Nuclear radiation spectrum dual-domain collaborative optimization method and related device

Abstract

The invention discloses a nuclear radiation energy spectrum double-domain collaborative optimization method and a related device, and belongs to the technical field of nuclear radiation measurement, and the method comprises the steps: obtaining an original distortion pulse sequence generated by nuclear radiation measurement; a double-domain collaborative energy spectrum optimization model is constructed, the double-domain collaborative energy spectrum optimization model comprises a pulse domain repair model and an energy spectrum domain reconstruction model which are arranged in parallel, and the pulse domain repair model is used for performing pulse-by-pulse repair on the amplitude and the arrival time of the original distorted pulse sequence and outputting a repaired pulse sequence; the energy spectrum domain reconstruction model is used for converting the repaired pulse sequence into an energy spectrum diagram; in the training process of the double-domain collaborative energy spectrum optimization model, the pulse domain repair model and the energy spectrum domain reconstruction model share the back propagation gradient of the joint loss function, so that bidirectional closed-loop collaborative optimization of the pulse repair model and the energy spectrum reconstruction model can be realized, the problem of step-by-step error amplification caused by a traditional serial processing mode is avoided, and the performance of the system is improved. And the authenticity and the accuracy of the output energy spectrum are obviously improved.

Description

Technical Field

[0001] This invention relates to the field of nuclear radiation measurement technology, and in particular to a dual-domain collaborative optimization method and related apparatus for nuclear radiation energy spectrum. Background Technology

[0002] In nuclear radiation measurements, the detector converts incident radiation into electrical pulse signals. By analyzing the pulse amplitude, an energy spectrum is generated, enabling qualitative and quantitative analysis of the nuclides. However, in actual measurement scenarios, the original pulse output by the detector often deviates from the ideal shape due to physical limitations, environmental disturbances, etc., resulting in distorted pulses.

[0003] Existing technologies for handling distorted pulses and spectral distortion typically involve pulse repair followed by spectral generation. This approach directly propagates and amplifies errors from the pulse repair stage to the spectral generation stage, while the overall spectral information cannot provide feedback to guide the pulse repair process. This sequential processing mechanism leads to progressively amplified errors, making it difficult to guarantee the quality of the final spectral spectrum, especially when dealing with complex distortions or multiple superimposed distortions. For example, amplitude distortion caused by pulse stacking, if not fully repaired, can create false peaks or cause peak position shifts in the spectral spectrum. Furthermore, existing technologies treat pulse repair and spectral generation as separate processes, making it difficult to utilize the overall spectral information to constrain and correct the pulse repair process. Even minor deviations in the pulse repair stage can be amplified in subsequent spectral generation, resulting in significant differences between the final spectral spectrum and the actual situation. Therefore, achieving coordinated optimization of pulse repair and spectral reconstruction to avoid error accumulation and amplification is a pressing technical problem that needs to be solved in this field. Summary of the Invention

[0004] The purpose of this invention is to overcome the problems of the prior art and provide a dual-domain collaborative optimization method and related apparatus for nuclear radiation energy spectrum.

[0005] The objective of this invention is achieved through the following technical solution: a dual-domain synergistic optimization method for nuclear radiation energy spectrum, comprising the following steps: Obtain the raw, distorted pulse sequence generated by nuclear radiation measurements; A dual-domain collaborative energy spectrum optimization model is constructed, which includes a pulse domain repair model and an energy spectrum domain reconstruction model set in parallel. The pulse domain repair model is used to repair the amplitude and arrival time of the original distorted pulse sequence pulse by pulse and output the repaired pulse sequence. The energy spectrum domain reconstruction model is used to convert the repaired pulse sequence into an energy spectrum. During the training process of the dual-domain collaborative energy spectrum optimization model, the pulse domain repair model and the energy spectrum domain reconstruction model share the backpropagation gradient of the joint loss function.

[0006] In one example, the pulse domain repair model employs a temporal feature extraction network, which can be either a lightweight UNet or a long short-term memory neural network. The energy spectrum domain reconstruction model uses an energy spectrum feature reconstruction network, which can be any one of the following: a spectrum Transformer, a deep residual network, or a multilayer perceptron. The energy spectrum feature reconstruction model embeds a learnable nuclide base function library. Through a soft alignment mechanism, the output energy spectrum of the energy spectrum feature reconstruction model is matched with the feature peak shape of the nuclide base function library. The calibration energy spectrum is used as a supervision signal to ensure that the relative entropy between the output energy spectrum and the calibration energy spectrum is less than a preset threshold.

[0007] In one example, during the training of the dual-domain collaborative energy spectrum optimization model, physical constraints are embedded in the joint loss function, which include at least one of an energy conservation term, a peak consistency term, and a noise lower limit term.

[0008] In one example, the energy conservation term is used to ensure that the integral count of the repaired pulse sequence output by the pulse domain repair model is equal to the integral count of the original distorted pulse sequence; the peak position consistency term is used to suppress peak position shift caused by temperature drift by using the characteristic peak of the internal standard element as an anchor point; and the noise lower limit term is used to introduce Fano factor and electronic noise power spectrum constraints.

[0009] In one example, the method further includes constructing a distorted pulse dataset: Initial distorted pulse datasets covering different nuclear radiation measurement scenarios, energy ranges, and count rates were generated through software simulation. Measured pulses are collected in a standard radiation field. A Bayesian inversion mapping relationship is established between the physical parameters to be corrected in the physical model used in the software simulation and the measured pulse output. The physical parameters are corrected through the mapping relationship. A SHAP value sensitivity analysis is performed on the physical model to correct the charge sharing coefficient and polarization correction factor in the physical model. This ensures that the peak position difference between the initial distorted pulse and the measured pulse is less than the preset number of channels, thus achieving the calibration processing of the initial distorted pulse. The calibrated pulse generation script is distributed to multiple nodes through a federated learning framework. Each node runs the pulse generation script locally to generate distorted pulses that conform to the characteristics of the local scene, trains the local model based on the local distorted pulse data, and uploads gradient statistics processed with differential privacy, thereby realizing the federated expansion of the initial calibrated distorted pulse dataset.

