# Novel Image State Ensemble Decomposition Method for M87 Imaging
## 4 Results and Discussion
The SSIM value of the 23 rd state in Figure 5c was 0.46, but it revealed more detail than the other two images in Figure 5b,d. The removal of the blue-biased glare from the image contributed to structural, luminal, and contrastive enhancement. In Figure 7b, the ISED filter contains more informative features than it does in Figure 7a,c. In fact, the SSIM value of the 23 rd state ISED filter was 0.61, which was higher than that of the 23 rd ISED-generated image. A low SSIM score does not mean that ISED generation was not performed favorably. In the 23 rd state ISED, the information sent to the filter contained substantial unwanted blue-biased glare. The SSIM scores for the 22 nd and 24 th state ISED filters were 0.24 and 0.23, respectively. Figure 10: SSIM values of 63 ISED-generated images. The cropped images of M87 can be seen in Figure 9. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Compared Methods**} & \multicolumn{6}{c}{**Image Quality Assessment Metrics**} \\ \cline{2-7}  & **SSIM** & **PSNR** & **IMSE** & **NIQE** & **BRISQUE** & **PIQE** \\ \hline M87 Full Original & NA & NA & NA & 5.54 & 43.56 & 57.37 \\ Average & 0.69 & 26.0 & 298.2 & 5.66 & 46.46 & 63.36 \\ M87 cropped & NA & NA & NA & 8.22 & 43.38 & 100.0 \\ Average & 0.70 & 22.8 & 473.1 & 7.22 & 42.90 & 46.23 \\ \hline \end{tabular}
\end{table} 
Table 3: Average values for image quality assessments (IQAs). SSIM: structural similarity index, PSNR: peak signal-to-noise ratio, IMSE: image mean squared error, NIQE: natural image quality evaluator, BRISQUE: natural image quality evaluator, PIQE: perception-based image quality evaluator. According to Figure 11 the PSNR appears to be in line with the SSIM. A higher PSNR corresponds in this case to a higher SSIM. PSNR was measured to determine how the states compare in relation to the original image. PSNR is often used to analyze image compression, and the decomposition in ISED can be comparable to a compression-like loss. The fourth state ISED had the highest PSNR for the full-sized image at 25.89 dB; the cropped image had a PSNR of 26.97 dB. Parenthetically, this corresponds to the worst PIQE value of 100 in the fourth ISED state. As a result of the nature of the algorithm's switching scheme, the PSNR trends downward, which is a result of filtering more information from the generated images. The lowest PSNR was that in the 63 rd state ISED image. For this state, all the state ensembles are activated, and the maximum amount of information is filtered. The PSNR of the full-sized image was 1.65 dB, and that of the cropped image was 2.85 dB. In Figure 12 the IMSE is also in line with the ISED states. A lower IMSE corresponds to a higher SSIM. The fourth ISED state had the lowest IMSE. The score of the full-sized image was 2.28 and that for the cropped image was 4.75. The IMSE trends upward as more information is removed from the original image and transferred to the ISED filter. The highest IMSE is in the 63 rd state. This is again a result of all of the ISED ensemble states being activated. Figure 11: PSNR values of 63 ISED-generated images. The cropped images of M87 can be seen in Figure 9.

Different informative features of the original image of M87 have different technical requirements. Some informative features should be kept and enhanced, whereas one should attempt to minimize or eliminate glare and noise. In Figure 13 the NIQE value of the full-sized original image was 5.54, and the average value of the ISED-generated images was 5.66. By contrast, the NIQE score of the galactic core cropped from the original was 8.22, and the average score of its ISED-generated images was 7.22. The lower scores indicate improved image quality. Therefore, the global perceptual image quality was improved. NIQE uses a quality-aware natural scene statistic feature model and compares it to a multivariate Gaussian fit model [25]. Figure 12: IMSE values of 63 ISED-generated images. The cropped images of M87 can be seen in Figure 9.

Figure 13: NIQE values of 63 ISED-generated images.