# Novel Image State Ensemble Decomposition Method for M87 Imaging
## 2 Materials and Methods  
In the proposed ISED experiments, MATLAB R2018a and R2019a were used to implement our proposed algorithm on the post-processed SST image sets. The images were sourced from NASA/JPL-Caltech/IPAC. The implemented hardware configuration was comprised of an Intel i7-8750H processor, 32 GB of RAM, and an NVidia GeForce GTX 1060 graphics processing unit. The experimental input data were sampled images of M87. The first file, \"ssc2019-05c.tif\", is 11.2 MB in size with a pixel resolution of 3580 \(\times\) 3580. The second image of M87, file name \"ssc2019-05b.tif\", is 11.1 MB in size with a pixel resolution of 3580 \(\times\) 3580. The inset of this second image contains an enlarged region of M87's core, in which the region of M87's black hole and its jets are shown. This inset was cropped by using GIMP 2.10.14 and saved as a lossless tagged image file (TIF) format for processing. The remainder of the image in file \"ssc2019-05b.tif\" was discarded, because \"ssc2019-05c.tif\" is the same image without the inset. The size of the cropped image was 1.54 MB with a pixel resolution of 730 \(\times\) 733. The two images were taken by the SST using an Infrared Array Camera (IRAC). The nominal values of the red, green, and blue channels were mapped to the IRAC infrared radiation wavelengths of 8.0, 4.5, and 3.5 \(\upmu\)m, respectively [14]. Both images were generated with chromatic ordering taken from the infrared portion of spectrum. Therefore, the images were an approximation of what we see if the sampled photons were in the visible range of the spectrum. The physical filter selection can cause part of the continuum sources (e.g., a star) to not exhibit true color, such as the case of a narrow-band filter not properly sampling the stellar blackbody [16]. The ISED filter can operate in a similar manner by reducing a narrow band of the image matrix information. The two images were separated into their constitute components. The intensities of the individual trichromatic components of red, green, and blue shall be referred to as \(R^{\prime}\), \(G\), and \(B^{\prime}\) respectively. The \(R^{\prime}\), \(G\), and \(B\) intensity values range from 0 to 255. The \"zero\" value represents black, and as the value increases on the scale, the pixel becomes lighter [1]. To generalize the problem, assume that the three color channels of the image do not have the same corresponding color channel pixel values for a discrete range between respective \(R^{\prime}\), \(G\), and \(B^{\prime}\) image matrices. Taking this into account,difference relationships were formulated between the color channels to modify the post-processed images. This process is implemented in the spatial domain; the ISED image is matrix-wise transformed or generated at the pixel level. For the sake of analogy, let us say that the image is analogous to the Gibbs microcanonical ensemble wherein a statistical ensemble is used to know all the possible states of a system [17]. The photons are converted to electrons via the photoelectric effect [18], counted discretely, and then categorized into three discretized groups, or color channels, to represent a single RGB pixel. Multiple pixels combine to form an image matrix. This matrix contains the information of many possible states, as ISED will later demonstrate. ISED can transfer photonic information in varying amounts from the ISED image to the ISED filter without losing any information. The sum of the image and filter equals the input image. Use of this method is possible because quantum mechanical objects (e.g., photons) can behave as waves or particles [19; 20], and waves can be observed as single quanta [21]. The proposed method decomposes images without loss, provided that the information of both the image and filter is stored. **Theorem 1**. : \(\phi_{n}\equiv\) _The scalar probability of an ensemble of states to either succumb to wave collapse and be measured or to not be detected.