# 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
In this case, the performance of both filters is very similar. Figure 5: Graphical evolution of the means of the PSNR\({}_{\text{HVS}}\) values obtained by all the filters in the test set versus noise density. (**a**) Complete figure. (**b**) Figure including only those filters that obtain the best results in general according to Table 2.

Figure 6: Restoration results, including the PSNR\({}_{\text{HVS}}\) values, of Hosseini, Wang and AWAM filters for the original image _7.10.2 tiff_ (an aerial photograph of a plane in a hanger) corrupted with 20%, 40% and 60% salt-and-pepper noise. A second experiment was performed on the image _I11.tiff_ (a test image of a bicycle and some other elements such as a clock, a plant and a tennis racket) which was corrupted with 80%, 90%, 95%, and 98% salt-and-pepper noise. The corrupted images were filtered with the Hosseini, the Wang and the AWAM filters. Results can be observed in Figure 7. In this case the results given by the Hosseini filter are very blurry and from the 90% to the 98% noise levels, the outputs of the filter are full of spots, leading to a bad visual performance. In the case of the Wang filter, for high density noise levels, the results provided by the AWAM and Wang filters are visually different, and it seems like the results obtained by the AWAM filter are slightly better, also shown by the differences of the PSNR\({}_{\text{HVS}}\) values. Indeed, the values of the PSNR\({}_{\text{HVS}}\) measure are lower because the restoration step of the Wang filter involves a lower number of pixels. On the contrary, for the AWAM filter, the visual performance seems more blurred, but the intensity levels are closer to the ones of the original image. Another experiment that was developed involves the study of some details of the output images given by these algorithms. The image _4.1.07.tiff_ was chosen and corrupted by 60% salt-and-pepper noise. As observed in Figure 8, the edges in the filtered images obtained by the Hosseini filter are not well defined meanwhile in the filtered images by Wang and AWAM they are preserved, although with the AWAM filter the edges have less drastic changes. Some other examples were performed obtaining similar results. Figure 7: Restoration results, including the PSNR\({}_{\text{HVS}}\) values, of Hosseini, Wang and AWAM filters for the original image _I11.tiff_ (bycicle test image) corrupted with 80%, 90%, 95% and 98% noise. Finally, a visual comparison study was performed with the results obtained by the Wang and AWAM filters for corrupted images with high levels of noise (namely, 80%, 90%, 95% and 98%). In Figure 9 we can observe some of them. In general, the results obtained with the AWAM filter are superior, both from the numerical and and the visual points of view. Since the Wang filter uses fewer pixels in order to restore each pixel of the noisy image, the obtained images look like a piecewise reconstructed image, as observed in the images 4.2.03.tiff and 5.1.09.tiff. On the contrary, the results obtained by the AWAM filter are more realistic, as they do not have these artifacts. From all these experiments it can be concluded that the AWAM filter outperforms the results obtained by other filters from the visual point of view. To end this section, a comparison of the computational processing time of the considered filters is carried out. In Figure 10a, the average computational processing times for the images of the test set are depicted for all the filters and noise densities considered in this section. Figure 10b shows a zoomed version of the previous graph with the vertical range restricted to the interval [0, 1], i.e., average computational processing times smaller or equal to 1 s. From this figure, several conclusions emerge. First, the filters SMF5, AMF9, AMF17, Fabijanska, OCS and OCSFlat have very low average processing times, but they constitute also the worst filters from both the statistical and visual points of view.