[0010] In one example, the method further includes a few-sample cross-domain robust training step: A joint physics engine with multiple distortion mechanisms is constructed, coupled with a circuit-level noise model, to generate multiple virtual distortion pulses; A twin network architecture with shared weights is constructed. The main network is input with real impulse samples, and the twin network is input with corresponding virtual distorted impulse samples. By contrastive learning, the distribution distance between real impulse samples and virtual distorted impulse samples in the latent space is reduced. At the same time, a physical regularization term is introduced to constrain the rationality of the generated samples. A three-dimensional parameter spatial hierarchical sampling strategy for temperature, dose, and device aging is designed to map real pulse samples to multiple domain distribution anchor points. Each anchor point represents a different combination of temperature, dose, and aging conditions. The maximum mean difference loss function is introduced for domain adaptive alignment. A federated transfer learning framework is adopted, in which each node stores the original data and only exchanges gradient statistics processed with differential privacy.

[0011] In one example, the method further includes a dual-domain collaborative energy spectrum optimization model deployment step: The end-side uses a silicon drift detector array in conjunction with a time-to-digital converter to achieve lossless digital processing of the original distorted pulse sequence; The side is based on FPGA and on-chip microprocessor, and deploys hardware IP cores for dual-domain collaborative energy spectrum optimization model. FPGA is used to realize parallel computing of pulse domain repair model and energy spectrum domain reconstruction model. On-chip microprocessor updates the parameters of dual-domain collaborative energy spectrum optimization model according to the federated aggregation gradient. The cloud side and the edge side maintain synchronization, receive gradient statistics processed by differential privacy, and update the parameters of the edge-side dual-domain collaborative energy spectrum optimization model through a federated learning protocol.

[0012] It should be further noted that the technical features corresponding to the above examples can be combined or replaced to form new technical solutions.

[0013] The present invention also includes a computer program product comprising a computer program that, when executed by a processor, implements the steps of the nuclear radiation energy spectrum dual-domain collaborative optimization method formed by any or a combination of the above examples.

[0014] The present invention also includes a storage medium storing computer instructions that, when executed, perform the steps of the nuclear radiation energy spectrum dual-domain collaborative optimization method formed by any or more of the above examples.

[0015] The present invention also includes a terminal comprising a memory and a processor, the memory storing computer instructions executable on the processor, wherein the processor, when executing the computer instructions, performs the steps of the nuclear radiation energy spectrum dual-domain collaborative optimization method formed by any or more of the above examples.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. By constructing a parallel pulse domain repair model and an energy spectrum domain reconstruction model, and enabling the two models to share the backpropagation gradient of the joint loss function during training, bidirectional closed-loop collaborative optimization of the pulse repair model and the energy spectrum reconstruction model can be achieved. This allows each parameter update in the pulse domain to be reflected in the energy spectrum output in real time, while the optimization objective in the energy spectrum domain can guide the pulse repair process in reverse. This avoids the problem of error amplification at each stage caused by traditional serial processing methods, and significantly improves the authenticity and accuracy of the output energy spectrum.

[0017] 2. A three-step method of software simulation, experimental calibration, and federated expansion is used to construct a distorted pulse dataset, which can generate a large-scale dataset with physical consistency and complete labels. The experimental calibration step uses Bayesian inversion and SHAP value sensitivity analysis to correct the parameters of the simulation physical model, so that the peak position difference between the simulated pulse and the measured pulse is less than the preset number of channels. At the same time, federated expansion is used to achieve distributed expansion of the dataset while protecting data privacy, providing a high-quality training data foundation for the dual-domain collaborative energy spectrum optimization model.

[0018] 3. By constructing a small-sample cross-domain robust training framework, the dual-domain collaborative energy spectrum optimization model can be enhanced to adapt to complex distortion scenarios by using a large number of virtual pulses under the condition of scarce real labeled samples. Domain adaptive alignment enables the model to maintain stable feature extraction capabilities under different temperature, dosage and aging conditions. At the same time, based on the federated learning framework, the model can still have excellent cross-scenario generalization performance when there are only a few real samples. Attached Figure Description

[0019] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. The accompanying drawings are provided to provide a further understanding of the present application and constitute a part of the present application. The same reference numerals are used in these drawings to denote the same or similar parts. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application.

[0020] Figure 1 This is a flowchart of a method provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the Unet structure provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a spectrum Transformer structure provided in an embodiment of the present invention; Figure 4 A schematic diagram of nine negative exponential pulse sequences with the same amplitude but different time parameters provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of a pulse sequence shaping result provided in an embodiment of the present invention; Figure 6This is a schematic diagram of a three-level edge-cloud collaborative framework provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the preferred embodiment of the method provided by an embodiment of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0023] In one example, such as Figure 1 As shown, a dual-domain collaborative optimization method for nuclear radiation energy spectrum is proposed, which includes the following steps: S11: Obtain the raw distorted pulse sequence generated by nuclear radiation measurement.

[0024] In step S11, the raw pulse signal without any correction processing is acquired in real time by a detector. For example, a NaI(Tl) scintillation detector or a silicon drift detector is used to acquire the raw voltage pulses, and the raw voltage pulses are digitized and sampled, recording the waveform sampling points and arrival time of each pulse to form a raw distorted pulse sequence arranged in chronological order. This raw distorted pulse sequence includes various distortion types such as normal single pulses, stacked pulses, baseline drift, and reset abrupt changes.

[0025] S12: Construct a dual-domain collaborative energy spectrum optimization model. The dual-domain collaborative energy spectrum optimization model includes a pulse domain repair model and an energy spectrum domain reconstruction model set in parallel. The pulse domain repair model is used to repair the amplitude and arrival time of the original distorted pulse sequence pulse by pulse and output the repaired pulse sequence. The energy spectrum domain reconstruction model is used to convert the repaired pulse sequence into an energy spectrum.

