# Edge-Preserving Image Denoising Based on Lipschitz Estimation
## 5 Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**House**} & \multicolumn{3}{c}{**Lena**} \\ \hline
**Sigma** & **Input (dB)** & **SSplit (dB)** & \(\Delta\) & **Sigma** & **Input (dB)** & **SSplit (dB)** & \(\Delta\) \\ \hline
15 & 24.61 & 31.50 & \(\approx\)6 & 15 & 24.61 & 32.08 & \(\approx\)7 \\ \hline
20 & 22.11 & 29.93 & \(\approx\)7 & 20 & 22.11 & 30.80 & \(\approx\)8 \\ \hline
25 & 20.17 & 29.09 & \(\approx\)8 & 25 & 20.17 & 29.98 & \(\approx\)9 \\ \hline
30 & 18.59 & 28.89 & \(\approx\)10 & 30 & 18.59 & 29.09 & \(\approx\)10 \\ \hline
35 & 17.25 & 27.85 & \(\approx\)10 & 35 & 17.25 & 28.43 & \(\approx\)11 \\ \hline \multicolumn{3}{c}{**Pepper**} & \multicolumn{3}{c}{**Hand**} \\ \hline
**Sigma** & **Input (dB)** & **SSplit (dB)** & \(\Delta\) & **Sigma** & **Input (dB)** & **SSplit (dB)** & \(\Delta\) \\ \hline
15 & 24.61 & 29.34 & \(\approx\)5 & 15 & 24.61 & 28.77 & \(\approx\)4 \\ \hline
20 & 22.11 & 29.53 & \(\approx\)7 & 20 & 22.11 & 28.13 & \(\approx\)6 \\ \hline
25 & 20.17 & 28.89 & \(\approx\)8 & 25 & 20.17 & 27.74 & \(\approx\)Figure 16: (**a**) Original image, (**b**) Image with the addition of Gaussian white noise (Input PSNR = 22.11 dB), (**c**) Denoising with proposed method (Output PSNR = 29.82 dB). Figure 9:0 (**a**) Original image, (**b**) Image with the addition of Gaussian white noise (Input PSNR = 22.11 dB), (**c**) Denoising with proposed method (Output PSNR = 26.12 dB). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sigma** & **Input (dB)** & **SURE-LET (dB)** & **Sureshrink** & **Visu Shrink** & **Bivariate Shrinkage** & **SSplit (dB)** \\ \hline
15 & 24.65 & 32.17 & 31.59 & 27.48 & 32.06 & 32.08 \\ \hline
20 & 22.14 & 30.94 & 30.22 & 26.46 & 30.73 & 30.81 \\ \hline
25 & 20.17 & 30.03 & 29.14 & 25.67 & 29.81 & 29.97 \\ \hline
30 & 18.62 & 29.32 & 28.38 & 25.14 & 28.94 & 29.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PSNR values for Lena test images with different noise levels and denoised with: the SURE LET, SureShrink, VisuShrink, Bivariate shrinkage function, and SSplit methods. Figure 18: (**a**) Original image, (**b**) Image with the addition of Gaussian white noise (Input PSNR = 19.27 dB), (**c**) Denoising with proposed method (Output PSNR = 26.42 dB). Tables 3 and 4 present the qualitative analysis in terms of the Structural SIMilarity (SSIM) of the proposed method with the other denoised images obtained from the wavelet-based denoising methods [22]. The SSIM can estimate the similarity index between two images and, therefore, can be viewed as a quality measure of one of the image degraded or altered with the other which is regarded as of perfect quality. We performed analysis on the 'Lena' and 'Peppers' images. It can be observed that the denoised images obtained better results than the Bishrink and NeighSure method and were competitive to the SURE LET denoising method in terms of SSIM. We also analyzed the performance of the method using another criterion, which focused only around the edges. At first, we applied a Canny edge detector as shown in Figure 20a to highlight strong edges. Then, we applied morphological dilation of \(5\times 5\) to generate a binary mask as shown in Figure 20b. The Mask represents the dilated binary image of edges, and the estimated error is:  
\[\epsilon=PSNR\{(I_{restored}-I_{original})*Mask\} \tag{24}\]  
We estimated the error corresponding to the area of the edge points with the SURE LET denoising method with the proposed method based on the splitting of edges as shown in Figure 20, and we observed increased improvement in SNR with both methods with the difference of \(\approx\)1 dB. Figure 19: (**a**) Original image, (**b**) Image with the addition of Gaussian white noise (Input PSNR = 18.59 dB), (**c**) Denoising with proposed method (Output PSNR = 24.59 dB).