# Novel Image State Ensemble Decomposition Method for M87 Imaging
## 4 Results and Discussion
\[\text{R}_{\text{n}} =\text{R}\prime-\frac{1}{\sqrt{2}}(\psi_{1}+\psi_{2}+\psi_{3}+\psi _{4}+\psi_{5}+\psi_{6}) \tag{6}\] \[\text{G}_{\text{n}} =\text{G}\prime-\frac{1}{\sqrt{2}}(\psi_{1}+\psi_{2}+\psi_{3}+\psi _{4}+\psi_{5}+\psi_{6})\] forms the modified \(\text{R}_{\text{n}}\), \(\text{G}_{\text{n}}\), and \(\text{B}_{\text{n}}\) color \[\text{B}_{\text{n}} =\text{B}\prime-\frac{1}{\sqrt{2}}(\psi_{1}+\psi_{2}+\psi_{3}+\psi _{4}+\psi_{5}+\psi_{6})\]

channels. These channels are used to build the _ISED Image_. 7: Recombine the color channels to form a newly generated ISED image in (RGB)\({}_{\text{n}}\). 8: Output the ISED image
9: Optional Output the ISED filter image. Original image - ISED image = ISED filter image or equivalently combine recombine the color channels from \(\psi\)\(R\), \(\psi\)\(G\), and \(\psi\)\(B\)_to build \(\psi\)(RGB)_.

Figure 1: Algorithm flow chart for image state ensemble decomposition (ISED). According to Figure 2b, the ISED image produces well-defined regions in M87, and previously obscured structures become more pronounced. Some of the more distant galaxies have been reduced or removed; however, the larger structure is observed in greater detail with the additional advantage of reduced glare, making the detailed structure of the core of the galaxy more prominent. This unique process makes it possible to see somewhat into the interior structure of the galactic structures, similar to how an X-ray can see the bones in the human body. There appears to be a great deal of information that can be learned for the chromatic ordered images by using ISED: much more detail than the original image (Figure 2a), the ISED image (Figure 2b) has SSIM (0.79), IMSE (128.8), PSNR (26 dB), NIQE (5.32), PIQE (58.1), and BRISQUE (44.1) values. See Appendices B and C.

Figure 2: Image results for a full-sized tagged image file (TIF)-format image of M87 (**a**) original high resolution, credited to NASA/JPL-Caltech/IPAC, (**b**) ISED-generated image for the sixth ensemble state condition, and (**c**) image of the sixth ISED filter. The states in Table 1 correspond to Equation (5), where the simplified state ensemble of the ISED image generated (in Figure 2b) is produced from Equation (7). \[ \begin{array}{l}R_{n}=R\prime=\frac{1}{\sqrt{2}}(\psi_{4}+\psi_{5})\\ G_{n}=G\prime=\frac{1}{\sqrt{2}}(\psi_{4}+\psi_{5})\\ B_{n}=B\prime=\frac{1}{\sqrt{2}}(\psi_{4}+\psi_{5})\\ \end{array}  \tag{8}\]

Finally, the ISED image is made after the three color channels \(\mathrm{R}_{n}\), \(\mathrm{G}_{n}\), and \(\mathrm{B}_{n}\) are combined to form the image (RGB)\({}_{n}\). In Figure 3b, the branch on the left side of the color cloud has been removed, and Figure 3c presents the information remaining from the original image: the ISED filter. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ensemble State** & **Balanced** & & & & \(\Phi_{n}\) & & \\ \hline Image & & \(\psi_{1}\) & \(\psi_{2}\) & \(\psi_{3}\) & \(\psi_{4}\) & \(\psi_{5}\) & \(\psi_{6}\) \\ Original image & (RGB)\({}_{n}\) & 0 & 0 & 0 & 0 & 0 & 0 \\ The 6 th ISED & (RGB)\({}_{n}\) & 0 & 0 & 0 & 1 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Balanced state ensemble of the sixth ISED generated image (seen in Figure 2b). RGB: red, green, and blue. Figure 3: Pixel distributions over an RGB color cube as color clouds of the (**a**) original image (in Figure 2a), (**b**) ISED image of state 6 (in Figure 2b), and (**c**) corresponds to the ISED filter image (in Figure 2c). The third histogram is state 6 \(\psi\) and that of the ISED filter. A standard horizontal axis of a histogram ranges from 0 to 255; however, in this instance, nothing substantial occurs in the image for the intensity value above 100, and the scales for the histograms have been adjusted accordingly. The image is rather dark, so most of the information and interesting features are under 80 for the RGB value displayed in Figure 4. With this filter, some information is shifted to increase the dark pixel count, yet it maintains a majority of the SSIM (0.79).