[0026] In step S12, the pulse domain repair model is used to process the original distorted pulse sequence pulse by pulse. By analyzing the waveform characteristics of each pulse, the amplitude value and arrival time of the pulse are accurately corrected, and the repaired pulse sequence is output. The energy spectrum domain reconstruction model is used to receive the repaired pulse sequence and convert the repaired pulse sequence into a high-resolution energy spectrum using an energy spectrum reconstruction algorithm.

[0027] S13: During the training process of the dual-domain collaborative energy spectrum optimization model, the pulse domain repair model and the energy spectrum domain reconstruction model share the backpropagation gradient of the joint loss function.

[0028] In step S13, the parameters of the pulse domain repair model and the energy spectrum domain reconstruction model are updated simultaneously by backpropagating the gradient through the joint loss function. This allows the output of the energy spectrum domain reconstruction model to constrain the parameter updates of the pulse domain repair model, and vice versa. As a result, the amplitude fine-tuning of each pulse in the pulse sequence output by the pulse domain repair model is transmitted to the energy spectrum domain reconstruction model during backpropagation and reflected in the energy spectrum output by the energy spectrum domain reconstruction model, forming a pulse domain-energy spectrum domain closed-loop optimization, which maps the original distorted pulse to a high-fidelity energy spectrum.

[0029] In one embodiment, the dual-domain collaborative energy spectrum optimization model adopts a pulse domain-energy spectrum domain dual-channel parallel architecture, and the pulse domain repair model uses a temporal feature extraction network, which can be either a lightweight UNet or a long short-term memory neural network. Figure 2 As shown, this embodiment employs a lightweight UNet, including an encoder and a decoder. The encoder comprises a first coding layer, a second coding layer, a third coding layer, and a fourth coding layer connected in sequence. The first coding layer is connected to the input layer of the UNet. The decoder comprises a fourth decoding layer, a third decoding layer, a second decoding layer, and a first decoding layer connected in sequence. The first decoding layer is connected to the output layer of the UNet, and the first coding layer skips connections to the first decoding layer, the second coding layer skips connections to the second decoding layer, the third coding layer skips connections to the third decoding layer, and the fourth coding layer skips connections to the fourth decoding layer. This embodiment deploys a lightweight UNet in the pulse domain, using the original distorted pulse sequence as input, and utilizes local temporal convolution and four layers of downsampling-upsampling cross-scale skip connections to achieve a 10 5 Node, 10 6 Millisecond-level inference can be completed on a large-scale dynamic graph with only 8 layers, and the amplitude, arrival time and waveform shape can be corrected pulse by pulse. The number of network parameters is only 0.8 M, and 1024 pulse batch processing can be completed in 8 ms on the FPGA.

[0030] Furthermore, the spectral domain reconstruction model employs a spectral feature reconstruction network, which can be any one of a spectral Transformer, a deep residual network, or a multilayer perceptron. For example... Figure 3As shown, this embodiment uses a spectrum Transformer, which includes a sequentially connected input layer, a fully connected block, a scaled dot product attention block, a first splicing layer, a fourth fully connected layer, a first normalized layer LN1, a fifth fully connected layer, an exponential linear unit layer ELU, a sixth fully connected layer, a first normalized layer LN2, and an output layer. The fully connected block includes several groups of fully connected layers, each group including a first fully connected layer FC1, a second fully connected layer FC2, and a third fully connected layer FC3 arranged in parallel. The scaled dot product attention block includes several scaled dot product attention layers, and the three input terminals of the fully connected layer group are connected between the fourth fully connected layer and the first normalized layer. An element-wise addition operation is performed between the fourth fully connected layer and the first normalized layer, and an element-wise addition operation is performed between the sixth fully connected layer and the second normalized layer. At this point, the repaired pulse sequence is input into three independent fully connected layers of a fully connected layer group via the input layer. A linear transformation generates a triplet of query Q, key K, and value V. The Q, K, and V triplets are then input into a scaled dot product attention block for attention weight calculation and feature aggregation, yielding the attention feature output. This attention feature output is then processed by multi-head feature concatenation in the first concatenation layer and input into the fourth fully connected layer for linear transformation. The output of the fourth fully connected layer is then element-wise added to its input and input to the first normalization layer for normalization. The normalization result is then processed nonlinearly through the fifth fully connected layer, the exponential linear unit layer, and the sixth fully connected layer. The output of the sixth fully connected layer is then element-wise added to its input and input to the second normalization layer for normalization. Finally, the reconstructed energy spectrum is output through the output layer. In this embodiment, the energy spectrum feature reconstruction model resamples the repaired pulse sequence into a 2048-channel energy spectrum with a precision of 1eV. It captures long-range inter-peak relationships through a self-attention mechanism and uses an embedded learnable nuclide basis function library. Through a soft alignment mechanism, the output energy spectrum of the energy spectrum feature reconstruction network is aligned with the feature peak shapes of the nuclide basis function library. The calibration energy spectrum is used as a supervision signal to ensure that the KL divergence between the output energy spectrum and the calibration energy spectrum is less than a preset threshold, such as 0.01, thereby improving the accuracy and reliability of nuclide identification.

[0031] In this embodiment, the pulse domain repair model and the energy spectrum domain reconstruction model share gradients during backpropagation, ensuring that every fine-tuning of the pulse correction is reflected in the energy spectrum shape in real time, achieving true pulse-energy spectrum closed-loop optimization. The final dual-domain collaborative energy spectrum optimization model has a parameter count controlled at 2.3 M, and can complete one inference cycle in 8ms on the heterogeneous computing platform Zynq Ultrascale+ FPGA, laying the foundation for a real-time, high-precision, and interpretable core engine for subsequent edge-cloud collaborative systems.

[0032] In one embodiment, during the training of the dual-domain collaborative energy spectrum optimization model, physical constraint terms are embedded in the joint loss function. These physical constraint terms include at least one of an energy conservation term, a peak consistency term, and a noise lower bound term; preferably, they include these three terms. The energy conservation term ensures that the integral count of the repaired pulse sequence output by the pulse domain repair model is equal to the integral count of the original distorted pulse sequence. The peak consistency term uses the characteristic peak of the internal standard element as an anchor point to suppress peak shift caused by temperature drift. The noise lower bound term introduces the Fano factor and electronic noise power spectrum constraints to prevent excessive denoising. This embodiment embeds physical constraints such as energy conservation, peak consistency, and noise lower bound terms into the joint loss function, integrating the fundamental physical laws of nuclear radiation measurement into the model training process, ensuring that the model output conforms to both data distribution characteristics and physical interpretability requirements.

