# An Advanced AFWMF Model for Identifying High Random-Valued Impulse Noise for Image Processing
## 2 Related Work
### Robust Outlyingness Ratio  
In order to be more robust and effective, we used a type of coarse-to-fine strategy based on the iterative framework for detecting random-valued impulse noise [12; 16; 24; 25; 26]. We used ROR to estimate whether the current pixel was a noise or not [16]. We briefly reviewed this algorithm as follows:  
* Coarse stage: 1. Let us consider parameters \(J_{C}=1\) and \(T_{c1}\), \(T_{c2}\), \(T_{c3}\) as coarse thresholds. We initialized all of them with zeros in the tag matrix. 2. For every pixel in the image, we found its ROR; if it ranged in the fourth level, as shown in Table 1, then that pixel was noise-free. We set the tag to 1; else, we found the relative divergence d among the filtering window's median and active pixels. Then, based on the ROR value of d, we compared it to \(T_{ck}\). We checked whether it was noisy or noise-free. We checked if d was bigger than \(T_{ck}\). According to the r, we updated the tag matrix. 3. If \(J_{c}\leq m_{c},\;J_{c}=J_{c}+1\), then we repeated Step 2; else, this stage was completed.
* Fine stage: 1. Let us consider parameters \(J_{f}=1\) and \(T_{f1},\;T_{f2},\;T_{f3},\;T_{f4}\) as fine thresholds. We initialized all of them with zeros in the tag matrix. 2. For every pixel in the image, we found its ROR; if it ranged in fourth level, as shown in Table 1, then that pixel was noise-free. We set the tag to 1, or else found the relative divergence d among the filtering window's median and active pixel. Then, based on the ROR value of d, we compared it to \(T_{fk}\). We checked whether it was noisy or noise-free. We checked if d was bigger than \(T_{fk}\). According to the r, we updated the tag matrix. Similarly, we calculated the values for all the pixels. 3. If \(J_{f}\leq m_{f},\;J_{f}=J_{f}+1\), then we repeated Step 2; else, this stage was completed. \(m_{c}\) and \(m_{f}\) are shown in Table 2.  
For the ROR algorithm, the operation was carried out in two stages--i.e., detection followed by filtering. For detection, first the ROR was measured to find the impulse of  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Level Name** & **Fourth Level** & **Third Level** & **Second Level** & **The Most Like Level** \\ \hline ROR values & \(0\leq ROR\leq 1\) & \(1<ROR\leq 2\) & \(2<ROR\leq 3\) & \(3<ROR\) \\ thresholds of & -1 & \(T_{c3}=50\) & \(T_{c2}=40\) & \(T_{c1}=30\) \\ thresholds of fine & \(T_{f4}=25\) & \(T_{f3}=20\) & \(T_{f2}=10\) & \(T_{f1}=7\) \\ stage & & & & \\ \hline \hline \end{tabular}  
* No given value for this field.  
\end{table}
Table 1: Level of ROR and its corresponding threshold.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Noise Ratio (\%)** & **The Number of Coarse Iterations (\(m_{c}\))** & **The Number of Fine Iterations (\(m_{f}\))** \\ \hline \([0\%\), \(30\%\) & \([3,5]\) & \([1,2]\) \\ \([0\%\), \(60\%\) & \([5,7]\) & \([3,5]\) \\ \([60\%\), \(70\%]\) & \([8,10]\) & \([6,8]\) \\ \hline \hline \end{tabular}  
* No given value for this field.  
\end{table}
Table 2: Iterations to be performed on coarse and fine stages.  
each pixel; then, all the pixels were divided into four levels according to their ROR values. Second, different decision rules were used to detect the impulse noise based on the absolute deviation from the median in each cluster. In order to make the detection results more accurate and robust, the from-coarse-to-fine strategy and the iterative framework were used for filtering. The structural flowchart of ROR is shown in Figure 1.