# Novel Image State Ensemble Decomposition Method for M87 Imaging
## 4 Results and Discussion  
Image quality assessments (IQAs) were used to evaluate the experimental results; both full-reference and no-reference quality metrics were used. The no-reference metrics are able to analyze both the test image and those of the ISED images. The full-reference metrics compare the original image to the modified image for quality assessment. Full-reference quality metrics are used with the original NASA reference image, such that the modified image is compared with the original image. The full-reference quality metrics that were used are the peak signal-to-noise ratio (PSNR), image mean squared error (IMSE), and structural similarity (SSIM) index [22]. The SSIM generates a maximum score of one based on the images comparative contrast, local structure, and luminescence [22]. The IMSE is the squared error between the original image and a compressed image, whereas the PSNR is the peak error in the image. The IMSE and PSNR are used to show the amount of compression for an image, but for the case of decomposition, it can be used to gauge the relative change between the original image and the ISED image. A table of values was output for the SSIM, IMSE, and PNSR, and the results are detailed in Appendix B. For the experiment, the no-reference quality metrics statistically compare the features of the original image to those of the modified images. Furthermore, the image results shown in this paper and on the Supplemental website clearly indicate the potential worth of this filter method. In Fact, the no-reference IQAs in some instances have improved the perceptual quality over the original NASA image and show more details. The no-reference quality metrics implemented were the perception-based image quality evaluator (PIQE) [23; 24], natural image quality evaluator (NIQE) [25], and blind/reference-less image spatial quality evaluator (BRISQUE) [26; 27]. PIQE analyzes the local variance to see if the image has a block-wise distortion to calculate the quality of an image; lower scores are better [23]. NIQE is trained on a database of pristine images that uses nature scene statistics, in concert with Gaussian distributions, so that it can measure arbitrary distortions in the test image [25]. BRISQUE is also trained from a database of known distortions and pristine images; this method is limited to evaluating only the types of distortions that have been trained for the database [26; 27]. A table of values was output for PIQE, NIQE, and BRISQUE, as shown in Appendix C. The IQAs are discussed in the results and discussion sections. Furthermore, histograms and color clouds of the images were used to show the pixel distribution over the RGB color space. The following pseudocode flow chart in Figure 1 illustrates the design of ISED images and filters, and Algorithm 1 is for ISED generation. ```
1: Load the input image. 2: Separate the image into its color channels R', G', and B' in RGB color space. 3: Use Equation (3) is used to build the filters for \(\psi\)\(R\), \(\psi\)\(G\), and \(\psi\)\(B\). \(\psi_{1}=[0,1](\text{B}\prime-\text{G}\prime)\), \(\psi_{2}=[0,1](\text{R}\prime-\text{G}\prime)\), \(\psi_{3}=[0,1](\text{R}\prime-\text{B}\prime)\), \(\psi_{4}=[0,1](\text{G}\prime-\text{B}\prime)\), \(\psi_{5}=[0,1](\text{G}\prime-\text{R}\prime)\), and \(\psi_{6}=[0,1](\text{B}\prime-\text{R}\prime)\). 4: Set the [0,1] state conditions from Appendix A, for \(\psi_{1}\), \(\psi_{2}\), \(\psi_{3}\), \(\psi_{4}\), \(\psi_{5}\), \(\psi_{6}\). This defines the state ensemble conditions. 5: The ISED color channel filter is \(\frac{1}{\sqrt{2}}(\psi_{1}+\psi_{2}+\psi_{3}+\psi_{4}+\psi_{5}+\psi_{6})\) for \(\psi\)\(R\), \(\psi\)\(G\), and \(\psi\)\(B\). The combination of \(\psi\)\(R\), \(\psi\)\(G\), and \(\psi\)\(B\) would produce the _ISED filter image_. An example of an ISED filter image is shown in Figure 2c.