# Recovering Texture with a Denoising-Process-Aware LMMSE Filter
## 4 Experimental Results
### Image Denoising  
The PSNR and structural self-similarity (SSIM) [26] results for the denoised images from dataset I with different noise levels \(\sigma\) are given in Tables 1-3. Note that higher PSNR and SSIM values mean that the reference image is more similar to the original image. We highlight the highest PSNR and SSIM in each row in bold. We set the texture scaling  
Figure 3: Dataset I: The ten test images from [21] used in the experiments. parameter to \(\alpha=1\) because we wish to measure how much improvement is achieved in terms of the PSNR. We recover the texture using the LMMSE filter; thus, the MSE is likely to be low, meaning that the PSNR should be high. These tables show that our denoising method outperforms the other state-of-the-art methods in terms of both the PSNR and SSIM. The largest difference in the PSNR between WNNM and our method is 0.15 dB. Additionally, the averages of the denoising results on BSD100 at each noise level are shown in Table 4. This table shows that the performance improvement achieved with our method is independent of the dataset. For each image in BSD100, we performed one-tailed paired \(t\)-tests on the difference of each PSNR and SSIM between the proposed method and WNNM. In this test, the null hypothesis is that the PSNR/SSIM values obtained by proposed method are not greater than the corresponding values obtained by WNNM. The \(p\)-values are also shown in Table 4. From the results, since the \(p\)-values are small enough, we confirmed statistically significant differences between our proposed method and WNNM. Moreover, we show the averages of computational time of WNNM and the proposed method in Table 5. The computational times were measured on 10 distinct observed images (the noise value of each observation is different) for each test image from BSD100. The additional computational time of our texture recovery is 7-13% of the computational time of WNNM. The PSNR/SSIM gain obtained by our texture recovery method is considered to be sufficient for the users to accept this additional cost. \begin{table}
\begin{tabular}{c c c c c} \hline  & **BM3D** & **GHP** & **WNNM** & **Proposed** \\ \hline Image01 & 34.31/0.932 & 34.31/0.925 & 34.70/0.935 & **34.74**/**0.937** \\ Image02 & 32.99/0.887 & 32.97/0.884 & 33.12/0.889 & **33.23**/**0.896** \\ Image03 & 31.64/0.907 & 31.79/0.909 & 31.86/0.910 & **31.95**/**0.916** \\ Image04 & 30.58/0.898 & 30.66/0.904 & 30.76/0.900 & **30.80**/**0.905** \\ Image05 & 32.59/0.946 & 32.52/0.932 & 32.88/0.948 & **32.89**/**0.949** \\ Image06 & 33.61/0.917 & 33.61/0.905 & 33.90/0.921 & **33.99**/**0.925** \\ Image07 & 34.19/0.898 & 34.11/0.894 & 34.41/0.902 & **34.48**/**0.906** \\ Image08 & 31.48/0.908 & 31.51/0.907 & 31.73/0.912 & **31.80**/**0.917** \\ Image09 & 35.12/0.946 & 34.96/0.934 & 35.30/0.946 & **35.35**/**0.948** \\ Image10 & 31.71/0.912 & 31.76/0.907 & 31.84/0.913 & **31.92**/**0.917** \\ \hline Average & 32.82/0.915 & 32.82/0.910 & 33.05/0.918 & **33.11**/**0.922** \\ \hline \end{tabular}
\end{table} 
Table 1: The PSNR [dB] and SSIM results obtained after denoising on dataset I (with a noise standard deviation of \(\sigma=10\)).