# Convolved Feature Vector Based Adaptive Fuzzy Filter for Image De-Noising
## 4 Proposed Methodology: Convolved Feature Vector Based Fuzzy Filter
### Performance of the Proposed De-Noising Filter  
In this section, another quantitative analysis of de-noised images is performed to evaluate the performance of our proposed filter with other de-noising filters. Three performance measures, peak signal to noise ratio (PSNR), structure similarity index measure (SSIM) and edge preservation index (EPI) [33] are used on standard test images as shown in Figure 6 for basic quantitative comparisons. Figure 7 shows PSNR values for Lena, Bridge and Boat image against different noise densities of RVIN ranging from 30% to 60%. It is clear from the bar chart that that proposed de-noising filter gives excellent results in terms of PSNR against all the competing filters and outperforms them against different noise levels of RVIN with a good margin. Table 2 shows SSIM values for Lena, Bridge and Boat images against different noise densities of RVIN ranging from 30% to 60%. It can be noted from the table that the proposed filter gives best results in terms of SSIM except two ratios of 60% where two stage algorithm (TSA) [35] and quadrant based spatially adaptive fuzzy (QSAF) filter [38] gives best results but overall the proposed filter leaves behind all the competing filters. Table 3 shows running time comparison (in seconds) for Lena image against different noise densities of RVIN ranging from 30% to 60%. In this quantitative comparison, the proposed filter once again gives best results in terms of running time cost as the proposed filter is simple in implementation and require no further trainings and \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Ratio** & \multicolumn{3}{c}{**30\%**} & \multicolumn{3}{c}{**40\%**} & \multicolumn{3}{c}{**50\%**} & \multicolumn{3}{c}{**60\%**} \\
**Methods** & **MD** & **FD** & **Total** & **MD** & **FD** & **Total** & **MD** & **FD** & **Total** & **MD** & **FD** & **Total** \\ \hline DWM [16] & 9081 & 6550 & 15631 & 9499 & 7771 & 17,270 & 9511 & 11,380 & 20,891 & 12,701 & 12,298 & 24,999 \\ NWM [29] & 9578 & 6012 & 15,590 & 10,150 & 6220 & 16,370 & 11,126 & 8303 & 20,429 & 15,450 & 7551 & 23,001 \\ ACWM [8] & 14,340 & 2023 & 16,363 & 16,048 & **2164** & 18,212 & 23,690 & **3641** & 27,331 & 32,733 & 7702 & 40,435 \\ SDOOD [39] & 10,508 & 9672 & 20,180 & 12,273 & 10,325 & 22,598 & 13,745 & 15,599 & 27,344 & 14,952 & 12,833 & 27,785 \\ SRM [40] & 15,894 & **1998** & 17,892 & 21,076 & 2571 & 23,647 & 24,922 & 4204 & 29,126 & 32,719 & **6550** & 39,269 \\ AEPWM [41] & 9940 & 8028 & 17,968 & 10,910 & 7975 & 18,885 & 11,675 & 9617 & 21,292 & 13,571 & 9769 & 23,340 \\ AFIMM [42] & 7112 & 6334 & 13,404 & 8209 & 7069 & 15,278 & 8508 & 8375 & 15,483 & **8978** & 8894 & 17,872 \\ QSAF [38] & **5122** & 5899 & 11,021 & 5509 & 6311 & 11,820 & **6919** & 8025 & 14,944 & 9055 & 9240 & 18,295 \\ TSA [35] & 9890 & 5002 & 14,892 & 11,039 & 4215 & 15,254 & 13563 & 5284 & 18,847 & 15,070 & 7522 & 22,592 \\ Proposed & 5233 & 4865 & **10,098** & **5324** & 6208 & **11,532** & 7513 & 6828 & **14,341** & 9991 & 7428 & **17,419** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detection results comparison of different methods for Lena image when corrupted with 30% to 60% RVIN. Figure 5: Shows PSNR results up-to 10 iterations for Lena, Peppers, Baboon and Boat images at 50% RVIN. threshold computations. QSAF uses extra iterations and fuzzy control which increases its computational cost. We run our algorithm on a number of iterations but the PSNR value after 4 th iteration becomes constant which can be seen from Figure 5. We set this parameter manually for all the experiments conducted.