# Accelerated Tensor Robust Principal Component Analysis via Factorized Tensor Norm Minimization
## 5 Experimental Results
### Background Subtraction

Table 6: Experimental results for the “bus station” video sequence. The top two results in terms of execution time and F-score are bolded for comparison. \begin{table}
\begin{tabular}{l l l l l l} \hline
**Noise** & & **Iterations** & **Execution Time** & **PSNR (dB)** & **FSIM** \\ \hline
10\% & noisy image & - & - & 14.5079 & 0.0965 \\
**TRPCAAL** & 65.95 & 0.6039 & **29.6132** & **0.9305** \\  & FTTNN & 20.00 & **0.2796** & 4.7797 & 0.0898 \\  & IRCUR & 22.25 & 10.0694 & 15.5529 & 0.6053 \\  & TRPCA\_TNN & 63.00 & 1.2621 & 12.9168 & 0.6503 \\  & N-TRPCA & - & 6.2646 & **32.3481** & **0.9704** \\  & EATP-DCT & 24.25 & **0.3680** & 12.9846 & 0.3860 \\ \hline
20\% & noisy image & - & - & 11.5019 & 0.0263 \\
**TRPCAAL** & 67.45 & 0.6158 & **27.1214** & **0.9012** \\  & FTTNN & 20.00 & **0.2926** & 4.5666 & 0.0615 \\  & IRCUR & 21.35 & 9.6075 & 15.0562 & 0.5743 \\  & TRPCA\_TNN & 62.15 & 1.2326 & 10.6987 & 0.5592 \\  & N-TRPCA & - & 6.2572 & **29.5371** & **0.9449** \\  & EATP-DCT & 23.15 & **0.3483** & 8.9972 & 0.1999 \\ \hline
40\% & noisy image & - & - & 8.4811 & 0.0135 \\
**TRPCAAL** & 87.85 & 0.6828 & **21.9168** & **0.7935** \\  & FTTNN & 20.00 & **0.2797** & 4.5093 & 0.0427 \\  & IRCUR & 20.20 & 9.1873 & 13.8373 & 0.4780 \\  & TRPCA\_TNN & 62.00 & 1.2249 & 8.1658 & 0.4618 \\  & N-TRPCA & - & 6.2689 & **24.1166** & **0.8463** \\  & EATP-DCT & 24.00 & **0.3597** & 4.6647 & 0.0194 \\ \hline \end{tabular}
\end{table} 
Table 4: Experimental results for the “airplane” image with 10%, 20%, and 40% noise levels. The top two results in execution time and accuracy are bolded. \begin{table}
\begin{tabular}{l l l l l l} \hline
**Noise** & & **Iterations** & **Execution Time** & **Precision** & **Recall** & **F-Score** \\ \hline
**TRPCAAL** & 4 & **3.7391** & 0.5295 & 0.5672 & **0.5407** \\ FTNN & 25 & **32.6119** & 0.4749 & 0.1468 & 0.2041 \\ IRCUR & 24 & 513.9714 & 0.4855 & 0.5898 & **0.5269** \\ TRPCA\_TNN & 43 & 82.7404 & 0.0244 & 0.4375 & 0.0456 \\ N-TRPCA & - & 249.2075 & 0.0954 & 0.3753 & 0.1474 \\ EATP-DCT & 25 & 32.9607 & 0.4377 & 0.5587 & 0.4826 \\ \hline \end{tabular}
\end{table} 
Table 5: Experimental results for the “highway” video sequence. The top two results in terms of execution time and F-score are bolded for comparison. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Noise** & **Iterations** & **Execution Time** & **Precision** & **Recall** & **F-Score** \\ \hline
**TRPCAAL** & 4 & **4.9572** & 0.2727 & 0.4436 & **0.3294** \\ FTTNN & 24 & **35.0960** & 0.3105 & 0.0738 & 0.1157 \\ IRCUR & 23 & 658.9767 & 0.2541 & 0.5875 & **0.3475** \\ TRPCA\_TNN & 40 & 112.5505 & 0.6425 & 0.0201 & 0.0387 \\ N-TRPCA & - & 346.1222 & 0.0583 & 0.0329 & 0.0396 \\ EATP-DCT & 26 & 45.2597 & 0.1281 & 0.5621 & 0.2040 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Experimental results for the “park” video sequence. The top two results in terms of execution time and F-score are bolded for comparison. Figure 2: Test images used in color image recovery when the “airplane” image with 20% random noise is used. Figure 4: Empirical hyperparameter selection based on the variation in \(\mu\) and \(r\). Note that the “airplane” image with 20% random noise is used. Figure 3: Test images used in color image recovery when the “house” image with 20% random noise is used.