[0033] In one embodiment, based on the introduction of a physical constraint mechanism into the joint loss function, the weight coefficients of each physical constraint are dynamically adjusted according to the real-time statistical characteristics of the input pulse sequence. Specifically, by analyzing real-time statistical parameters such as the stacking rate, baseline drift rate, and noise power spectral density of the pulse sequence, the contribution of the corresponding physical constraint terms is adaptively enhanced or weakened. For example, when a high count rate scenario is detected, the weight of the energy conservation term is automatically increased to ensure the accuracy of the total count after stacked pulse repair; when temperature drift is detected, the constraint strength of the peak consistency term is automatically enhanced. Based on this dynamic adjustment mechanism of the weight coefficients of physical constraint terms, the dual-domain collaborative energy spectrum optimization model can always maintain optimal physical consistency under different measurement conditions, avoiding over-constraint or under-constraint problems caused by fixed weights when the scenario changes.

[0034] In one embodiment, training the pulse domain repair model specifically includes: A large amount of precisely labeled distorted pulse data is generated through Monte Carlo simulation. The distorted pulse data is then preprocessed to form a training dataset that can be used for supervised learning. This dataset is used to train the pulse domain restoration model, enabling the pulse domain restoration model to accurately predict the true pulse amplitude in the distorted waveform.

[0035] Specifically, pulse heights were randomly selected from the probability distributions of spectra from common gamma-ray sources (such as 22Na and 137Cs). The pulse height distributions were obtained from Monte Carlo simulation software using a Gaussian energy broadening method. The simulation code generates signals detected by a NaI(Tl) detector at its characteristic energy resolution. The Gaussian energy broadening coefficients used were calculated through parameter optimization. A total of 30,000 pulses (total = 300,000 pulses) were generated over 10 time series, with stacking rates of 70%, 80%, 90%, 95%, 96%, 97%, 98%, 99%, 99.5%, and 99.9%, respectively. The calculation formula is: in, Stacking refers to the number of stacked pulses. This represents the total number of pulses. When the time interval between a peak and the previous peak is less than 350 μs, the event is considered a stacking event, and the generated pulse signal is processed as follows: First, the peak position is found using the peak lookup function in the SciPy library; then, the pulse signal from the 20 channels before the peak to the 43 channels after the peak is sliced. The true pulse height of all pulse slices is matched by referencing the peak signal. For example, for paired datasets, 64-channel long pulse slices and their true pulse heights are extracted for all pulses in the generated signal, and the pulse slices and true pulse heights are given as input and desired output, respectively, to train the pulse domain repair model.

[0036] Furthermore, the energy spectrum domain reconstruction model takes the repaired pulse sequence output by the pulse domain repair model as input and the calibration energy spectrum obtained by actual measurement of a standard radioactive source as the supervision signal, and is trained by minimizing the relative entropy between the output energy spectrum and the calibration energy spectrum.

[0037] In one embodiment, the method further includes constructing a distorted pulse dataset: S01: Generate an initial distorted pulse dataset covering different nuclear radiation measurement scenarios, energy ranges, and count rates through software simulation.

[0038] Because the pulse morphology, amplitude, and distortion type vary depending on the nuclear radiation measurement scenario and the measuring device used, it is necessary to establish a unified, differentiable, and interpretable distortion pulse generation and characterization framework across scenarios (uranium mine exploration gamma spectrum and X-ray spectrum) to provide a physically consistent, fully labeled, and plug-and-play data foundation for the dual-domain collaborative spectrum optimization model. In this embodiment, the gamma scenario uses Geant4 to establish the geometry of two airborne detectors: φ76 mm NaI(Tl) and φ50 mm LaBr3(Ce), with built-in... 137 Cs、 40 K, 238 U、 232 The standard source is coupled with Garfield++ to simulate charge sharing; the X-ray scene uses MCNP6 to generate 5-30 keV characteristic X-rays, superimposed with SDD dead layer and carrier trapping effect; the general distortion engine uses Python to batch produce multiple types of distortions, including stacking, baseline drift, reset mutation, polarization gain attenuation, temperature noise increase, etc., and sets controllable parameters for each type of distortion, such as stacking order 0-3 and mutation ratio 10%-80%.

[0039] Specifically, the simulation modeling generates a dataset of distorted pulses in X-ray scenes, including: Taking the reset abrupt pulse as an example, assuming the pulse distortion time is... Its mathematical model is: In the formula, Indicates time The amplitude of the pulse voltage; A represents the amplitude of the negative exponential pulse, and τ represents the decay time constant. The sampling period is represented by . The mathematical model for a pulse sequence consisting of N distorted negative exponential pulses is: In the formula, u Indicates a step signal. For the first i The amplitude coefficient of the nuclear pulse, Indicates the first i The occurrence time of each nuclear pulse Indicates noise. Based on the sampling period. right Discretization yields the following negative exponential pulse sequence: Abnormal nuclear pulse sequence See as N A distorted negative exponential pulse sequence The mathematical model obtained after triangulation is as follows: in, This is a pulse sequence after triangulation. Indicates data labels; This indicates the forming rise time of the triangular forming process. The corresponding number of sampling points. The simulated distorted pulse dataset is taken from the pulse amplitude sampling values ​​after the distorted negative exponential pulse is triangulated and the parameter set P of the negative exponential pulse before triangulation, using the parameter set of the i-th negative exponential pulse. For example, this set includes the amplitudes of negative exponential pulses. Sampling period Time constant and the rise time of the triangular formation The matrix of the dataset is: The dataset contains N triangulation pulse sequences, each pulse sequence corresponding to a row in the matrix; each row contains n+1 columns, the first n columns corresponding to each amplitude value of the distorted pulse triangulation result.

