Backbone Network

This study adapted the ResNet-18 architecture [30] for a one-dimensional implementation. The backbone network consists of repeated residual blocks of varying output sizes [31]. In particular, the proposed block structure incorporates skip connections, allowing the network to learn the residual mapping between the input and output. This effectively mitigates issues such as vanishing and exploding gradients in deep neural network training.

This study retains only the convolutional layers from the original ResNet-18 model and replaces the fully connected layers with a multiscale CNN (MSNN) module. The model input is a one-dimensional vector representing the energy spectrum (). The input energy spectrum is processed using a convolutional neural network to obtain the initial feature map (F_resnet) and size (1 × 64 × 512).(1)

MSNN Module

In the radionuclide spectra, some full-energy peaks covered large areas. Larger convolution kernels were required to capture larger spatial features. However, some radionuclide peaks are small (e.g., the full-energy peak of ²⁴¹Am occupies approximately 3/1024 of the spectrum), or mixed radionuclide spectra contain overlapping peaks with similar positions (e.g., 662 keV for ¹³⁷Cs and 605 keV for ¹³⁴Cs). In such cases, smaller convolution kernels are necessary to capture finer features.

The input spectrum is processed through the backbone network to extract a deep and dense feature map using a (1 × 3) convolution kernel, similar to the original ResNet-18 architecture. This study introduced an MSNN module for multiscale convolutional feature fusion designed to model the full-energy peak context of the spectrum, as shown in Fig. 1. By aggregating the multiscale context across different spectral regions, the model can simultaneously capture both local and global contextual information. This concept is widely used in computer vision. Contextual features refer to the spatial arrangement and relative positioning of pixels, which can enhance the performance in areas such as small object detection [32] and visual place recognition [33, 34].

Fig. 1Full-screen View

(Color online) Overall structural flow chart

The MSNN module uses four convolution kernels of different sizes: (1×1), (1×3), (1×5) and (1×7). These convolution kernels extract features from the input spectrum, generating feature maps of varying sizes, each with 128 channels. To align and aggregate feature maps at multiple scales, upsampling using nearest-neighbor interpolation is applied, resizing them to . The feature maps are then concatenated, resulting in a multiscale context-aggregated feature map (F_MSNN) with a size of .(2)The final multiscale feature map is flattened into a one-dimensional vector, followed by incorporating a fully connected layer. Finally, the linear output vector is resized to (3×1×S). If the center of the full-energy peak falls within a grid cell, then the cell is responsible for detecting the object. Thus, the proposed model divides the input energy spectrum into (1×S) grids.(3)As shown in Fig. 2, each grid cell predicts one bounding box and its associated confidence scores, specifically, the center’s coordinates (xc), width (w), and confidence score (c).

Fig. 2Full-screen View

(Color online) Feature map predicted by the model

The coordinate (xc) represents the center of the bounding box relative to the grid cell boundaries. The width (w) is predicted relative to the entire spectrum. The confidence score (c) reflects the model’s confidence in the presence of a peak within the box. If no peak is predicted in the cell, then the confidence score is zero. The final confidence prediction represents the Intersection over Union (IoU) between the predicted bounding box and the ground truth box.

The IoU measures the overlap between bounding boxes and is calculated as the ratio of the intersection area to the union area of the two regions. In this study, the boundaries are one-dimensional coordinates, which differ from those in image-based domains. Therefore, the "area" in this context is expressed as the difference in coordinates, as shown in Fig. 3. Specifically, A and B are predicted boxes with coordinate ranges and , respectively. The IoU is calculated as follows:(4)

Fig. 3Full-screen View

(Color online) IoU calculation schematic diagram

All the output variables are constrained within the range , which is achieved using the sigmoid function. Its mathematical representation is expressed as:(5)The final output of the network is a (3×1×S) tensor of the predictions. In this study, S=384, and the minimum resolution for the full-energy peak center interval is 3 channel bins.

Loss Function

During network training, three loss functions are jointly optimized for backpropagating the target boundary and confidence parameters, as shown in Eq. 6.(6)The loss function expressions for the three components are provided in Eqs. (7)–(9) as follows:(7)(8)(9) optimizes the predicted peak center coordinates (xi) and width (wi) to minimize the error between the predicted and labeled values and . In addition, to reduce the difference between large and small areas, we take the square root of the width(w).

minimizes the error between the predicted confidence (Ci) and the labeled confidence when an object is present () for the corresponding .

optimizes confidence when no object is present in bbox_i.

