# Novel Deep Level Image State Ensemble Enhancement Method for M87 Imaging
## 3 Materials and Methods
The \(\tau_{\text{n,44}}\) images in Figure 13a-f possibly may not converge. The shifting of the peaks indicates that it may be converging to the original image, but this ensemble condition is not conclusive from the above histograms. For the \(\tau_{\text{n,44}}\) cases, the histograms in Figure 14a-f indicate that the image is evolving into what we call a convergent case. This is logical due to the increased SSIM, PSNR, and improved MSE scoring as Ln increases. The ISED deep Ln image has a rapid decomposition; this causes more information to be contained in filter S\({}^{-}\)m,n. The ISEE reconstruction \(\tau_{\mathbf{n,46}}\) is a movement towards convergence. If \(\tau_{\mathbf{n,46}}\) is given enough Ln to evolve, it will replicate the original image. In Figure 15a-f, note the rapid evolution in the histograms that begin to evolve to the shape of the original test image's histogram. This is an interesting feature of select deep Ln ensemble states for ISEE reconstructions. The ISEE images produced from \(\tau_{\mathbf{n,47}}\) are also convergent for deep Ln. The histogram in Figure 15f is associated with ISEE image \(\tau_{6,47}\). This image has the highest SSIM (.99), greatest PSNR (39.73), and the lowest MSE (6.91). The reconstruction has a narrow band of pixels that highlight the vortex,outburst, globular structures, and emphasizes regions in M87's shock waves.The Histograms are shown below in Figure 16.  
The CDF is presented in Figure 17a-f. The test images were separated into red, blue, and green color channels. Then the test images were compared for Ln 1-6 where R', G' and B' is the CDF for the original image. CDF is shown to validate how ISEE evolves for Ln and to test for convergence. \(\tau_{\text{m},30}\), \(\tau_{\text{m},44}\), \(\tau_{\text{m},45}\), \(\tau_{\text{m},46}\), and \(\tau_{\text{m},47}\) are represented by their corresponding lines in the legend. Figure 17f shows that \(\tau_{\text{m},45}\), \(\tau_{\text{m},46}\), and \(\tau_{\text{m},47}\) are convergent for L6 and that it appears from the trends in Figure 17a-f that \(\tau_{\text{m},30}\) will converge. It is also possible that \(\tau_{\text{m},44}\) will converge as well, but at a deeper level than L6. Table 10 is the average values for the image quality analysis conducted for 63 ISED-generated images from the previous study on the same M87 test image [1]. There were 62 ISEE images generated per Ln. Then, the averages were taken from the full-reference quality metrics and the no-reference quality metrics for each Ln. The results are above in Table 11. It is apparent that overall, the proposed method of deep Ln ISEE is an improvement for the full-reference quality metrics SSIM, PSNR, and MSE. The average NIQE is better than the average ISED L1 values for L1 and L2 ISEE reconstructions. L3 ISEE is on par with L1 ISED reconstructions. L4, L5, and L6 ISED NIQE are close to the average L1 ISED filters (the highest quality metrics of Ln overall). All average ISEE are better than that of the original M87 test image. The BRISQUE scores seem to be best for L1 ISEE, and from L2-L6, it appears to plateau around 51. The first level reconstruction on average scores is better than the original image. The PIQE scores are all better than the original image score of 100, which indicates poor quality. It stands to reason that the PIQE scores would be higher on average than the ISED filters due to the reconstruction process in ISEE. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**States**} & \multicolumn{5}{c}{**Image Quality Assessment Metrics ISED**} \\ \cline{2-7}  & **SSIM** & **PSNR** & **MSE** & **NIQE** & **BRISQUE** & **PIQE** \\ \hline Original & 1.00 & NA & NA & 8.22 & 43.38 & 100 \\ Average ISED L1 & 0.70 & 22.8 & 473.1 & 7.22 & 42.90 & 46.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Average values for IQAs. Figure 17: Cumulative distribution function (CDF) of the original image and \(\tau_{\rm m,n}\) for each color channel.