Compton sequence estimation based on the deep learning method Open Access

A Compton camera is an imaging system that can trace the source location based on sequential interactions of Compton scattering and photoelectric absorption. The original source position can be traced by the backprojection of multiple cones calculated using the position and scattering angles on the image plane. Figure 1 shows a schematic of a typical Compton camera system. Various Compton camera systems have been developed to locate radioisotopes in industrial fields, including monitoring nuclear facilities and verifying medical diagnosis and treatment.^1–7 

Compton imaging reconstruction requires that the sequence of the interactions be known to minimize artifacts and loss of source intensity in the reconstructed image. During data acquisition, however, the sequences of each Compton interaction are difficult to determine using the timing information attributed to the finite timing resolution of the system. The conventional comparison method, based on the energy information of each interaction, is generally used because of its simplicity. However, not all Compton sequences can be determined correctly using a simple comparison method because all predicted sequence cases are physically possible unless the energies of each interaction exceed the Compton edge of the original γ-ray energy.^8–11 

The deep learning method is used for various classification or regression studies.¹² It is also applicable to Compton sequence estimation, which can be regarded as a classification study that determines the forward or backward direction as shown in Fig. 2. In addition, position information can also be utilized for sequence estimation as initial information to the input nodes of artificial neural networks, and deep learning models are trained based on this information. The effect of the positional information during the training process can be evaluated.

In this study, we modeled using a Monte Carlo simulation code a cadmium zinc telluride (CZT) Compton camera system that can acquire energies and positions inside the detectors for each radiation interaction, and a deep learning method was applied to the sequence estimation. The performances of the deep learning models, depending on the source energies and fields of view, were investigated and compared to those of the conventional comparison method. The effect of the position information on the Compton sequence estimation was also analyzed by estimating the weights of the deep learning models connected to each node.

A CZT Compton camera system was simulated using Monte Carlo N-particle extended (MCNPX) code. The size of the detector was 2 × 2 × 2 cm³, and the CZT density was 5.8 g/cm³. The position and energy data of the Compton events were acquired using a particle tracking (PTRAC) card provided by the MCNP codes. Python codes were used to extract the position and energy information from the raw PTRAC data, and only photoelectric events followed by the Compton events were selected. The orders of position and energy information for each Compton and photoelectric absorption after the scattering sequence were mixed randomly to prevent the deep learning models from bias generated by always having the first event listed first and labeled with numbers that represent the sequential condition. Each data point was labeled 1 if the sequence was correct and labeled 0 if the sequence was reversed.

The data for training were obtained under the conditions of various limited surfaces emitting photons and energies. The artificially limited surfaces varied from 60° to 360° along the z axis and energies varied from 100 to 1300 keV at 100 keV intervals to estimate the changes in performance depending on the energy and source position distributions. The steradian surfaces for starting positions of the photons are equal to the field of views (FOVs) of the reconstructed Compton images, and the deep learning models were trained to decide the sequence only in those limited surfaces. Figure 3 shows the FOVs used in this study. The iteration number for each simulation was 10⁹ for each FOV and source energy. The number of data points in each dataset varied depending on the simulation conditions, but it was sufficiently large to minimize fluctuations in the performance of each model. Table I lists the number of data points depending on the FOVs and source energies. Each dataset was divided into training and test datasets for performance estimation, and the ratio of the numbers of the two datasets was 8:2.

Fully connected neural networks (FCNN) were constructed using the Tensorflow 2.0 library and trained to estimate the sequence. The input layer of the model consisted of eight nodes representing the position and energy information of Compton and photoelectric absorption events. The hidden layers consisted of five layers, with 100 nodes per layer. The signals were activated using a rectified linear unit (ReLU) function. The output layer is a single node that shows a prediction result of 0 or 1. This layer was activated by a sigmoid function, which is suitable for the classification of positives and negatives. The model was optimized using the adaptive momentum (Adam) function, and the learning rate of the model was 0.001. One hundred epochs were set for training, but early stopping was applied to the training process to prevent overfitting when the value of the loss function no longer decreased.

