# Accelerated Tensor Robust Principal Component Analysis via Factorized Tensor Norm Minimization
## 5 Experimental Results
### Color Image Recovery
Compared to the other algorithms known for their faster execution, TRPCAAL still outperforms them in execution time. An additional experiment was conducted using the \"airplane\" image with impulse noises containing extremely large magnitudes--50 times greater than the maximum pixel brightness--to simulate gross corruptions or outlier entries in sparse locations. All hyper-parameters for algorithms were selected empirically. Table 4 presents the experimental results. Similar to the experiments with random pixel noise, Algorithm 1 and N-TRPCA achieved the highest accuracy, as indicated by high PNSR and FSIM values. However, aside from these two algorithms, the others failed to produce meaningful outputs in the presence of outliers, even though some of them exhibited a faster execution time. Overall, the proposed algorithm achieves reasonably high recovery accuracy while offering the fastest execution speed, making it a highly appealing solution for large-scale color image recovery problems. Figure 1: Test images used in color image recovery when the “peppers” image with 20% random noise is used. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Noise** & & **Iterations** & **Execution Time** & **PSNR (dB)** & **FSIM** \\ \hline
10\% & noisy image & - & - & 17.4030 & 0.7873 \\  & **TRPCAAL** & 7.00 & **0.1922** & **30.8806** & **0.9564** \\  & FTTNN & 26.00 & **0.3211** & 26.5445 & 0.8668 \\  & IRCUR & 5.95 & 3.2608 & 26.0213 & 0.8629 \\  & TRPCA\_TNN & 58.10 & 1.0414 & 28.1301 & 0.9327 \\  & N-TRPCA & - & 5.0506 & **32.2581** & **0.9691** \\  & EATP-DCT & 19.70 & 0.3506 & 26.8569 & 0.8964 \\ \hline
20\% & noisy image & - & - & 14.3960 & 0.6763 \\  & **TRPCAAL** & 12.00 & **0.1444** & **27.0307** & **0.9083** \\  & **FTNN** & 26.00 & **0.3311** & 24.6861 & 0.8249 \\  & IRCUR & 5.90 & 3.2266 & 23.1291 & 0.7837 \\  & TRPCA\_TNN & 58.10 & 1.0400 & 26.4528 & 0.9040 \\  & N-TRPCA & - & 5.0613 & **29.3179** & **0.9409** \\  & EATP-DCT & 19.05 & 0.3411 & 23.8989 & 0.8517 \\ \hline
40\% & noisy image & - & - & 11.4025 & 0.5574 \\  & **TRPCAAL** & 14.00 & **0.1090** & **21.4635** & **0.7780** \\  & FTTNN & 24.00 & 0.2807 & 19.4878 & 0.6968 \\  & IRCUR & 5.85 & 2.3384 & 17.9545 & 0.6502 \\  & TRPCA\_TNN & 57.60 & 1.0468 & 20.0816 & 0.7619 \\  & N-TRPCA & - & 5.0344 & **23.6163** & **0.8286** \\  & EATP-DCT & 14.45 & **0.2787** & 15.3644 & 0.6345 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: 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} \hline \hline
**Noise** & & **Iterations** & **Execution Time** & **PSNR (dB)** & **FSIM** \\ \hline
10\% & noisy image & - & - & 17.4030 & 0.7873 \\  & **TRPCAAL** & 7.00 & **0.1922** & **30.8806** & **0.9564** \\  & FTTNN & 26.00 & **0.3211** & 26.5445 & 0.8668 \\  & IRCUR & 5.95 & 3.2608 & 26.0213 & 0.8629 \\  & TRPCA\_TNN & 58.10 & 1.0414 & 28.1301 & 0.9327 \\  & N-TRPCA & - & 5.0506 & **32.2581** & **0.9691** \\  & EATP-DCT & 19.70 & 0.3506 & 26.8569 & 0.8964 \\ \hline
20\% & noisy image & - & - & 14.3960 & 0.6763 \\  & **TRPCAAL** & 12.00 & **0.1444** & **27.0307** & **0.9083** \\  & FTTNN & 26.00 & **0.3311** & 24.6861 & 0.8249 \\  & IRCUR & 5.90 & 3.2266 & 23.1291 & 0.7837 \\  & TRPCA\_TNN & 58.10 & 1.0400 & 26.4528 & 0.9040 \\  & N-TRPCA & - & 5.0613 & **29.3179** & **0.9409** \\  & EATP-DCT & 19.05 & 0.3411 & 23.8989 & 0.8517 \\ \hline
40\% & noisy image & - & - & 11.4025 & 0.5574 \\  & **TRPCAAL** & 14.00 & **0.1090** & **21.4635** & **0.7780** \\  & FTTNN & 24.00 & 0.2807 & 19.4878 & 0.6968 \\  & IRCUR & 5.85 & 2.3384 & 17.9545 & 0.6502 \\  & TRPCA\_TNN & 57.60 & 1.0468 & 20.0816 & 0.7619 \\  & N-TRPCA & - & 5.0344 & **23.6163** & **0.8286** \\  & EATP-DCT & 14.45 & **0.2787** & 15.3644 & 0.6345 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental results for the “peppers” image with 10%, 20%, and 40% noise levels. The top two results in execution time and accuracy are bolded.