# Novel Deep Level Image State Ensemble Enhancement Method for M87 Imaging
## 3 Materials and Methods  
For this study, we used Table 1 and (4) to generate the S\({}_{\text{m},63}\) ISED images that are used in part to produce ISEE images from (9). Table 2 is the settings for generating the filters S\({}^{-}\)\({}_{\text{m},\text{n}}\), which are recovered by processing Equations (4) and then (7). States 30, 44, 45, 46, and 47 were chosen to provide a sample of the image set that was produced. In total, for L1\(\sim\)6, there were 372 ISEE generated images. This sample of ISEE images are evaluated and will be discussed in further detail in the following section. Algorithm 1 shows the process involved in generating ISED images, filters, and ISEE reconstruction. Table 1 displays the ensemble matrices state settings to generate S\({}_{\text{m},63}\) for ISEE generation. The generated images from Table 1 can be seen in Figure 1b-g. Please recall that in order to produce ISEE reconstructions, you must first perform ISED. The S\({}_{\text{m},\text{n}}\) first comes from ISED; then, it is applied to Equation (9). Although all possible balanced Ln ISED images and filters and ISEE images were generated, only select images are shown in detail in this study. The remaining images will be available for perusal online at [2]. Table 2 is \(\psi\)-ensemble matrices state settings for filter recovery to generate the ISEE images presented in this paper. So, both Tables 1 and 2 are used to produce the ISEE images in (9) for this study. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(\mathbf{S_{m,n}}\)} & \multicolumn{1}{c}{**Balanced**} & \multicolumn{5}{c}{\(\phi_{mn}\)} \\ \hline
**Level Ln** & & \(\psi_{1}\) & \(\psi_{2}\) & \(\psi_{3}\) & \(\psi_{4}\) & \(\psi_{5}\) & \(\psi_{6}\) \\ \hline S\({}_{1,63}\) & (RGB)\({}_{\text{m},\text{n}}\) & 1 & 1 & 1 & 1 & 1 & 1 \\ S\({}_{2,63}\) & (RGB)\({}_{\text{m},\text{n}}\) & 1 & 1 & 1 & 1 & 1 & 1 \\ S\({}_{3,63}\) & (RGB)\({}_{\text{m},\text{n}}\) & 1 & 1 & 1 & 1 & 1 & 1 \\ S\({}_{4,63}\) & (RGB)\({}_{\text{m},\text{n}}\) & 1 & 1 & 1 & 1 & 1 & 1 \\ S\({}_{5,63}\) & (RGB)\({}_{\text{m},\text{n}}\) & 1 & 1 & 1 & 1 & 1 & 1 \\ S\({}_{6,63}\) & (RGB)\({}_{\text{m},\text{n}}\) & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Balanced state settings for ISED-generated S\({}_{\text{m},63}\) images. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Ensemble Filter S\({}^{-}\)\({}_{\text{m,n}}\)** & **Balanced** & \multicolumn{6}{c}{\(\phi_{mm}\)} \\ \hline
**State** & & \(\psi_{1}\) & \(\psi_{2}\) & \(\psi_{3}\) & \(\psi_{4}\) & \(\psi_{5}\) & \(\psi_{6}\) \\ \hline
30 & (RGB)\({}_{\text{m,n}}\) & 0 & 1 & 1 & 1 & 1 & 0 \\
44 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 0 & 0 \\
45 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 0 & 1 \\
46 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 1 & 0 \\
47 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ISED settings for filter generation S\({}^{-}\)\({}_{\text{m,n}}\), ISEE construction \(\tau_{\text{m,n}}\), and ISED images S\({}_{\text{m,n}}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ensemble Filter S\({}^{-}\)\({}_{\text{m,n}}\)** & **Balanced** & \multicolumn{6}{c}{\(\phi_{mm}\)} \\ \hline
**State** & & \(\psi_{1}\) & \(\psi_{2}\) & \(\psi_{3}\) & \(\psi_{4}\) & \(\psi_{5}\) & \(\psi_{6}\) \\ \hline
30 & (RGB)\({}_{\text{m,n}}\) & 0 & 1 & 1 & 1 & 1 & 0 \\
44 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 1 & 0 \\
45 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 0 & 1 \\
46 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 1 & 0 \\
47 & (RGB)\({}_{\text{m,n}}\) & 1 & 0 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ISED settings for filter generation S\({}^{-}\)\({}_{\text{m,n}}\), ISEE construction \(\tau_{\text{m,n}}\), and ISED images S\({}_{\text{m,n}}\). Basic quantum mechanics played a key role in formulating Theorem 1 and the resulting ISED and ISEE equations. Deep Ln ISED and ISEE can filter out some of the unwanted effects and, as a byproduct, enhance others.