We optimized the sum of the squared errors in the model output. The corresponding weights are used to adjust the contributions of positioning errors and confidence in nontarget regions to the overall network error, thus preventing the gradient from being dominated by large noise baseline areas.

In this study, we increase the loss of the bounding box coordinate prediction and reduce the loss of confidence prediction when no object is present using two parameters, λ_coord and λ_noobj, with λ_coord = 1 and λ_noobj=0.5.

NaI(Tl) Detector

NaI(Tl) detectors are widely used in gamma spectroscopy because of their high light yield, low background, low cost, ability to operate at room temperature, and ease of manufacturing into large sizes. However, their relatively low energy resolution can cause peak overlap, making automatic spectral analysis challenging.

In this study, a homemade NaI(Tl) detector was modeled using Monte Carlo simulations, as shown in Fig. 4. The detector consisted of a 2-mm-thick stainless-steel shell containing Fe, Cr, Ni, and C; a 3-inch cylindrical NaI(Tl) scintillator; a 0.3-mm-thick MgO reflective layer; and a SiPM photoelectric converter.

Fig. 4Full-screen View

(Color online) Gamma detector structure and Monte Carlo simulation layout

Monte Carlo Simulation

The simulated spectra of the six common artificial radionuclides (listed in Table 1) at various distances were generated using Geant4-11.1.3 [35]. The simulation model included a point source with a gamma ray energy range of 40 keV to 3000 keV. Each simulation involved calculation of 100 million photons. We used FTFP_BERT as the reference physics list. G4EmStandardPhysics was added to the physis list to simulate the physical processes of the photoelectric reaction. The energy deposition spectrum of the detector was obtained by inputting the nuclide energy and branching ratio. The relative statistical uncertainty of the simulated results ranged from 0.0002 to 0.0016. Gaussian broadening was applied to simulate the electronic noise.(10)(11)where E₀ is the energy deposition from the simulation; E is the broadened energy; is a random variable following the standard normal distribution; and C₁, C₂ and C₃ are the experimental coefficients with values of-0.0067, 0.0612, and -0.0451, respectively.

Data Augmentation

Data augmentation was performed using random gross counts, SNR, and nuclide mixing ratios. These methods have been widely used in previous studies and have proven to be effective in simulating statistical fluctuations and peak overlap in measured energy spectra [8, 22, 24].

Random gross count and Random SNR: Random gross count (C_gross) is achieved by sampling the spectrum as a probability distribution across energy.(12)(13)Given a randomly selected low SNR, we calculated the background count (C_bq) and nuclide count (C_source) by sampling. A background spectrum was obtained by measuring the shielded detector with lead bricks for 3600 seconds, which included natural radiation from the ⁴⁰K isotope. Then, the simulated spectrum is linearly combined with the measured background spectrum under different SNR conditions.

Nuclide mixing and Superposition: The count of each nuclide was obtained separately based on gross count, SNR, and random proportion, then linearly superimposed. Mixed nuclides are generated through permutations and combinations. Assuming n mixed nuclides, n ratios kn are randomly generated. To prevent large variations in nuclide counts, the initial mixed-ratio range was set between 0.1 and 0.5.(14)Then, we normalize K values to the sum 1:(15)According to the gross count C_source required by the random SNR, the count Cs for each nuclide source is obtained as follows:(16)Data augmentation can be performed based on the number of samples required to meet the requirements of training and performance evaluation.

Figure 5 shows the comparison between the simulated synthetic spectrum (orange) and the measured spectrum (blue). For the simulated spectra, we manually adjusted the counts of ¹³⁷Cs and the background to 3×10³, and the counts of ⁶⁰Co to 1×10³. We used a detector with the same structure as shown in Fig. 4 and obtained the measured energy spectra based on ¹³⁷Cs and ⁶⁰Co point sources. We calculated the cosine similarity between the simulated synthetic spectrum and measured spectrum as 0.965, indicating a good fit between the two.

Fig. 5Full-screen View

(Color online) Measured and Simulated ¹³⁷Cs+⁶⁰Co mixed spectra

The constructed dataset generally included six common artificial radionuclides and a natural radionuclide, ⁴⁰K. Among them, ²⁴¹Am and ⁵⁷Co have low energies, and their full-energy peaks occupy a small area that overlaps the strong low-energy Compton scattering region. ¹³¹I, ⁶⁰Co, ¹³⁴Cs, and ¹³⁷Cs are commonly released during nuclear power plant accidents [36-38]. When they coexist with the natural radionuclide background ⁴⁰K, full-energy peak overlap may occur.