[0040] To achieve the desired shaping effect, the tail portion of the negative exponential pulse needs to maintain a sufficient pulse width. If the pulse width is insufficient in the time domain, the lost sampling points exceed the threshold set by the shaping method (usually determined by the rise time), resulting in significant loss. Nine negative exponential pulse sequences with the same amplitude but different time parameters are taken as follows: Figure 4 As shown, when the rise time of the triangular forming is 80 and the width of the flat top is 0, the corresponding forming result is as follows. Figure 5 As shown, Figures 4-5 In the text, A represents the amplitude parameter label, and T represents the time parameter label. V s This represents the amplitude after shaping. According to... Figures 4-5 The digital shaping results clearly show that the traditional digital triangulation method for pulse parameter estimation is significantly affected by the distortion time parameter. Table 1 presents the amplitude estimates obtained by the digital shaping method when the amplitude parameter is the same but the distortion time parameter is different, further verifying the correlation between the parameter estimation performance of the traditional digital shaping method and the pulse distortion time parameter. Taking the rise time of the triangulation as the critical point, the smaller the distortion time parameter, the fewer effective sampling points the negative exponential pulse contains, resulting in a larger amplitude error after shaping. However, when the number of sampling points increases to around 80, the traditional digital shaping method can still accurately estimate the pulse amplitude parameter. On the other hand, the moment when the amplitude jump of the negative exponential pulse occurs maintains a one-to-one correspondence with the amplitude rise inflection point in the shaping result. Therefore, the digital shaping method can accurately predict the distortion time of the negative exponential pulse and has excellent performance in time parameter estimation.

[0041] Table 1. Comparison of pulse amplitude prediction results under different time parameters

[0042] The pulse domain repair model (UNet model) proposed in this invention is mainly used for parameter prediction of distorted negative exponential pulses with insufficient width. Table 1 shows that a typical characteristic of such pulses is that the distortion time parameter is less than 80. Therefore, when generating simulated distorted pulses, the time parameter value of each pulse ranges from 40 to 80, and the 41 pulses with different distortion time parameters represent 41 different degrees of distortion. During training, these pulse datasets with different amplitude parameters and different distortion time parameters are used as input to the UNet model. After training, the UNet model outputs the amplitude and time parameters of each pulse. To verify the noise resistance performance of different UNet models, these pulses are mixed with white noise to obtain test sets with different signal-to-noise ratios. The trained UNet model is then used to predict the parameters of the pulses in these test sets to demonstrate the excellent noise resistance performance of the UNet model.

[0043] Furthermore, adopt The mathematical model generates N pulses and their corresponding amplitude and time parameters, which constitute dataset I. In dataset I, the first 256 columns represent the amplitude values ​​of the digitized negative exponential pulses, and the last two columns represent the amplitude parameter and pulse distortion time parameter for each pulse. In the matrix, A represents the amplitude label, and T represents the time label. This represents the voltage amplitude sample value without triangulation. V s This represents the amplitude after the shape is formed.

[0044] In practical applications, the pulse height analyzer used to generate energy spectrum maps processes digitally shaped pulses, not the original negative exponential pulses. Therefore, this paper uses dataset I as the data source and triangulates it to obtain dataset II: In Dataset II, the first 256 columns are the sampling amplitudes obtained after pulse digital shaping, and the last two columns are the amplitude parameters and pulse distortion time parameters for each pulse.

[0045] Specifically, the simulation modeling generates a dataset of distorted pulses in a gamma-ray scene, including: To verify the model's performance, this invention generated typical gamma spectra and detected them using a NaI(Tl) scintillation detector. To generate a pulse dataset for training a general neural network model under various test conditions, a mathematical model of the scintillation pulse was defined by modifying the pulse of the scintillation signal, such as rise time, decay time, and dip, to generate a pulse signal considering baseline dip. The noiseless scintillation pulse model is as follows: in, It is the slope of the rising pulse. It is the time constant of the decaying pulse. That is the peak time. B is the decay time, and B is the amplitude of baseline recovery from the undershoot. This is the baseline recovery time. The slope of the rising pulse is calculated using the following formula: In the formula, H represents the pulse height.

[0046] S02: Acquire measured pulses in a standard radiation field, establish a Bayesian inversion mapping relationship between the physical parameters to be corrected and the measured pulse output in the physical model used in the software simulation, correct the physical parameters through the mapping relationship, and perform SHAP value sensitivity analysis on the physical model to correct the charge sharing coefficient and polarization correction factor in the physical model, so that the peak position difference between the initial distorted pulse and the measured pulse is less than the preset number of channels, such as 1 channel, thereby realizing the calibration processing of the initial distorted pulse.

[0047] In step S02, in the γ reference radiation field ( 137 Cs、 60 Co) Collect no less than 5,000 measured pulses and use an X-ray machine to collect no less than 5,000 measured pulses. Automatically correct the charge sharing coefficient and polarization correction factor in the physical model through Bayesian inversion so that the peak position difference between the simulated pulse and the measured pulse is less than 1 channel.

[0048] S03: Distribute the calibrated pulse generation script to multiple nodes through a federated learning framework. Each node runs the pulse generation script locally to generate distorted pulses that conform to the characteristics of the local scene, trains the local model based on the local distorted pulse data, and uploads the gradient statistics processed by differential privacy, thereby realizing the federated expansion of the initial calibrated distorted pulse dataset.

[0049] In step S03, before distributing the calibrated pulse generation script to multiple nodes through the federated learning framework, a field-programmable pulse generator (FPGA-DDS) is used to feed back simulated pulses to the front-end electronics, forming a semi-physical sample where the waveform is generated by software simulation but the signal path is processed by real hardware. This embodiment performs federated expansion on the initial calibrated distorted pulse dataset, resulting in a distorted pulse dataset with an energy range of 5 keV-3 MeV and a count rate of 1 k⁻¹ Mcps. Within 3 months, the initial distorted pulses can be expanded to 10... 6 Label accuracy > 99%.

