# Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images
## 3 Results and Discussion  
Flower [38], Parrots [38], and Lena test images depicted in Figure 1 were employed to analyze the efficiency of the introduced algorithm. Moreover, the detail of each test image was employed to better perceive the efficiency of the filtering method. These images were contaminated with Gaussian and/or impulsive noise. The white additive Gaussian classical model [1] was used for Gaussian noise, and for impulsive noise the uncorrelated random-value case [1,2] was considered. The widely utilized metrics PSNR, MAE, and NCD were employed to analyze the filter efficiency [1,3]. These metrics measure the detail preservation ability, the color preserving capability, and the noise suppression ability, respectively. In [34], the authors observed optimal performance for the \(FROD\) filter by setting \(th_{1}\in\left[0.90,0.97\right],\)\(th_{2}\in\left[0.87,0.93\right],\) and \(th_{3}\in\left[0.97,0.98\right]\). Moreover, they proposed sub-optimal performance by setting \(th_{1},\)\(th_{2},\) and \(th_{3}\) proportionally to \(p\) as follows: \(th_{1}=0.90+\frac{p}{0.4}0.07,\)\(th_{2}=0.87+\frac{p}{0.4}0.06,\) and \(th_{3}=0.97+\frac{p}{0.4}0.01.\) The filters combined in the hybrid structure should be adjusted to the mixed noise and to each other. For this purpose, we studied the method efficiency in terms of PSNR, depending on the parameters \(th_{1},\)\(th_{2},\)\(th_{3},\) and \(F_{\sigma}\). Taking as a starting point the sub-optimal values obtained in [34], we analyzed the adjustment of the parameters \(th_{1},th_{2},\) and \(th_{3}\) in the hybrid structure in presence of mixed noise. By means of extensive experiments, we have observed that sub-optimal performance in terms of PSNR can be obtained for \(th_{1},th_{2},\) and \(th_{3}\) as a function of the amount of noise \(\sigma\) and \(p\). The results reveal that for \(p\in\left[0,0.4\right]\), and \(\sigma\in\left[0,40\right]\), we can achieve sub-optimal performance by setting \(th_{1},th_{2},\) and \(th_{3}\) as a function of \(p\) and \(\sigma\) as follows,  
\[th_{1} = 0.90+\frac{\beta_{p,\sigma}}{0.4}0.07,\] \[th_{2} = 0.87+\frac{\beta_{p,\sigma}}{0.4}0.06,\] \[th_{3} = 0.97+\frac{\beta_{p,\sigma}}{0.4}0.01, \tag{4}\]  
where \(\beta_{p,\sigma}=p-2\sigma/100\) depends on the impulsive noise \(p\), and \(\sigma\), the standard deviation for the Gaussian noise. There exist different techniques to estimate \(\sigma\) and \(p\); e.g., \(p\) can be estimated with the technique used in [39] and \(\sigma\) can be estimated by the approach introduced in [40]. Then, using estimations of \(\sigma\) and \(p\), the parameters \(th_{1},th_{2},\) and \(th_{3}\) can be automatically adjusted. The optimal  
Figure 1: Images used in experiments. (**a**) Lena, (**b**) Flower, (**c**) Parrots, and (**d**–**f**) details taken for the experiments. We analyzed the influence of the filtering window size \(n\) and the \(\alpha,\ \alpha^{\prime}\) parameters on the denoising efficiency with respect to the PSNR. The simulations revealed that the optimal settings of \(n,\ \alpha\), and \(\alpha^{\prime}\) parameters coincide with those obtained in previous research [34]. Therefore, in the experiments we considered \(3\times 3\) filtering windows (\(n=3\)) and \(\alpha=3,\ \alpha^{\prime}=1\). For evaluation of the performance of the method introduced here, various competitive, state-of-the-art noise removal techniques were evaluated:  
* Adaptive nearest neighbor filter (ANNF) [6];
* Alternating projections filter (APF) [24];
* Color block-matching 3D filter (C-BM3 DF) [41];
* FPGA [10];
* Fuzzy vector median filter (FVMF) [7];
* Fuzzy wavelet shrinkage denoising filter (FWSDF) [42];
* Graph regularization filter (GRF) [23];
* Iterative peer group switching vector filter (IPGSVF) [14];
* Partition-based trimmed vector median filter (PBTVMF) [21];
* Peer group filter (PGF) [12];
* Trilateral filter (TF) [18], applied in a component-wise fashion.