For each nuclide category, the central position (xc), area width (w), and corresponding confidence (c) of the full-energy peaks are labeled in all the spectral samples to construct the dataset used in this study. All the energy spectra are normalized to ensure that the input depends solely on the shape.

Evaluation Metrics

Evaluation metrics, widely used in computer vision object detection models, including precision (P), recall (R), F1 score (F1), and average precision (AP), were used to evaluate our method [39, 40].

Recall: The percentage of correctly detected targets relative to the total number of targets.(17)Precision: The proportion of correctly detected targets relative to the total predicted targets.(18)F1 score: The harmonic mean of precision and recall, which evaluates model performance in a balanced manner, considering both false positives and false negatives.(19)where TP denotes the number of correctly identified targets, FP denotes the number of falsely detected targets, and FN denotes the number of undetected targets.

AP: A measure of the area under the precision–recall (P-R) curve, with recall on the x-axis and precision on the y-axis. AP effectively evaluates the average detection precision across varying recall levels. The calculation formula for AP is shown in Eq. 20.(20)

Compared Methods

Morphological-based: Rui Luo et al. [17] compared five traditional peak search methods with a new morphology-based method using mixed spectra generated from multiple nuclides. These results indicate that the morphological method is more suitable for peak searches in the mixed spectra generated from multiple nuclides. Therefore, this method served as a baseline for comparison in this study.

The morphological peak search method consists of three steps: spectrum smoothing, morphological top-hat transformation, and false-peak screening. Finally, the significant peaks in the energy spectra are retained. Spectral smoothing is performed using the Savitzky–Golay filter [41]. The parameters to be adjusted are the window size (w) and polynomial order (k). As w increases and k decreases, the smoothing effect becomes more pronounced. In the morphological top-hat transformation, the structural element size (L) should be adjusted. If L is extremely small, then excessive noise is detected. If L is extremely large, then the ability of the algorithm to distinguish between adjacent peaks diminishes. After morphological white-hat transformation, the spectrum is divided into continuous nonzero regions.

The width (wi) of each region is calculated, and the threshold (W_T) is set. If wi < W_T, then it is classified as a false peak. Multiple candidate peaks are detected. When the difference between the detected peak and ground truth is within the energy window (set to 2% in this study), the search is deemed correct, whereas the others are classified as false peaks [42].

The four parameters were manually adjusted. The adjusted parameters and their ranges are presented in Table 2. The best parameter configuration was identified by iterating different parameters and using F1 as the evaluation metric, as listed in Table 2. In subsequent tests, it was labeled MorPh.

ResNet-18: An ablation test was performed to evaluate the effectiveness of the proposed MSNN module. To ensure experimental fairness, the MSNN module was removed from the architecture (Fig. 1). The feature map F_resnet was then directly expanded and connected to the following fully connected layer, labeled ResNet-18, in the test. The method proposed in this study was labeled ResNet-18+MSNN.

Model Training

During the model training process, the dataset was split into an 80% training set and 20% validation set. The initial learning rate was set to Ir = 1 × 10^-4 and the batch size was set to 256. The learning rate decreased by a factor of 10 every 30 epochs. The Adam optimizer was used for parameter optimization.

Notably, during each data reading in the training process, uniformly distributed noise in the range of 0.001~0.02 and peak displacements in the range of 0~200 were randomly added to further augment the dataset and ensure its diversity. These two data-augmentation steps were applied only during training to ensure that the test dataset remained exclusive and did not overlap with the training data.

Figure 6a presents the trend of the total loss curves during the training process. Figure 6b shows the performance of various indicators on the validation dataset, with an upward trend corresponding to the loss.

Fig. 6Full-screen View

(Color online) Performance of validation dataset during training; (a) loss curve during training; (b) performance of validation dataset

Evaluation Results and Analysis

A comprehensive performance evaluation was first performed, followed by control of the gross count, SNR, and nuclide category for quantitative analysis. Subsequently, qualitative evaluation and inference time performance were assessed.

Comprehensive performance: Values for the SNR and gross count ware randomly selected based on the range specified in Table 1, and a test set of 60,000 samples is generated. Figure 7 and Table 3 show the recall and precision performances of the three methods for the test set.