[0050] In one embodiment, the method further includes a few-sample cross-domain robust training step: S21: Construct a joint physics engine with multiple distortion mechanisms, couple a circuit-level noise model, and generate multiple virtual distortion pulses to provide a data foundation for subsequent training.

[0051] In step S21, Geant4 can be used to establish a joint physics engine that includes 12 distortion mechanisms such as charge sharing, pulse accumulation, and polarization drift, coupled with a circuit-level SPICE noise model, to generate 10 batches of noise models. 5 A high-fidelity virtual distortion pulse.

[0052] S22: Construct a twin network architecture in which the main network and the twin network share weights. The main network is input with real pulse samples, and the twin network is input with corresponding virtual distorted pulse samples. By comparing and learning, the distribution distance between real pulse samples and virtual distorted pulse samples in the latent space is narrowed. At the same time, physical regularization terms such as energy conservation and TOF residuals are introduced to constrain the rationality of the generated samples, thereby achieving stable convergence under small sample conditions. This enables the dual-domain collaborative energy spectrum optimization model to learn generalization ability from finite real samples.

[0053] S23: Design a three-dimensional parameter space hierarchical sampling strategy for temperature, dose, and device aging, map real pulse samples to multiple domain distribution anchor points, each anchor point represents a different combination of temperature, dose, and aging conditions, and introduce the maximum mean difference loss function for domain adaptive alignment.

[0054] In this embodiment, 1000 real samples are mapped to 27 domain distribution anchor points, and the dual-domain collaborative energy spectrum optimization model automatically aligns the feature distribution based on the domain adaptive loss with the maximum mean difference.

[0055] S24: Adopting a federated transfer learning framework, each local node in the application scenario saves the original data without uploading it, and only exchanges gradient statistics processed by differential privacy, which satisfies data security and compliance, and enables cross-scenario knowledge sharing.

[0056] This embodiment constructs a small-sample cross-domain robust training framework, enabling the dual-domain collaborative energy spectrum optimization model to maintain an anomaly detection accuracy of greater than 92% and an energy spectrum repair error of less than 3% under different temperature, dose, and device aging conditions, even with only hundreds of real labels.

[0057] In one embodiment, the method further includes a dual-domain collaborative energy spectrum optimization model deployment step: The device employs a high-performance silicon drift detector on the end side, combined with a 50 ps time-to-digital converter and on-chip timestamp, to achieve lossless digitization of the original distorted pulse sequence.

[0058] The edge computing platform is based on a heterogeneous computing platform FPGA and on-chip microprocessor, such as Zynq Ultrascale+ MPSoC, which deploys the hardware IP core of the dual-domain collaborative energy spectrum optimization model. The FPGA is used to realize the parallel computing of the pulse domain repair model and the energy spectrum domain reconstruction model. The on-chip microprocessor updates the hyperparameters of the dual-domain collaborative energy spectrum optimization model according to the federated aggregation gradient issued by the cloud side. The overall static random access memory usage is <2 MB, the inference latency is <8 ms, and the power consumption is <15 W. It can be directly embedded in drones, mobile inspection vehicles, or surgical robots.

[0059] The cloud-side graphics processing unit (GPU) cluster maintains synchronization with the edge via gigabit Ethernet. To ensure data security, a lightweight federated learning protocol is introduced, where local nodes only upload gradient statistics processed with differential privacy noise, and the original pulse waveform never leaves the domain. At the same time, a trusted execution environment is used to update the parameters, such as weights, of the dual-domain collaborative energy spectrum optimization model and store them in encrypted form.

[0060] This implementation uses a three-tiered collaborative architecture of endpoint-edge-cloud, as follows: Figure 6 As shown, the edge-side high-performance silicon drift detector includes a detector and a preamplifier connected in sequence. The preamplifier amplifies the raw pulse output from the detector and outputs it to the edge. The edge-side high-performance silicon drift detector also includes a high-voltage power supply and a low-voltage power supply. The high-voltage power supply provides the operating voltage for the detector, and the low-voltage power supply provides the operating voltage for the preamplifier. The edge is used to acquire high-speed nuclear signals, i.e., voltage pulses after preamplification. This voltage pulse is then filtered and gain-adjusted by a signal conditioning circuit, converted from analog to digital by a signal acquisition card, and input to the FPGA motherboard. The FPGA motherboard transmits the digitized voltage pulse to the on-chip microprocessor via a communication interface for high-speed signal processing, including analog-to-digital conversion configuration, high-speed serial interface JESD204B configuration, distorted pulse modeling, dual-domain collaborative energy spectrum optimization, small-sample cross-domain training, and communication interface control. The processed data and model update parameters are transmitted to the cloud-side GPU cluster via Gigabit Ethernet for subsequent model aggregation and optimization.

[0061] This embodiment deploys a dual-domain collaborative energy spectrum optimization model through a three-level collaborative architecture of edge-cloud. The edge side realizes lossless digital acquisition of the original pulses, while the edge side uses FPGA and on-chip microprocessor as the core to realize parallel accelerated calculation and real-time parameter update of the dual-domain model. The cloud side aggregates the gradients of each edge side through a federated learning protocol and distributes the updated model parameters. This can build a complete closed-loop system from data acquisition and real-time processing to continuous model optimization. While meeting the low latency and low power consumption processing requirements of the edge, it can realize the continuous fusion of cross-scene knowledge and the continuous evolution of model performance.

[0062] Combining the above embodiments yields preferred embodiments of the present invention, such as... Figure 7 As shown, it includes the following steps: S1: Physical modeling and characterization of distorted pulses: (1) Cross-scene distorted pulse simulation: The initial distorted pulse dataset covering different nuclear radiation measurement scenarios, different energy ranges and count rates is generated through software simulation; (2) Calibration of measured pulses in different scenarios: Measured pulses are collected in the standard radiation field, and a Bayesian inversion mapping relationship is established between the physical parameters to be corrected and the measured pulse output in the physical model used in the software simulation. The physical parameters are corrected through the mapping relationship, and the SHAP value sensitivity analysis is performed on the physical model. The charge sharing coefficient and polarization correction factor in the physical model are corrected so that the peak position difference between the initial distorted pulse and the measured pulse is less than the preset number of channels, thereby realizing the calibration of the initial distorted pulse; (3) Differential privacy federated learning expansion: The pulse generation script after calibration is distributed to multiple nodes through the federated learning framework. Each node runs the pulse generation script locally to generate distorted pulses that conform to the local scene characteristics, and trains the local model based on the local distorted pulse data. The gradient statistics after differential privacy processing are uploaded to realize the federated expansion of the initial distorted pulse dataset after calibration, thereby providing physically consistent and labeled training samples.

