![create folder structure diagram in listmode create folder structure diagram in listmode](https://media.springernature.com/full/springer-static/image/art%3A10.1038%2Fs41598-021-86015-6/MediaObjects/41598_2021_86015_Fig1_HTML.png)
Finally, we show that the energy information can be used to accurately normalize the scatter sinogram to the data. We also describe an accurate and robust object-specific method for estimating these 1D E-PDFs based on a decomposition of the total energy spectra detected across the scanner into primary and scattered components. Next, we derive two new formulae which allow estimation of the 2D (coincidences) energy probability density functions (E-PDF) of primary and scatter coincidences from the 1D (photons) E-PDFs associated with each photon. To estimate the spatial distribution of scatter coincidences we use the single scatter simulation (SSS).
![create folder structure diagram in listmode create folder structure diagram in listmode](https://www.eclipse.org/sirius/doc/specifier/diagrams/images/elkAlgorithmSelection.png)
First, we rewrite the Poisson likelihood function of list-mode PET data including the energy distributions of primary and scatter coincidences and show that this expression yields an MLEM reconstruction algorithm containing both energy and spatial dependent corrections. We propose a novel scatter approach that incorporates the energy of individual photons in the scatter correction and reconstruction of list-mode PET data in addition to the spatial information presently used in clinical scanners. With the widespread use of PET crystals with greatly improved energy resolution (e.g., 11.5% with LYSO as compared to 20% with BGO) and of list-mode acquisitions, the use of the energy of individual events in scatter correction schemes becomes feasible.