# Novel Deep Level Image State Ensemble Enhancement Method for M87 Imaging
## 3 Materials and Methods
The L6 BRISQUE score for the ISEE reconstruction has not improved over that of the ISED image **S1\({}_{\mathbf{1},30}\)**. The PIQE L6 is fairly close, but for the assessment range, **S1\({}_{\mathbf{1},30}\)** falls into the fair category with a score of 48.14, while \(\tau_{6,30}\) is 54.9 in the poor category. The original photo PIQE was 100 and is in the bad category for the PIQE assessment range. For the higher SSIM ISED images, the ISEE images of L1 have better scores for the no-reference quality metrics and lower scores for the full-reference quality metrics. For deep Ln for ISED images **S\({}_{\mathbf{m},30}\)**, there is a decrease in SSIM, PSNR, and MSE. The L1 ISEE image \(\tau_{\mathbf{1},\mathbf{44}}\) in Figure 4b has a well-defined outer IR dust ring, and the IR core is pronounced. The shockwaves and surrounding dust structures have good contrast against the black backdrop, where most of the blue channel information has been eliminated except the blue-biased glare portion of the image. Therefore, the image looks a bit blurred. As Ln increases, this blurring effect is reduced as the \(S^{-}_{\mathbf{m},\mathbf{44}}\) information shifts. From the ISED image in Figure 4k, one can discern that there are two prominent features in the IR core of the **S\({}_{\mathbf{6},\mathbf{44}}\)** image. The northwest image is the outburst that originates from the environs of the black hole in M87 and HST-1. The other feature relates to the vortex structure that coincides with the location of the black hole. In Figure 4l, L6 ISEE image \begin{table}
\begin{tabular}{c c} \hline \hline
**Quality Assessment** & **Definition** \\ \hline Structural Similarity Index (SSIM) & \(SSIM(x,y)=\frac{(2\mu_{x}\mu_{y}+C_{1})(2\sigma_{xy}+C_{2})}{(\mu_{x}^{2}+\mu_{y }^{2}+C_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+C_{2})}\) \\  & for the images x,y: \(\mu_{x}\), \(\mu_{y}\), \(\alpha_{x}\),\(\sigma_{y}\), and \(\alpha_{xy}\) are the local means, standard deviations, and cross-covariance. \(C_{1}=(K_{1}L)^{2}\), where \(k<1\) is a small constant and L is the dynamic range for the pixel values. Likewise, \(C_{2}=(K_{2}L)^{2}\), where \(k<1\) is a small constant and L is the dynamic range for the pixel values, when \(\alpha=\beta=\gamma=1\). \\ \hline Peak Signal to Noise Ratio (PSNR) & \(PSNR=10 log_{10}~{}\left(\frac{M\alpha_{y}^{2}}{MSE}\right)\) \\  & where \(Max_{f}^{2}\) is the maximum frequency squared \\ \hline Mean Squared Error (MSE) & \(MSE=\frac{1}{MN}\sum\limits_{X=0}^{M-1}\sum\limits_{y=0}^{N-1}\left[I_{1}(i,j)- I_{2}(i,j)\right]^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Image quality assessment techniques [20; 21]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Quality Scale** & **Excellent** & **Good** & **Fair** & **Poor** & **Bad** \\ \hline
**Score range** & [0; 20] & [21; 35] & [36; 50] & [51; 80] & [81; 100] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Perception-based Image Quality Evaluator (PIQE) assessment range [27]. \(\tau_{6,44}\), there is an interesting horizontal band structure that is perpendicular to the C-like shockwave on the western side of the image. This is either an artifact of the image or some mechanism that causes the appearance of planer shockwaves. This C-like structure is produced by a superluminal counter-jet that is traveling toward us and is not directly observable due to relativistic beaming [28]. The ISEE images in Figure 4 are constructed from an ISED filter (S\({}^{-}_{\text{m,44}}\)) with sparse information in L1. Then, as the decomposition progresses for deeper Ln, the information in the filter increases. Conversely, there is a lowering in SSIM for the ISED filter. This attributes to the trend of higher SSIM and PSNR for the ISEE reconstructions for \(\tau_{\text{m,44}}\), displayed in Table 6. Likewise, the MSE decreases for the most part, where L2 values for this filter seems to oscillate towards convergence to the test images as Ln increases.