[0063] S2: Dual-Domain Cooperative Energy Spectrum Optimization: Acquire the original distorted pulse sequence generated by nuclear radiation measurement; construct a dual-domain cooperative energy spectrum optimization model, which includes a pulse domain repair model and an energy spectrum domain reconstruction model set in parallel. The pulse domain repair model is a lightweight model used to identify and classify different types of distorted pulses from continuous pulse sequences, i.e., to achieve distorted pulse discrimination, and is also used to repair the amplitude and arrival time of the original distorted pulse sequence pulse by pulse, and output the repaired pulse sequence. The energy spectrum domain reconstruction model uses a spectrum transformer to convert the repaired pulse sequence into an energy spectrum. During the training of the energy spectrum optimization model, the pulse domain repair model and the energy spectrum domain reconstruction model share the backpropagation gradient of the joint loss function. Simultaneously, a learnable nuclide basis function library is embedded in the energy spectrum feature reconstruction model. Through a soft alignment mechanism, the output energy spectrum of the energy spectrum feature reconstruction model is matched with the characteristic peak shape of the nuclide basis function library. The calibration energy spectrum is used as a supervision signal for energy spectrum correction, so that the relative entropy between the output energy spectrum and the calibration energy spectrum is less than a preset threshold. Furthermore, during the training of the dual-domain collaborative energy spectrum optimization model, physical constraint terms are embedded in the joint loss function. The physical constraint terms include an energy conservation term, a peak position consistency term, and a noise lower limit term.

[0064] S3: Small-sample cross-domain robust training model: Construct a joint physics engine with multiple distortion mechanisms, coupled with a circuit-level noise model, to generate virtual distortion pulses in batches; Construct a twin network architecture with shared weights between the main network and the twin network. The main network is input with real pulse samples, and the twin network is input with corresponding virtual distortion pulse samples. Through contrastive learning, the distribution distance between real pulse samples and virtual distortion pulse samples in the latent space is reduced, while a physical regularization term is introduced to constrain the rationality of the generated samples; Design a hierarchical sampling strategy for the three-dimensional parameter space of temperature, dose, and device aging, mapping real pulse samples to multiple domain distribution anchor points. Each anchor point represents a different combination of temperature, dose, and aging conditions, and the maximum mean difference loss function is introduced for domain adaptive alignment; Adopt a federated transfer learning framework, where each node saves the original data and only exchanges gradient statistics processed by differential privacy.

[0065] S4: Edge-Cloud Three-Level Collaborative Real-Time Energy Spectrum Optimization: The dual-domain collaborative energy spectrum optimization, which has completed robust training across domains with small samples, is deployed to the edge-cloud architecture. In this architecture, the edge uses a silicon drift detector array in conjunction with a time-to-digital converter to achieve lossless digitization of the original distorted pulse sequence. The edge uses an FPGA and an on-chip microprocessor as its core to deploy the hardware IP core of the dual-domain collaborative energy spectrum optimization model. The FPGA is used to implement parallel computation of the pulse domain repair model and the energy spectrum domain reconstruction model. The on-chip microprocessor updates the parameters of the dual-domain collaborative energy spectrum optimization model according to the federated aggregated gradients. The cloud side keeps synchronized with the edge side, receives gradient statistics processed with differential privacy, and updates the parameters of the edge-side dual-domain collaborative energy spectrum optimization model through a federated learning protocol.

[0066] The present invention also provides a computer program product, comprising a computer program that, when executed by a processor, implements the steps of the nuclear radiation energy spectrum dual-domain collaborative optimization method formed by any or a combination of the above examples. The processor may be a single-core or multi-core central processing unit or a specific integrated circuit, or one or more integrated circuits configured to implement the present invention.

[0067] The present invention also provides a storage medium having the same inventive concept as the nuclear radiation energy spectrum dual-domain collaborative optimization method formed by any or more of the above examples, wherein computer instructions are stored thereon, and the computer instructions, when executed, perform the steps of the nuclear radiation energy spectrum dual-domain collaborative optimization method formed by any or more of the above examples.

[0068] Based on this understanding, the technical solution of this embodiment, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0069] This invention also provides a terminal having the same inventive concept as any or a combination of examples corresponding to the aforementioned dual-domain collaborative optimization method for nuclear radiation energy spectrum, including a memory and a processor. The memory stores computer instructions executable on the processor, and the processor executes the steps of the aforementioned dual-domain collaborative optimization method for nuclear radiation energy spectrum when executing the computer instructions. The processor may be a single-core or multi-core central processing unit or a specific integrated circuit, or one or more integrated circuits configured to implement this invention.

[0070] In one example, the terminal, i.e., the electronic device, is represented in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit (processor) mentioned above, at least one storage unit mentioned above, and a bus connecting different system components (including storage units and processing units).

[0071] The storage unit stores program code that can be executed by the processing unit, causing the processing unit to perform the steps described in the "Exemplary Methods" section above, based on various exemplary embodiments of the present invention. For example, the processing unit can execute the aforementioned dual-domain collaborative optimization method for nuclear radiation energy spectrum.

[0072] The storage unit may include readable media in the form of volatile storage units, such as random access memory (RAM) and / or cache storage units, and may further include read-only memory (ROM).

[0073] The storage unit may also include a program / utility having a set (at least one) of program modules, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0074] A bus can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus that uses any of the various bus structures.

[0075] The electronic device can also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable a user to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be performed via input / output (I / O) interfaces. Furthermore, the electronic device can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via a network adapter. The network adapter communicates with other modules of the electronic device via a bus. It should be understood that other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0076] Through the above description, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solution according to this exemplary embodiment can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the method of the exemplary embodiment of this application.