Fig. 7Full-screen View

(Color online) Comprehensive performance comparison chart; (a) comprehensive performance of P-R curve; (b) comprehensive performance of F1-Confidence

The DL-based method calculates the corresponding recall and precision at different confidence thresholds and generates a P-R curve. The morphology-based method visualizes the calculation results during the parameter iteration process in a scatter plot. The DL-based method outperformed the morphology-based method in terms of both recall and precision, particularly in terms of high precision.

Compared to the morphology-based method, ResNet-18’s precision, recall rate, and best F1 score improved by 0.517, 0.082, and 0.352, respectively. After implementation of the MSNN module, these values increased by 0.521, 0.199, and 0.391, respectively. Table 3 shows that compared with the ResNet-18 model, the AP improved by 0.072 after implementing the MSNN module. Furthermore, Fig. 7b shows that, after implementing the MSNN module, the optimal confidence threshold is lower, which typically results in a higher recall rate. Therefore, the results indicate that the main advantage of the MSNN module is an improvement in the recall rate.

Low gross count: The peaks in the low-count spectrum are influenced by statistical fluctuations, which in turn are affected by factors such as the radiation source intensity, detector efficiency, and measurement time. This results in the misidentification of numerous false peaks. The stronger detection capability of peaks in the low-count spectrum indicates that the proposed algorithm has enhanced anti-noise ability and can analyze low-activity radionuclide spectra more efficiently.

The fixed gross counts were set to 1×10³, 2×10³, 4×10³, 6×10³, 8×10³, and 2×10⁴. To reduce the impact of a low SNR, the random SNR was controlled within the range of 0.5~1, and 20,000 samples were regenerated for performance testing. The best F1 score, precision, and recall among the three methods were evaluated based on the test set.

As shown in Fig. 8, as the gross count decreased, the performance indicators of all three methods also decreased. However, the F1 score of the ResNet-18+MSNN model outperformed those of the other two methods, as shown in Fig. 8a.

Fig. 8Full-screen View

(Color online) Performance of different low gross count; (a) F1-score at different gross count; (b) precision at different gross count; (c) Recall at different gross count

As shown in Fig. 8c, the recall of the morphology-based method is less affected and matches that of the DL-based method. This is because large statistical fluctuations can increase the false alarm rate; however, the method can still identify existing peaks.

The increased false-alarm rate led to a rapid decrease in precision, as shown in Fig. 8b. As shown in Fig. 8c, the recall rate of the method without the MSNN module gradually decreases as the statistical fluctuations increase.

Overall, as shown in Fig. 8b, the DL-based method consistently maintained the advantage of high precision. The MSNN module effectively improved the recall rate.

Low SNR: The SNR of the spectrum indicates the prominence of the peak relative to the background, which is typically influenced by the intensity of the radioactive source’s background. The stronger peak detection capability in the low SNR spectra suggests that the proposed algorithm can effectively identify low-intensity peaks buried in a strong background.

To evaluate the performance under low SNR conditions, the SNR values were set to 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and 0.5. To minimize the impact of low gross counts, the random gross count range was controlled between 4×10⁴~1×10⁵, and 20,000 samples were regenerated for performance testing. The impact of SNR on the three methods was evaluated (Fig. 9).

Fig. 9Full-screen View

(Color online) Performance of different low SNR; (a) F1-score at different SNR; (b) precision at different SNR; (c) recall at different SNR

The DL-based method consistently maintained higher precision at all the SNR values. Although the F1 score decreased at low SNRs, it remained higher than that of the morphology-based method. As shown in Fig. 9c, the recall rate is significantly improved by the MSNN module, particularly for a low SNR (SNR<0.3).

Radionuclide category: Different radionuclide categories can represent peaks with different half-widths to a certain extent; a smaller FWHM corresponds to a smaller peak area. Small-object detection remains challenging in computer vision [43]. Previous experimental results show that when the MSNN module is applied, the improvement in the recall rate exceeds that in the precision metric. To further investigate the underlying mechanisms, we separately evaluated the detection performance of DL-based methods for peaks of varying widths.

The test set comprised samples containing only one type of radionuclide. To reduce the impact of a low gross counts and SNRs, the random gross count range was set to 5×10⁴~1×10⁵; the SNR range was set to 0.5~1.0, and 20,000 samples were regenerated for the performance test.

