# An Unsupervised Image Denoising Method Using a Nonconvex Low-Rank Model with TV Regularization
## 4 Experimental Results and Analysis
### Natural Image Denoising
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Noise Type** & **Images** & **RPCA** & **AMlogtv** & **NonRPCA** & **WNNM\(-\)RPCA** & **TDV** & **Ours** \\ \hline \multirow{10}{*}{Impulse noise} & Butterfly & 0.9635 & 0.6670 & 0.9318 & 0.7651 & 0.6336 & 0.9863 \\  & House & 0.9455 & 0.6096 & 0.8849 & 0.6157 & 0.7367 & 0.9735 \\  & Peppers & 0.9025 & 0.5965 & 0.8651 & 0.6368 & 0.6742 & 0.9220 \\  & Lena & 0.9514 & 0.5835 & 0.9172 & 0.6705 & 0.6469 & 0.9783 \\  & Room & 0.9694 & 0.5389 & 0.9442 & 0.7807 & 0.4661 & 0.9859 \\  & Bird & 0.9086 & 0.5658 & 0.8395 & 0.6933 & 0.6691 & 0.9280 \\  & Camera & 0.8935 & 0.5237 & 0.8128 & 0.7930 & 0.6357 & 0.9174 \\  & Starfish & 0.9226 & 0.5696 & 0.9301 & 0.8667 & 0.5382 & 0.9403 \\  & **Average** & **0.9321** & **0.5818** & **0.8907** & **0.7277** & **0.6251** & **0.9539** \\ \hline \multirow{10}{*}{Poisson noise} & Butterfly & 0.9559 & 0.8563 & 0.9652 & 0.9600 & 0.6689 & 0.9902 \\  & House & 0.9255 & 0.8427 & 0.9220 & 0.9104 & 0.7622 & 0.9764 \\  & Peppers & 0.8913 & 0.8196 & 0.8981 & 0.8910 & 0.7094 & 0.9310 \\  & Lena & 0.9366 & 0.7906 & 0.9482 & 0.9420 & 0.6774 & 0.9857 \\  & Room & 0.9578 & 0.6895 & 0.9646 & 0.9597 & 0.4969 & 0.9905 \\  & Bird & 0.8936 & 0.8164 & 0.8997 & 0.8920 & 0.7045 & 0.9410 \\  & Camera & 0.8784 & 0.7814 & 0.8803 & 0.8731 & 0.6741 & 0.9241 \\  & Starfish & 0.9119 & 0.7654 & 0.9086 & 0.9155 & 0.5388 & 0.9324 \\  & **Average** & **0.9188** & **0.7952** & **0.9233** & **0.6540** & **0.9180** & **0.9589** \\ \hline \multirow{10}{*}{Gaussian noise} & Butterfly & 0.9581 & 0.8154 & 0.9589 & 0.9684 & 0.7226 & 0.9848 \\  & House & 0.9339 & 0.8100 & 0.9256 & 0.9316 & 0.7593 & 0.9706 \\  & Peppers & 0.8933 & 0.7645 & 0.8948 & 0.9107 & 0.7017 & 0.9258 \\  & Lena & 0.9416 & 0.7445 & 0.9437 & 0.9539 & 0.6737 & 0.9795 \\  & Room & 0.9598 & 0.6556 & 0.9618 & 0.9476 & 0.4881 & 0.9851 \\  & Bird & 0.8912 & 0.7688 & 0.8906 & 0.9125 & 0.6947 & 0.9306 \\  & Camera & 0.8812 & 0.7513 & 0.8744 & 0.8705 & 0.6626 & 0.9168 \\  & Starfish & 0.9175 & 0.7217 & 0.9198 & 0.9321 & 0.5382 & 0.9421 \\  & **Average** & **0.9220** & **0.7539** & **0.9212** & **0.9284** & **0.6551** & **0.9544** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SSIM comparisons of RPCA, AMlogtv, NonRPCA, WNNM\(-\)RPCA, TDV, and the proposed method for noise removal in natural test images (optimal value: red line; suboptimal value: cyan line). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Noise Type** & **Images** & **RPCA** & **AMlogtv** & **NonRPCA** & **WNNM\(-\)RPCA** & **TDV** & **Ours** \\ \hline \multirow{10}{*}{Impulse noise} & Butterfly & 0.9802 & 0.9860 & 0.9592 & 0.9015 & 0.7521 & 0.9911 \\  & House & 0.9751 & 0.9725 & 0.9519 & 0.8593 & 0.7616 & 0.9880 \\  & Peppers & 0.9551 & 0.9436 & 0.9374 & 0.8510 & 0.7726 & 0.9647 \\  & Lena & 0.9768 & 0.9737 & 0.9596 & 0.8735 & 0.7423 & 0.9888 \\  & Room & 0.9827 & 0.9717 & 0.9720 & 0.9307 & 0.5929 & 0.9925 \\  & Bird & 0.9588 & 0.9526 & 0.9333 & 0.8878 & 0.7480 & 0.9666 \\  & Camera & 0.9530 & 0.9579 & 0.9148 & 0.9165 & 0.7002 & 0.9594 \\  & Starfish & 0.9558 & 0.9583 & 0.9638 & 0.9452 & 0.7004 & 0.9676 \\  & **Average** & **0.9671** & **0.9645** & **0.9490** & **0.8956** & **0.7212** & **0.9773** \\ \hline \multirow{10}{*}{Poisson noise} & Butterfly & 0.9755 & 0.9848 & 0.9804 & 0.9792 & 0.7675 & 0.9942 \\  & House & 0.9667 & 0.9774 & 0.9655 & 0.9611 & 0.7848 & 0.9883 \\ \cline{1-1}  & Peppers & 0.9495 & 0.9415 & 0.9538 & 0.9513 & 0.7925 & 0.9697 \\ \cline{1-1}  & Lena & 0.9694 & 0.9843 & 0.9746 & 0.9718 & 0.7626 & 0.9929 \\ \cline{1-1}  & Room & 0.9782 & 0.9746 & 0.9824 & 0.9806 & 0.6177 & 0.9950 \\ \cline{1-1}  & Bird & 0.9547 & 0.9661 & 0.9576 & 0.9542 & 0.7619 & 0.9709 \\ \cline{1-1}  & Camera & 0.9496 & 0.9578 & 0.9502 & 0.9472 & 0.7118 & 0.9641 \\ \cline{1-1}  & Starfish & 0.9561 & 0.9682 & 0.9541 & 0.9582 & 0.7005 & 0.9690 \\ \cline{1-1}  & **Average** & **0.9624** & **0.9693** & **0.9648** & **0.9630** & **0.7374** & **0.9805** \\ \hline \hline \end{tabular}
\end{table}