# Nonconvex Nonlinear Transformation of Low-Rank Approximation for Tensor Completion
## 5 Numerical Experiments
### Grayscale Video Completion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Data**} & \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**SR = 2.5\%**} & \multicolumn{2}{c}{**SR = 5\%**} & \multicolumn{2}{c}{**SR = 10\%**} & \multicolumn{2}{c}{**SR = 20\%**} \\ \cline{3-10}  & & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** \\ \hline \multirow{4}{*}{suzie} & Observed & 7.146 & 0.0061 & 7.259 & 0.0093 & 7.494 & 0.0133 & 8.003 & 0.0194 \\  & TNN & 21.185 & 0.5208 & 25.747 & 0.6780 & 28.075 & 0.7569 & 30.661 & 0.8364 \\  & UTNN & 22.939 & 0.5938 & 26.417 & 0.7048 & 28.676 & 0.7795 & 31.512 & 0.8578 \\  & FTNN & 25.662 & 0.7290 & 27.793 & 0.7925 & 30.008 & 0.8502 & 31.786 & 0.8680 \\  & NTTNN & 24.566 & 0.6079 & 27.021 & 0.7258 & 29.300 & 0.8115 & 30.943 & 0.8631 \\  & **OUR** & **27.285** & **0.7664** & **28.963** & **0.8152** & **30.461** & **0.8466** & **32.206** & **0.8816** \\ \hline \multirow{4}{*}{hall} & Observed & 4.730 & 0.0042 & 4.843 & 0.0071 & 5.077 & 0.0123 & 5.589 & 0.0241 \\  & TNN & 18.602 & 0.5442 & 28.041 & 0.9021 & 30.899 & 0.939 & 33.718 & 0.9613 \\  & UTNN & 18.662 & 0.5475 & 28.324 & 0.9089 & 31.267 & 0.9428 & 34.159 & 0.9630 \\  & FTNN & 25.159 & 0.8426 & 29.768 & 0.9376 & 32.666 & 0.9**628** & 35.488 & **0.9769** \\  & NTTNN & 26.978 & 0.9009 & 29.891 & 0.9388 & 32.617 & 0.9591 & 35.019 & 0.9723 \\  & **OUR** & **27.342** & **0.9047** & **30.244** & **0.9407** & **32.954** & 0.9598 & **35.491** & 0.9741 \\ \hline \multirow{4}{*}{carphone} & Observed & 6.701 & 0.0087 & 6.814 & 0.0143 & 7.048 & 0.0231 & 7.559 & 0.0391 \\  & TNN & 20.084 & 0.5216 & 25.077 & 0.7206 & 27.216 & 0.7905 & 29.745 & 0.8588 \\ \cline{1-1}  & UTNN & 20.242 & 0.5316 & 25.674 & 0.7475 & 27.980 & 0.8179 & 30.827 & 0.9237 \\ \cline{1-1}  & FTNN & 24.425 & 0.7516 & 26.699 & 0.8192 & 28.907 & **0.8803** & 31.425 & 0.9223 \\ \cline{1-1}  & NTTNN & 24.372 & 0.7149 & 26.855 & 0.8033 & 29.468 & 0.8739 & 32.103 & 0.9223 \\ \cline{1-1}  & **OUR** & **25.634** & **0.7697** & **27.601** & **0.8284** & **29.775** & 0.8754 & **32.437** & **0.9254** \\ \hline \multirow{4}{*}{container} & Observed & 4.524 & 0.0040 & 4.637 & 0.0067 & 4.871 & 0.0115 & 5.382 & 0.0228 \\ \cline{1-1}  & TNN & 18.729 & 0.5534 & 28.253 & 0.8828 & 32.489 & 0.9406 & 37.145 & 0.9728 \\ \cline{1-1}  & UTNN & 18.713 & 0.5536 & 28.042 & 0.8816 & 32.843 & 0.9454 & 39.128 & **0.9803** \\ \cline{1-1}  & FTNN & 24.706 & 0.8021 & 28.636 & 0.9001 & 32.200 & **0.9501** & 36.621 & 0.9782 \\ \cline{1-1}  & NTTNN & 26.415 & 0.8665 & 29.315 & **0.9114** & 33.384 & 0.9484 & 38.461 & 0.9759 \\ \cline{1-1}  & **OUR** & **26.660** & **0.8670** & **29.666** & 0.9090 & **33.768** & 0.9453 & **39.241** & 0.9734 \\ \hline \end{tabular}
\end{table} 
Table 1: TNN, UTNN, FTNN, NTTNN, and our model’s PSNR and SSIM results for the recovery of videos “suzie”, “hall”, “carphone”, and “container” at different sampling rates, with the optimal values highlighted in bold. Figure 3: The results of various grayscale video data using different methods at different sampling rates (from top to bottom: SR = 5%, 10%, 20%).