# Impulsive Noise Removal with an Adaptive Weighted Arithmetic Mean Operator for Any Noise Density
## 3 Weighted Arithmetic Mean Based Fuzzy Filter Algorithm
### Noise Detection Phase Based on Fuzzy Open-Close Operators
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & & & & & & & & \\ \hline \multirow{2}{*}{**FilterDensity**} & \multirow{2}{*}{**5**} & \multirow{2}{*}{**10**} & \multirow{2}{*}{**15**} & \multirow{2}{*}{**20**} & \multirow{2}{*}{**25**} & \multirow{2}{*}{**30**} & \multirow{2}{*}{**35**} & \multirow{2}{*}{**40**} & \multirow{2}{*}{**45**} & \multirow{2}{*}{**50**} \\  & & & & & & & & & & \\ \hline \multirow{2}{*}{SMF5} & 26.9347 & 26.1864 & 25.173 & 24.0986 & 22.9593 & 21.9985 & 21.1476 & 20.1334 & 19.1332 & 17.7891 \\  & (3.4878) & (3.225) & (2.9323) & (2.7744) & (2.6622) & (2.4855) & (2.5378) & (2.4787) & (2.3318) & (1.9789) \\ \hline \multirow{2}{*}{AMF9} & 39.1894 & 37.7209 & 36.4263 & 34.8658 & 33.7104 & 32.3589 & 31.3176 & 30.2051 & 29.1403 & 28.0795 \\  & (6.9303) & (6.1117) & (5.7789) & (5.1215) & (4.817) & (4.2517) & (4.0607) & (3.7715) & (3.6024) & (3.3279) \\ \hline \multirow{2}{*}{AMF17} & 39.1485 & 37.6654 & 36.3827 & 34.8425 & 33.695 & 32.3458 & 31.3053 & 30.1976 & 29.1294 & 28.1076 \\  & (6.9364) & (6.0918) & (5.7734) & (5.1105) & (4.8189) & (4.2572) & (4.0652) & (3.7706) & (3.6024) & (3.3646) \\ \hline \multirow{2}{*}{DBA} & 24.649 & 23.1323 & 24.3758 & 23.8099 & 24.1931 & 24.0316 & 24.0347 & 24.2327 & 26.9072 & 26.6071 \\  & (6.7212) & (6.0807) & (6.4933) & (6.2379) & (6.1899) & (6.5102) & (4.3064) & (6.4104) & (3.973) & (3.2205) \\ \hline \multirow{2}{*}{OCS} & 26.4768 & 30.3077 & 31.5089 & 30.7622 & 29.5329 & 28.3702 & 27.329 & 26.4405 & 25.6827 & 24.8736 \\  & (2.9584) & (3.6476) & (4.2357) & (3.9525) & (3.719) & (3.4508) & (3.2533) & (3.0966) & (3.0112) & (2.9657) \\ \hline \multirow{2}{*}{OCSFlat} & 26.4194 & 27.8637 & 29.3509 & 30.1432 & 30.6669 & 30.5093 & 29.8363 & 29.2399 & 28.5 & 27.7513 \\  & (3.2332) & (3.2693) & (3.5016) & (3.5182) & (3.8569) & (3.8045) & (3.6878) & (3.5902) & (3.5297) & (3.4699) \\ \hline \multirow{2}{*}{c-FMMOCSFlat} & 42.8134 & 39.4501 & 36.4781 & 34.552 & 33.1435 & 31.8472 & 31.1221 & 30.0079 & 29.1688 & 28.298 \\  & (6.4137) & (5.2994) & (4.5702) & (4.0504) & (4.2453) & (3.9334) & (3.7794) & (3.5827) & (3.477) & (3.3272) \\ \hline \multirow{2}{*}{c-FMMOCSFlat} & 42.8533 & 39.4158 & 35.8379 & 33.6664 &



Figure 5 shows the plots of the evolution of the \(\mathrm{PSNR_{HVS}}\) means depending on the noise densities for each filter. For most of the noise densities, the AWAM filter is positioned at the top of the other filters displaying the best results. For the other performance measures, the conclusions are similar. In summary, the AWAM filter represents a significant advance in the salt-and-pepper noise removal with respect to the existing filters in the literature. From the above statistical analysis, we conclude that AWAM improves the results of the other algorithms from the numerical point of view. Anyway, we will analyse visually the results given by some of the algorithms comparing them visually to the ones obtained by the proposed AWAM filter. To develop this visual comparison, the Hosseini and the Wang algorithms were chosen due to their numerical performance. First, Figure 6 shows the results of these filtering algorithms for the image \(7.1.02.\)_iff_ (which is an aerial photograph of a plane in a hanger) that has been corrupted with 20%, 40%, 60% salt-and-pepper noise.