRTV, tSVDLRTV, and TTLRTV) were superior to other close low tensor rank-based methods. The UnfoldingLRTV method provided the best results among all the methods examined. Figure 11: The visual and numerical PSNR (dB)/SSIM comparisons of our methods for recovering the pepper image under 80% random missing patterns. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**PSNR (dB)/SSIM of Different Color Images Under Different Missing Patterns**} \\ \cline{3-8}
**No.** & **Methods** & \multicolumn{2}{c}{**House Random 50\%**} & \multicolumn{2}{c}{**Peppers Text**} & \multicolumn{2}{c}{**Lena**} & \multicolumn{2}{c}{**Airplane Random Line**} & \multicolumn{2}{c}{**Baboon**} & \multicolumn{2}{c}{**Boots Random 80\%**} \\ \hline
1 & MatrixLR & 9.38/0.8970 & 33.23/0.9814 & 13.34/0.5850 & 7.118/0.1308 & 27.62/0.9343 & 19.18/0.5680 \\
2 & TV & 29.70/0.8816 & 34.14/0.9913 & 29.21/0.9107 & 22.85/0.8463 & 23.18/0.9066 & 20.32/0.6103 \\ \hline
3 & TTLR & 30.21/0.9251 & 34.86/0.9892 & 31.79/0.9559 & 25.77/0.8796 & 25.42/0.9239 & 21.44/0.7144 \\
4 & tSVDLR & 29.79/0.8989 & 33.86/0.9840 & 31.20/0.9561 & 18.91/0.8386 & **28.03**/**0.9373** & 21.34/0.6879 \\
5 & UnfoldingLR & **32.58/0.9416** & **36.86**/**0.9938** & **33.45**/**0.9771** & **28.75**/**0.9464** & 22.22/0.9238 & **23.46**/**0.8139** \\ \hline
6 & TTLRTV & 33.02/0.9579 & 37.27/0.9945 & **34.94**/**0.9823** & 28.82/0.9561 & 29.46/0.9559 & 22.37/0.7487 \\
7 & tSVDLRTV & 32.20/0.9550 & 37.49/0.9950 & 34.70/0.9818 & 28.03/0.9507 & 29.56/**0.9574** & 22.86/0.8021 \\
8 & UnfoldingLRTV & **35.61/0.9689** & **37.72/0.9952** & 34.87/0.9821 & **29.55**/**0.9639** & **29.59**/0.9556 & **25.43**/**0.8863** \\ \hline \hline \end{tabular}
\end{table}