# Novel Image State Ensemble Decomposition Method for M87 Imaging
## 4 Results and Discussion
The cropped images of M87 can be seen in Figure 9.

The BRISQUE shown in Figure 14 is another no-reference quality metric. Its value for the full-sized original image was 43.56; the average value of its ISED-generated images was 46.46. Lower BRISQUE scores indicate superior perceptual image quality. The average score for the full-sized original image is close to the average score of the generated images. The BRISQUE of the cropped image was 43.38 and the average score for its generated images was 42.92, indicating improvement in the overall perceptual image quality. Scores for the PIQE no-reference quality metric in Figure 15, were 57.37 for the full-sized original image and 63.36 for the averaged ISED-generated images. Table 4 presents the PIQE assessment scale ranges from excellent to bad image quality [23]. A lower PIQE score indicates higher image quality. The original image, depicted in Figure 4a, is in the poor quality range, and the average score for the generated images is similar. However, some individual ISED-generated images have PIQE values higher than that of the original. The PIQE value of the cropped original image was 100, which indicates bad quality. The average score of its ISED-generated images was 46.23, which is fair quality. Some of the ISED-generated images fall within the excellent and good ranges. The 24 th state ISED-generated image had the best PIQE value (16.41), which was a marked improvement. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Quality Scale** & **Excellent** & **Good** & **Fair** & **Poor** & **Bad** \\ \hline
**Score range** & [0,20] & [21,35] & [36,50] & [51,80] & [81,100] \\ \hline \end{tabular}
\end{table} 
Table 4: PIQE assessment range [23]. Figure 14: BRISQUE values of 63 ISED-generated images. The cropped images of M87 can be seen in Figure 9.

## 5 Conclusions

The results suggest that ISED is a novel and effective astrophysical image processing method. New revealing ISED-generated images expose previously unknown structures that were imbedded in the information and were presented. M87s core, knots, and jets are much clearer that the original image in many cases. Therefore, we have provided clear evidence of the merit of the proposed method. A mathematical framework for the application of ISED was provided, and two sets of 63 balanced state ISED image and filters were analyzed and compared to those of the original image. Only the balanced ISED state conditions were covered in this paper. Additionally, the majority of the generated images produced improved IQAs over that of NASA's post-processed image. Particularly, the no-reference quality metrics used indicated that in most cases, the image perceptional quality improved dramatically. The SSIM results did not necessarily reflect the perceived quality of the images, because of the decomposition nature of ISED images and filter, the change in SSIM for the ensemble states was an expected result. Further development of the method will be reported in a follow-up paper. **Supplementary Materials:** The following are available online at [[https://sites.google.com/view/isedisee/home-m87](https://sites.google.com/view/isedisee/home-m87)]([https://sites.google.com/view/isedisee/home-m87](https://sites.google.com/view/isedisee/home-m87)), Figure 2: Image results for a full-sized TIF-format image of M87, Figure 5: Cropped images of M87, Figure 8: Magnification of M87's galactic core structure, Figure 9: Collage of M87's galactic core for 63 ISED generated images. **Author Contributions:** Conceptualization, T.R.T. ; Methodology, T.R.T. ; Software, T.R.T. ; Validation, T.R.T. and C.-T.C. ; Formal analysis, T.R.T. ; Investigation, T.R.T. ; Resources, T.R.T. ; Data curation, T.R.T. ; Writing--original draft preparation, T.R.T. ; Writing--review and editing, T.R.T. and C.-T.C. ; Visualization, T.R.T. ; Supervision, C.-T.C. and J.-S.C.; Project administration, J.-S.C. All authors have read and agreed to the published version of the manuscript.