## 5 Experiment and Application
### Experiment with Gaussian Noise  
To compare denoising performance, Gaussian noise with different noise variance was added to different original images, and other denoising methods such as DTCWT, median filter, wiener filter, bilateral filter, and wavelet decomposition filter were used to remove the noise of the image. The image quality evaluation strategies were peak signal to noise ratio (PSNR) and two-dimensional correlation coefficient of image matrix \(r\). The PSNR and \(r\) here were calculated from denoised images and original images. Denoising results are listed in Tables 2-4.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**MethodsParameters**} & \multicolumn{2}{c}{\(\sigma\) = 0.01} & \multicolumn{2}{c}{\(\sigma\) = 0.05} & \multicolumn{2}{c}{\(\sigma\) = 0.1} & \multicolumn{2}{c}{\(\sigma\) = 0.2} \\ \cline{2-9}  & **PSNR** & **r** & **PSNR** & **r** & **PSNR** & **r** & **PSNR** & **r** \\ \hline Noised & 20.07 & 0.8837 & 13.64 & 0.6441 & 11.32 & 0.5053 & 9.518 & 0.3731 \\ Median & 27.86 & 0.9766 & 23.41 & 0.9362 & 20.93 & 0.8945 & 18.40 & 0.8281 \\ Wiener & 27.70 & 0.9726 & 20.90 & 0.8881 & 18.66 & 0.8105 & 16.93 & 0.7062 \\ WDF & 27.48 & 0.9745 & 23.94 & 0.9411 & 21.77 & 0.9008 & 19.57 & 0.8289 \\ Bilateral & 25.44 & 0.9600 & 14.93 & 0.6971 & 11.98 & 0.5345 & 9.863 & 0.3877 \\ BM3D & 31.96 & 0.9909 & 16.02 & 0.7419 & 12.52 & 0.5543 & 10.26 & 0.3975 \\ DTCWT & 31.01 & 0.9887 & 26.51 & 0.9687 & 24.30 & 0.9525 & 21.70 & 0.9229 \\ IFOA-DTCWT-BF & 28.66 & 0.9807 & 26.34 & 0.9685 & 24.15 & 0.9512 & 21.57 & 0.9155 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the five methods (Lena with Gaussian noise). WDF: wavelet decomposition filter; BM3D: block-matching and 3D filtering; DTCWT: dual-tree complex wavelet transform; IFOA-DTCWT-BF: enhanced dual-tree complex wavelet optimized by fruit fly algorithm and bilateral filter.  
Figure 11: Optimization result using FOA and IFOAs to remove Gaussian noise from noisy image (Lena).  
The image denoising results showed that IFOA-DTCWT-BF had powerful performance dealing with Gaussian noise. In Table 3, we could see that although DTCWT acquired good data of PSNR, the \(\mathbf{r}\) was not always better than the proposed method. Moreover, the proposed method got clearer edge information. Median filter, Wiener filter and WDF had general performance. BM3D was incapable of dealing with heavy noise. Bilateral filter was not good at denoising Gaussian noise and acquired worst results, while, in the proposed method, it played an important role, as shown in Figure 12. The edge information of denoised Lena images processed by DTCWT and the proposed method is shown in Figure 13. The denoised images are shown in Figures 14-16.  
Figure 14: Denosing results of Lena with Gaussian noise using IFOA-DTCWT-BF. (**A**) Lena of noise \(\sigma=0.01\); (**B**) Lena of noise \(\sigma=0.05\); (**C**) Lena of noise \(\sigma=0.1\); (**D**) Lena of noise \(\sigma=0.2\); (**E**) Denoised image of \(\sigma=0.01\); (**F**) Denoised image of \(\sigma=0.05\); (**G**) Denoised image of \(\sigma=0.1\); (**H**) Denoised image of \(\sigma=0.2\).  
Figure 13: The edge information comparison of DTCWT and proposed method: left image is denoised by DTCWT, and right is proposed method. (**A**) Part of lena of noise \(\sigma=0.01\); (**B**) Part of lena of noise \(\sigma=0.05\); (**C**) Part of lena of noise \(\sigma=0.1\); (**D**) Part of lena of noise \(\sigma=0.2\).