# An Improved Image Filtering Algorithm for Mixed Noise
## 3 Experiment
### Experimental Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**FSIM** & \(\rho\)/\(\sigma\) & **KSVD** & **NCSR** & **OCTOBOS** & **TWSC** & **BM3D** & **WNNM** & **Ours** \\ \hline  & 0.03/0.01 & 0.9912 & 0.9919 & 0.9822 & 0.9892 & **0.9941** & 0.9880 & 0.9933 \\  & 0.06/0.02 & 0.9847 & 0.9862 & 0.9690 & 0.9829 & _0.9907_ & 0.9791 & **0.9927** \\ lena & 0.09/0.03 & 0.9787 & 0.9799 & 0.9573 & 0.9768 & _0.9866_ & 0.9727 & **0.9907** \\  & 0.12/0.04 & 0.9728 & 0.9734 & 0.9482 & 0.9701 & _0.9822_ & 0.9671 & **0.9874** \\  & 0.15/0.05 & 0.9675 & 0.9696 & 0.9386 & 0.9644 & _0.9785_ & 0.9594 & **0.9810** \\ \hline  & 0.03/0.01 & 0.9923 & _0.9928_ & 0.9876 & 0.9911 & **0.9936** & 0.9898 & 0.9825 \\  & 0.06/0.02 & _0.9871_ & 0.9862 & 0.9780 & 0.9847 & **0.9897** & 0.9828 & 0.9829 \\ boat & 0.09/0.03 & 0.9826 & 0.9812 & 0.9691 & 0.9797 & **0.9860** & 0.9771 & _0.9848_ \\  & 0.12/0.04 & 0.9781 & 0.9769 & 0.9606 & 0.9753 & _0.9827_ & 0.9719 & **0.9828** \\  & 0.15/0.05 & 0.9735 & 0.9712 & 0.9528 & 0.9700 & _0.9782_ & 0.9669 & **0.9791** \\ \hline  & 0.03/0.01 & 0.9920 & _0.9923_ & 0.9844 & 0.9902 & **0.9938** & 0.9890 & 0.9922 \\  & 0.06/0.02 & 0.9851 & 0.9860 & 0.9718 & 0.9823 & _0.9905_ & 0.9807 & **0.9918** \\  & 0.09/0.03 & 0.9803 & 0.9803 & 0.9597 & 0.9777 & _0.9861_ & 0.9721 & **0.9905** \\  & 0.12/0.04 & 0.9734 & 0.9728 & 0.9505 & 0.9711 & _0.9819_ & 0.9650 & **0.9869** \\  & 0.15/0.05 & 0.9689 & 0.9664 & 0.9420 & 0.9633 & _0.9767_ & 0.9603 & **0.9815** \\ \hline  & 0.03/0.01 & 0.9752 & _0.9814_ & 0.9696 & 0.9748 & **0.9830** & 0.9735 & 0.9771 \\  & 0.06/0.02 & 0.9647 & 0.9703 & 0.9559 & 0.9654 & _0.9764_ & 0.9611 & **0.9765** \\ cameraman & 0.09/0.03 & 0.9560 & 0.9612 & 0.9468 & 0.9580 & _0.9697_ & 0.9554 & **0.9740** \\  & 0.12/0.04 & 0.9468 & 0.9516 & 0.9394 & 0.9537 & _0.9643_ & 0.9504 & **0.9705** \\  & 0.15/0.05 & 0.9393 & 0.9461 & 0.9331 & 0.9466 & _0.9578_ & 0.9431 & **0.9646** \\ \hline  & & & & & & & & & \\ \end{tabular}
\end{table} 
Table 4: Denoising data of mixed noise by different algorithms on test images (PSIM). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**SSIM** & \(\rho\)/\(\sigma\) & **KSVD** & **NCSR** & **OCTOBOS** & **TWSC** & **BM3D** & **WNNM** & **Ours** \\ \hline  & 0.03/0.01 & 0.5098 & 0.5939 & 0.3513 & 0.5421 & _0.6538_ & 0.5057 & **0.8178** \\  & 0.06/0.02 & 0.3677 & 0.4668 & 0.2547 & 0.4545 & _0.5672_ & 0.3846 & **0.7945** \\ lena & 0.09/0.03 & 0.2947 & 0.3849 & 0.2089 & 0.3959 & _0.4887_ & 0.3270 & **0.7566** \\  & 0.12/0.0  
In the tables, the optimal value of the denoising effect for each row is expressed in bold and the sub-optimal value is expressed in italics. As can be seen from the data of each metric in the four tables, the algorithm proposed in this paper has the best denoising effect among the denoised images with various noise levels, while the metric value of the BM3D algorithm is relatively high due to its strong ability to denoise Gaussian noise. The denoising effect of the BM3D algorithm is closer to the proposed algorithm when the noise level is relatively low, but as the noise increases, especially as the density of salt and pepper noise increases, its limitation in removing salt and pepper noise is highlighted. Because the extreme gray value of the salt and pepper noise point will destroy the self-similarity of image, resulting in an invalid filtering result [46], the denoising effect is significantly reduced. However, it should be pointed out that the BM3D algorithm performs quite well in FSIM, especially when the noise level is relatively low; its FSIM value is the largest in the six test images compared with other algorithms. It fully illustrates that the block-matching mode of the BM3D algorithm is helpful for improving the feature similarity of denoised images, but when the noise level increases, the matching accuracy of similar blocks decreases. Excessive noise interferes with the feature search and block matching between blocks, so the FSIM value decreases significantly as the noise level increases.