The performance of the models was estimated by the accuracy, which can be obtained by dividing the number of correct predictions by the total number of data points used for the test. The accuracies depending on the energies and FOVs were analyzed to verify whether the deep learning models performed better than the conventional method. The conventional comparison method and the Compton edge test, which only use energy information to estimate the sequence, were also evaluated, and the results acquired by both the conventional comparison method with the Compton edge test and deep learning method were compared to each other. The Compton edge test, which considered the interactions that deposited more energy than the Compton edge of the incident source energy as photoelectric effect events, was applied first. The conventional comparison method was applied after the Compton-edge test by comparing the energies of the two interactions acquired. The application of this method is dependent on the source energy. When the source energies were lower than 300 keV, the events that deposited less energy were regarded as Compton scattering events, and the other events were regarded as photoelectric events. If the source energies were 300 keV or higher, the events that deposited more energy were regarded as Compton scattering interactions.

The effect of the position information used in the deep learning method was analyzed by verifying the weights of all nodes in the model. The weights represent the extent to which the signals from the previous nodes affect the results. Thus, we created images that showed the nodes and weights connected to each node to visualize the effects of each node. Figure 4 shows an example of these images. All arrows from the previous nodes to the next nodes were drawn with different thicknesses to represent the magnitude of the weights, and different colors represent the signs of the weights. The green arrows indicate that the weights have positive values, whereas the red arrows indicate that the weights have negative values. The models simplified to investigate weighting had eight nodes for the input and each hidden layer and one node for the output. The thickness of arrows in the figures, representing the amount of weights and the threshold of weights in the figures, was set to 0.5 and 1 for simplicity.

Datasets for the Compton sequence estimation models were acquired, and their performance was analyzed, as shown in Fig. 5. The accuracies of both the deep learning method and simple comparison method in the Compton edge test from 500 to 600 keV were lower than those of other energy ranges, regardless of the angles of the FOVs, because the magnitudes of energy deposition for Compton scattering and photoelectric absorption were similar to each other in the energy range. This type of event was, therefore, difficult to determine correctly because both directions of the sequences are physically possible.

The accuracies improved as the FOV became narrower when the deep learning models were used. The magnitude of the improvement was higher in the range of 300–400 keV than in other ranges. The magnitudes of the accuracy improvements increased as the FOVs became narrower, which showed that the position information affected the sequence estimation when the FOVs were limited. The energy histograms in Fig. 6 show the energy distributions, whose energies for the first and second interactions were smaller than the Compton edge. The more the source energy increased, the fewer the first and second interactions overlapped, which increased the accuracy of determining the sequence of Compton scattering and photoelectric absorption. In addition, the distribution of the z-axis position of the Compton scattering and photoelectric absorption interactions became biased as the FOVs became narrower, whereas the distribution of the x-axis and y-axis positions remained unchanged, as shown in Fig. 6. These types of biases can be useful in the calculation of deep learning models for sequence estimation. Weight analysis can explain the effect of position information on sequence estimation.

Figures 7 and 8 show the results of the weight analysis representing the effect of the nodes. The energy information of each interaction was the most important information for the deep learning models according to the weight analysis. As shown in Fig. 6, the main difference between the Compton and photoelectric absorption events is the energy distribution. Deep-learning models primarily utilize energy information.

The weight analyses representing the weights over 0.5 show the effect of the position information on the deep learning model. These results show that the weights from the position input nodes, particularly the z-position input nodes, increased as the FOV became narrower. This implies that deep learning models utilize position information, and the accuracy can be improved based on the position information. However, further studies would be required because the interaction sequence filtering method in this study was idealized not to reflect the effects of other types of sequences, such as multiple Compton scatterings, chance coincidences, or background radiations.

In this study, Compton sequence estimation was performed using a deep learning method, and the effectiveness of the deep learning model was investigated. Datasets for the training and testing of the sequence estimation models were acquired using MCNP code. The performances of the deep learning models were improved compared to those of simple comparison methods for the Compton-edge test in most energy ranges from 100 to 1300 keV. The magnitudes of the improvement were relatively high in the range except for 500 and 700 keV. The performances of the deep learning models were improved for every source energy used in this study as the FOV narrowed along the z axis. The use of position information was verified by a weight analysis of the trained models. The weights connected from the position input nodes, especially the z-position, increased as the FOV of the system decreased, which proved that the position information affected the prediction of the interaction sequence. The weights of the position information nodes were high in energy ranges where accuracies were high.

This work was supported by the Nuclear Safety Research Program through the National Research Foundation of Korea (NRF) granted by the Ministry of Science and ICT (MSIT) of the Republic of Korea (Grant Nos. 2020R1A2C1005924 and 2021M2E8A1046041) and the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korean government (MOTIE) (Grant No. 20214000000070, Promoting of Expert for Energy Industry Advancement in the Field of Radiation Technology).