[0077] The above detailed embodiments are a description of the present invention. It should not be considered that the specific embodiments of the present invention are limited to these descriptions. For those skilled in the art, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the protection scope of the present invention.

Claims

1. A dual-domain collaborative optimization method for nuclear radiation energy spectrum, characterized in that, Includes the following steps: Obtain the raw, distorted pulse sequence generated by nuclear radiation measurements; A dual-domain collaborative energy spectrum optimization model is constructed, which includes a pulse domain repair model and an energy spectrum domain reconstruction model set in parallel. The pulse domain repair model is used to repair the amplitude and arrival time of the original distorted pulse sequence pulse by pulse and output the repaired pulse sequence. The energy spectrum domain reconstruction model is used to convert the repaired pulse sequence into an energy spectrum. During the training process of the dual-domain collaborative energy spectrum optimization model, the pulse domain repair model and the energy spectrum domain reconstruction model share the backpropagation gradient of the joint loss function.

2. The dual-domain collaborative optimization method for nuclear radiation energy spectrum according to claim 1, characterized in that, The pulse domain repair model uses a temporal feature extraction network, which can be either a lightweight UNet or a long short-term memory neural network. The energy spectrum domain reconstruction model uses an energy spectrum feature reconstruction network, which can be any one of the following: a spectrum Transformer, a deep residual network, or a multilayer perceptron. The energy spectrum feature reconstruction model embeds a learnable nuclide base function library. Through a soft alignment mechanism, the output energy spectrum of the energy spectrum feature reconstruction model is matched with the feature peak shape of the nuclide base function library. The calibration energy spectrum is used as a supervision signal to ensure that the relative entropy between the output energy spectrum and the calibration energy spectrum is less than a preset threshold.

3. The dual-domain collaborative optimization method for nuclear radiation energy spectrum according to claim 1, characterized in that, During the training of the dual-domain collaborative energy spectrum optimization model, physical constraint terms are embedded in the joint loss function. The physical constraint terms include at least one of the following: energy conservation term, peak position consistency term, and noise lower limit term.

4. The dual-domain synergistic optimization method for nuclear radiation energy spectrum according to claim 3, characterized in that, The energy conservation term is used to ensure that the integral count of the repaired pulse sequence output by the pulse domain repair model is equal to the integral count of the original distorted pulse sequence; the peak position consistency term is used to suppress peak position shift caused by temperature drift by using the characteristic peak of the internal standard element as the anchor point; the noise lower limit term is used to introduce the Fano factor and electronic noise power spectrum constraint.

5. The dual-domain collaborative optimization method for nuclear radiation energy spectrum according to claim 1, characterized in that, The method also includes constructing a distorted pulse dataset: Initial distorted pulse datasets covering different nuclear radiation measurement scenarios, energy ranges, and count rates were generated through software simulation. Measured pulses are collected in a standard radiation field. A Bayesian inversion mapping relationship is established between the physical parameters to be corrected in the physical model used in the software simulation and the measured pulse output. The physical parameters are corrected through the mapping relationship. A SHAP value sensitivity analysis is performed on the physical model to correct the charge sharing coefficient and polarization correction factor in the physical model. This ensures that the peak position difference between the initial distorted pulse and the measured pulse is less than the preset number of channels, thus achieving the calibration processing of the initial distorted pulse. The calibrated pulse generation script is distributed to multiple nodes through a federated learning framework. Each node runs the pulse generation script locally to generate distorted pulses that conform to the characteristics of the local scene, trains the local model based on the local distorted pulse data, and uploads gradient statistics processed with differential privacy, thereby realizing the federated expansion of the initial calibrated distorted pulse dataset.

6. The dual-domain collaborative optimization method for nuclear radiation energy spectrum according to claim 1, characterized in that, The method also includes a small-sample cross-domain robust training step: A joint physics engine with multiple distortion mechanisms is constructed, coupled with a circuit-level noise model, to generate multiple virtual distortion pulses; A twin network architecture with shared weights is constructed. The main network is input with real impulse samples, and the twin network is input with corresponding virtual distorted impulse samples. By contrastive learning, the distribution distance between real impulse samples and virtual distorted impulse samples in the latent space is reduced. At the same time, a physical regularization term is introduced to constrain the rationality of the generated samples. A three-dimensional parameter spatial hierarchical sampling strategy for temperature, dose, and device aging is designed to map real pulse samples to multiple domain distribution anchor points. Each anchor point represents a different combination of temperature, dose, and aging conditions. The maximum mean difference loss function is introduced for domain adaptive alignment. A federated transfer learning framework is adopted, in which each node stores the original data and only exchanges gradient statistics processed with differential privacy.

7. The dual-domain collaborative optimization method for nuclear radiation energy spectrum according to claim 1, characterized in that, The method also includes a dual-domain collaborative energy spectrum optimization model deployment step: The end-side uses a silicon drift detector array in conjunction with a time-to-digital converter to achieve lossless digital processing of the original distorted pulse sequence; The side is based on FPGA and on-chip microprocessor, and deploys hardware IP cores for dual-domain collaborative energy spectrum optimization model. FPGA is used to realize parallel computing of pulse domain repair model and energy spectrum domain reconstruction model. On-chip microprocessor updates the parameters of dual-domain collaborative energy spectrum optimization model according to the federated aggregation gradient. The cloud side and the edge side maintain synchronization, receive gradient statistics processed by differential privacy, and update the parameters of the edge-side dual-domain collaborative energy spectrum optimization model through a federated learning protocol.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the dual-domain collaborative optimization method for nuclear radiation energy spectrum as described in any one of claims 1-7.

9. A storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed, they perform the steps of the dual-domain collaborative optimization method for nuclear radiation energy spectrum as described in any one of claims 1-7.

10. A terminal comprising a memory and a processor, wherein the memory stores computer instructions executable on the processor, characterized in that, When the processor executes the computer instructions, it performs the steps of the nuclear radiation energy spectrum dual-domain collaborative optimization method according to any one of claims 1-7.

Images