# 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
It can be observed that

\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**FilterDensity**} & \multirow{2}{*}{**55**} & \multirow{2}{*}{**60**} & \multirow{2}{*}{**65**} & \multirow{2}{*}{**70**} & \multirow{2}{*}{**75**} & \multirow{2}{*}{**80**} & \multirow{2}{*}{**85**} & \multirow{2}{*}{**90**} & \multirow{2}{*}{**95**} & \multirow{2}{*}{**98**} \\  & & & & & & & & & & & \\ \hline \multirow{2}{*}{SMF5} & 16.1569 & 14.1935 & 12.0668 & 9.9239 & 7.9577 & 6.1402 & 4.5567 & 3.2217 & 2.1765 & 1.6803 \\  & (1.6077) & (1.198) & (0.877) & (0.6396) & (0.5416) & (0.4179) & (0.4047) & (0.3631) & (0.3863) & (0.4412) \\ \hline \multirow{2}{*}{AMF9} & 27.0453 & 25.8747 & 24.5091 & 22.4308 & 19.502 & 15.9104 & 12.0141 & 8.3751 & 4.8385 & 2.6712 \\  & (3.1569) & (3.0251) & (2.7761) & (2.1461) & (1.589) & (0.8369) & (0.6363) & (0.4419) & (0.3515) & (0.4341) \\ \hline \multirow{2}{*}{AMF17} & 27.045 & 26.0632 & 24.8973 & 23.7544 & 22.569 & 21.2255 & 19.298 & 15.194 & 9.4361 & 5.1718 \\  & (3.1703) & (3.142) & (2.9137) & (2.7435) & (2.5939) & (2.4493) & (2.077) & (1.1932) & (0.505) & (0.5598) \\ \hline \multirow{2}{*}{DBA} & 25.3809 & 24.1253 & 22.6324 & 21.5187 & 20.0383 & 18.6933 & 17.0736 & 15.2665 & 13.0719 & 10.9203 \\  & (2.9644) & (2.6811) & (2.5245) & (2.2547) & (2.1528) & (2.1624) & (2.107) & (2.0022) & (1.9046) & (1.9457) \\ \hline \multirow{2}{*}{OCS} & 24.2041 & 25.7589 & 22.8804 & 22.2886 & 21.7155 & 21.0545 & 20.4362 & 19.4644 & 16.4843 & 11.2404 \\  & (2.8768) & (2.8554) & (2.8421) & (2.7981) & (2.7549) & (2.7269) & (2.7145) & (2.5245) & (2.186) & (2.5592) \\ \hline \multirow{2}{*}{OCSFlat} & 26.8645 & 26.2566 & 25.3074 & 24.5294 & 23.7089 & 22.7825 & 21.0451 & 17.3356 & 11.7075 & 9.9308 \\  & (3.3489) & (3.3167) & (3.2162) & (3.1596) & (2.9871) & (2.9117) & (2.5221) & (1.8085) & (1.9025) & (2.3418) \\ \hline \multirow{2}{*}{c-FMMOCSFlat} & 27.3265 & 26.4624 & 25.4045 & 24.2952 & 23.1807 & 21.7395 & 19.9983 & 17.1692 & 10.0703 & 8.0481 \\  & (3.1853) & (3.0734) & (2.883) & (2.7772) & (2.5495) & (2.5019) & (2.3031) & (1.8636) & (0.8482) & (1.2007) \\ \hline \multirow{2}{*}{c-FMMOCSFlat} & 26.9152 & 26.3061 & 25.3437 & 24.5772 & 23.7466 & 22.8735 & 21.5205 & 19.3401 & 12.2416 & 9.8104 \\  & (3.3247) & (3.2959) & (3.1893) & (3.1193) & (2.9502) & (2.8895) & (2.6805) & (2.1972) & (1.6844) & (2.2395) \\ \hline \multirow{2}{*}{Toh} & 27.1508 & 26.3527 & 25.5438 & 24.7032 & 23.8548 & 22.883 & 21.7604 & 19.7102 & 14.3217 & 8.8001 \\  & (3.5172) & (3.4021) & (3.2867) & (3.1317) & (2.9828) & (2.8443) & (2.6886) & (2.1894) & (1.2432) & (0.9735) \\ \hline \multirow{2}{*}{[PERSON]} & 26.9871 & 26.2216 & 25.4466 & 24.6587 & 23.8507 & 23.0056 & 22.0251 & 20.75 & 18.8201 & 16.4288 \\  & (3.5592) & (3.4031) & (3.3092) & (3.1502) & (3.0261) & (2.9335) & (2.8302) & (2.6438) & (2.5114) & (2.2721) \\ \hline \multirow{2}{*}{[PERSON]} & 22.1063 & 20.0846 & 20.2878 & 20.2099 & 19.3982 & 18.814 & 17.4689 & 16.7872 & 15.3009 & 13.0979 \\  & (5.609) & (4.8323) & (5.0741) & (4.9746) & (4.9636) & (4.3512) & (4.2545) & (3.488) & (2.9712) & (2.2259) \\ \hline \multirow{2}{*}{Hosseini} & 30.0239 & 28.9768 & **28.041** & **26.9753** & **25.9183** & **24.7778** & **23.4** & **21.8856** & **19.773** & **17.515** \\  & (4.1804) & (3.841) & (3.6149) & (3.4019) & (3.1632) & (3.0602) & (2.8982) & (2.6415) & (2.4639) & (2.2823) \\ \hline \multirow{2}{*}{i-FMMOCSFlat} & 28.1693 & 27.3407 & 26.4693 & 25.5716 & 24.7957 & 23.8411 & 22.7121 & 21.2317 & 19.1874 & 16.7463 \\  & (3.4019) & (3.2942) & (3.1205) & (3.0302) & (2.9575) & (2.9289) & (2.8233) & (2.6221) & (2.5334) & (2.2941) \\ \hline \multirow{2}{*}{i-FMMOCSFlat} & 28.1264 & 27.2828 & 26.3977 & 25 the Hosseini algorithm has a bad performance when the noise is 60%, obtaining as a result an image with undesirable blurred areas. Besides, the values of the PSNR\({}_{\text{HVS}}\) are lower than the values obtained by the AWAM filter. With respect to the results of the Wang filter, they are very similar to the ones obtained by the AWAM filter.