Figure 10 shows the performance of the DL-based method for different radionuclides. These results are obtained by evaluating the performance of the model for narrower and broader peaks. As shown in Fig. 10c, without the MSNN module, the recall rates for the ²⁴¹Am and ⁵⁷Co peaks are significantly lower than those for the other nuclides. This result suggests that the missed detection rate is higher because of the small area under the narrow peaks. After applying the MSNN module, the recall rate improves significantly, which demonstrates the effectiveness of the proposed method.

Fig. 10Full-screen View

(Color online) Performance of different radionuclide; (a) F1-score at different radionuclide; (b) Precision at different radionuclide; (c) Recall at different radionuclide

As shown in Fig. 10c, the recall rate for ¹³⁷Cs is significantly lower than those for ¹³⁴Cs and ⁶⁰Co, despite the similar FWHM values of their peaks. This observation can be attributed to the small number of characteristic peaks of ¹³⁷Cs. In other words, the effective area occupied by the characteristic peak of ¹³⁷Cs in the complete energy spectrum is small, and the numbers of positive and negative samples are highly unbalanced.

Qualitative analysis: Figure 11 and Fig. 12 illustrate the peak search and segmentation results of the morphological methods, ResNet-18 and ResNet-18+MSNN. The morphological peak search results are indicated by red arrows. The DL model output includes the confidence (blue bar graph), characteristic peak area (red rectangle), and ground truth (gt) value, as indicated by a green dotted rectangle.

Fig. 11Full-screen View

(Color online) Qualitative analysis of ⁵⁷Co, ⁶⁰Co, ¹³⁴Cs, and ¹³⁷Cs mixed Radionuclides; (a) Morph based method; (b) ResNet-18 based method; (c) ResNet-18 + MSNN based method;

Fig. 12Full-screen View

(Color online) Qualitative analysis of ²⁴¹AM, ⁵⁷Co, ⁶⁰Co, ¹³⁴Cs, and ¹³⁷Cs mixed Radionuclides; (a) Morph based method; (b) ResNet-18 based method; (c) ResNet-18 + MSNN based method

As shown in Fig. 11, the energy spectrum contains peaks derived from mixed nuclides ⁵⁷Co, ⁶⁰Co, ¹³⁴Cs, and ¹³⁷Cs, with significant overall statistical fluctuations. In addition, overlapping characteristic peaks appear at 605 keV (¹³⁴Cs) and 662 keV (¹³⁷Cs).

In this case, the morphological method generates numerous false positives, leading to reduced precision. However, the ResNet-18 model does not provide sufficient confidence for the 605 keV (¹³⁴Cs) characteristic peak, resulting in a lower recall rate. The segmentation precision of the ResNet-18 model for the 1173 keV (⁶⁰Co) characteristic peak area is significantly lower than that of the ResNet-18+MSNN model.

The energy spectrum in Fig. 12 displays peaks corresponding to mixed nuclides ²⁴¹Am, ⁵⁷Co, ⁶⁰Co, ¹³⁴Cs, and¹³⁷Cs. The statistical fluctuation in this energy spectrum is relatively small, with challenges imposed by the narrow peaks (59 keV for ²⁴¹Am) and overlapping peaks (605 keV for ¹³⁴Cs and 662 keV for ¹³⁷Cs).

The morphology-based method has a lower false alarm rate. However, additional false peak screening or manual parameter adjustment is required.

The DL-based method retains its high-precision advantages. However, the ResNet-18 model overlooks the characteristic peak of ²⁴¹Am, and the confidence prediction of the 605 keV characteristic peak of ¹³⁴Cs is worse than that of ResNet-18+MSNN.

The morphological method inevitably generates numerous false peaks owing to the interference of strong statistical fluctuations in the low-count full-energy peaks. The DL-based method, with its strong nonlinear fitting ability, effectively processes noise interference and maintains a high precision. The MSNN module effectively models the intricate features of the overlapping peak areas, thereby further improving the recall rate.

Inference time: Real-time performance is a critical indicator of the applicability of practical monitoring systems. The NVIDIA Jetson AGX Orin 32GB module was used to evaluate the inference time performance, allowing users to set power consumption limits of 15, 30, 50, and 60 W. This setup enabled the evaluation of both inference time and power consumption under various application scenarios.

We conducted experiments on 60,000 samples to measure the inference times under various power consumption constraints using Python 3.8 and PyTorch 2.1. The results are presented in Table 4.

As shown in Table 4, under a 15 W power consumption limit, the average inference time per sample is 16.1941 ms, with a maximum of 112.4730 ms and minimum of 13.5004 ms. This result confirms the good real-time performance of the proposed model.