Among various deep learning models, convolutional neural networks (CNNs) have been established as the most entrenched algorithm due to their successful results at the ImageNet Large Scale Visual Recognition Competition in 20121. CNNs can directly learn feature vectors from the training datasets by continuously updating weight by decreasing the loss index2. One of the advantages of CNNs over conventional machine learning is the provision of a higher-level concept of expressing semantic insights about data domains by architectural design choices in the computational graph. However, to achieve this advantage, sufficient data and computation time are needed3. Fortunately, this limitation can be overcome by the application of Graphics Processor Units to an Artificial intelligence platform, which accelerates the development of deep learning models as well as CNNs4. Moreover, they have been developed and utilized in various fields, such as vision-based detection5, probability inference6,7, and medical image segmentation8,9.
CNN-based data reconstruction has been especially successful when utilized for charged particle tracking with good precision in accelerator and calorimeter experiments10–12. Additionally, CNN has effectively overcome the spatial resolution limitations of positron emission tomography (PET), which was essentially limited by the size of the detector array elements, such as the crystal scintillator and readout pixels used in medical imaging13. These high-performance results can be obtained through Monte Carlo (MC) simulations which can generate sufficient training data and represents the geometry of the detector well. Consequently, CNN is expected to be suitable for analyzing large amounts of data for background noise cut-off in the Kyungpook National University Advanced Positronium Annihilation Experiment (KAPAE) detector.
KAPAE, which is a 4π detector, comprises 200 Bi4Ge3O12 (BGO) crystal scintillators and 393 channels of silicon photomultipliers (SiPM). In the KAPAE detector, a 22Na radioactive source is used to generate positrons from β + decay. The instrument configuration is optimized to trigger on positrons by varying the polyethylene naphthalate (PEN) film plastic scintillator thickness14. KAPAE aims to study CPT-violation in positronium (Ps) annihilation physics14,15. Based on the relative spin orientations, the ground state of Ps has two possible configurations: the triplet state (3S1), ortho positronium (o-Ps), and the singlet state (1S0), para positronium (p-Ps). Due to C-parity conservation, p-Ps and o-Ps decay to even and odd numbers of photons, respectively. Since these processes possess different C-parity values, the precise distinction of p-Ps and o-Ps is important to test discrete symmetries of C, CP, and CPT in the lepton sector16.
In this study, data reconstruction based on a CNN focusing on the back-to-back 2-γ decay system is conducted. The 2-γ energies are deposited in the surrounding BGO scintillators, and this process is simulated by the GEANT4 simulation toolkit17. The simulation data are used to produce datasets for reconstructions based on the CNN and weighted k-means algorithm18. The k-means clustering algorithm is a conventional method to determine the clustering centroid for uncategorical datasets typically, and it had been utilized in the abovementioned fields of CNN applications. Through this 2-γ decay system data reconstruction, we can distinguish the p-Ps signal from the o-Ps signal for the background noise cut-off and detect o-Ps events more correctly with high efficiency. Also note that the size of the KAPAE detector is compact (150 × 150 × 150 mm3) and it can simultaneously detect γ-ray decays in all directions. This feature makes it possible to utilize the KAPAE detector with an 18F radioactive source in PET application for tumor localization of small animals19.