# Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images
## 3 Results and Discussion
All these methods were used on a filtering window (with size \(3\times 3\)) in an iterative manner, except the PBTVMF that was used recursively. The parameter values recommended by the corresponding authors were used for each filter, adjusting them experimentally if needed. For the new FRF-FPGA method, we employed the settings recommended in Equation (4). First, an experimental comparison was performed employing images contaminated with combinations of impulsive and Gaussian noise. The results presented in Tables 1-3 illustrate that the introduced method obtains the best efficiency in most experiments for the quality metrics PSNR, MAE, and NCD. The values of NCD are expressed \((\times 10^{2})\) as usual. These results indicate that the new filter can better reduce the noise, while better preserving the details of the image. In particular, it can be observed that FRF-FPGA exhibits a better performance than FPGA, mainly because the use of the FRF filter allows more accurate detection and reduction of impulsive noise. This is due to the fact that the peer groups in the FPGA do not include the adequate number of members to detect and remove small impulses. In terms of visual appearance, by inspecting the filtered images provided in Figures 6 and 7, we can conclude that the new method properly retains the image details and effectively reduces the mixed noise. Figure 5: Surface plots of the dependency of the PSNR measure on \(F_{\sigma}\) and \(\beta_{p,\sigma}\). Images corrupted by Gaussian \(\sigma=30\) and impulse \(p=0.3\). (**a**) Flower. (**b**) Parrots. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Noise**} & \multicolumn{2}{c}{**Gauss \(\sigma=5\)**} & \multicolumn{2}{c}{**Gauss \(\sigma=10\)**} & \multicolumn{2}{c}{**Gauss \(\sigma=20\)**} & \multicolumn{2}{c}{**Gauss \(\sigma=30\)**} \\  & \multicolumn{2}{c}{**Impulsive \(p=0.05\)**} & \multicolumn{2}{c}{**Impulsive \(p=0.1\)**} & \multicolumn{2}{c}{**Impulsive \(p=0.2\)**} & \multicolumn{2}{c}{**Impulsive \(p=0.3\)**} \\ \hline Filter & MAE & PSNR & NCD & MAE & PSNR & NCD & MAE & PSNR & NCD & MAE & PSNR & NCD \\ None & 7.90 & 20.77 & 8.26 & 14.29 & 18.23 & 15.24 & 27.68 & 14.75 & 28.26 & 37.45 & 13.16 & 38.06 \\ FRF-FPGA & **3.53** & **33.15** & 3.57 & **4.86** & **31.12** & **4.57** & **7.32** & **28.33** & 6.83 & **10.18** & **25.46** & 9.19 \\ ANNF & 6.82 & 26.97 & 4.41 & 7.44 & 26.62 & 5.23 & 9.39 & 25.36 & 7.46 & 12.30 & 23.59 & 10.06 \\ APF & 7.88 & 25.05 & 6.65 & 10.07 & 23.44 & 8.45 & 15.35 & 21.13 & 12.05 & 19.61 & 19.68 & 14.74 \\ C-BM3 DF & 6.38 & 24.06 & 5.61 & 9.34 & 25.69 & 7.62 & 16.72 & 21.69 & 13.98 & 21.52 & 19.80 & 17.83 \\ FPGA & 4.23 & 31.06 & **3.26** & 5.71 & 29.14 & 4.61 & 8.10 & 26.37 & 6.70 & 10.69 & 24.49 & 8.91 \\ FWMF & 6.54 & 27.02 & 4.35 & 7.28 & 26.62 & 5.14 & 9.38 & 25.02 & **6.81** & 11.89 & 23.74 & **9.15** \\ FWSDF & 7.63 & 21.09 & 7.51 & 12.17 & 19.44 & 12.46 & 18.11 & 18.69 & 17.51 & 22.42 & 18.16 & 20.31 \\ GRF & 5.47 & 29.34 & 3.94 & 7.89 & 26.65 & 5.86 & 11.71 & 24.04 & 9.65 & 16.62 & 21.38 & 13.93 \\ IPGSVF & 4.21 & 31.55 & 4.80 & 8.01 & 27.33 & 9.16 & 14.64 & 22.35 & 15.29 & 18.29 & 20.32 & 18.65 \\ PBTVMF & 3.88 & 32.82 & 3.91 & 6.24 & 29.14 & 6.48 & 9.53 & 25.45 & 8.35 & 13.03 & 22.90 & 11.74 \\ PGF & 5.21 & 29.80 & 4.05 & 7.27 & 27.60 & 6.09 & 10.15 & 24.94 & 8.43 & 12.92 & 23.01 & 10.75 \\ TF & 4.82 & 27.08 & 5.16 & 7.19 & 26.18 & 6.31 & 9.93 & 24.32 & 8.14 & 12.13 & 23.18 & 10.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative study with state-of-the-art techniques. Lena test image corrupted with various intensities of mixed noise. Bold values express the best restoration quality.