Discrimination of neutrons and gamma-rays in plastic scintillator based on pulse coupled neural network

Discrimination of neutrons and gamma-rays in plastic scintillator based on pulse coupled neural network 1 first-author https://orcid.org/0000-0003-0729-4526 1 https://orcid.org/0000-0003-1998-5068 1 2 corresp Zhuo Zuo 690870641@qq.com Zhuo Zuo 690870641@qq.com 690870641@qq.com https://orcid.org/0000-0003-2341-177X 1 1 https://orcid.org/0000-0002-8831-2281 The Engineering & Technical College of Chengdu University of Technology, Leshan 614000, China The Engineering & Technical College of Chengdu University of Technology, Leshan 614000, China Southwestern Institute of Physics, Chengdu 610225, China Southwestern Institute of Physics, Chengdu 610225, China Neutron and gamma-ray pulse signal discrimination technology is an essential part of many modern scientific fields, such as biology, geology, radiation imaging, and nuclear medicine. Neutrons are always accompanied by gamma rays due to their unique penetration characteristic; thus, the development of n- γ discrimination methods is especially crucial. In the present study, a novel n- γ discrimination method is proposed that implements a pulse-coupled neural network for n- γ discrimination. In addition, experiments were conducted on the pulse signals detected by an EJ299-33 plastic scintillator, which is especially suitable for n- γ discrimination. The proposed method was compared to three other discrimination methods, including the back-propagation neural network (BPNN), the fractal spectrum method, and the charge comparison method, with respect to two aspects: (i) the figure of merit ( FoM ) and (ii) discrimination time. The experimental results showed that the pulse-coupled neural network (PCNN) has a 26.49% improvement in FoM -value compared to the charge comparison method, a 72.80% improvement compared to the BPNN, a 66.24% improvement compared to the fractal spectrum method, and the second-fastest discrimination time of 2.22 s. In conclusion, the PCNN treats the input signal as a whole for analysis and processing, imparting it with an excellent anti-noise effect and the ability to process the dynamic information contained in a pulse signal. Pulse coupled neural network Charge comparison Back-propagation neural network Fractal spectrum n- γ discrimination 1 Introduction 1 In the past 50 years, neutron detection technology has become highly crucial in many areas, such as irradiation facilities [ 1 1 ], reactors [ 2 2 ], national defense [ 3 3 ], biology [ 4 4 ], geology [ 5 5 ], medical science [ 6 6 ], and deep-space exploration [ 7 7 ]. Because of the unique interaction between neutrons and the surrounding environment, neutrons are commonly accompanied by gamma rays. However, most radiation detectors used to detect neutrons are also sensitive to gamma rays, which makes n- γ discrimination especially important. In 1979, Brooks et al. [ 8 8 ] found that neutrons and gamma rays generated different pulse shapes when they interacted with organic detectors. Based on this difference between neutrons and gamma rays, pulse shape discrimination (PSD) has been studied [ 9 9 , 10 10 ], many novel detectors with excellent performance have been developed [ 11 11 , 12 12 ], and the feasibility of plastic scintillators for PSD applications has been studied [ 13 13 - 15 15 13-15 ]. Various discrimination methods and discussions of their performance have been introduced and Liu et al. presented a fractal spectrum method in 2016 [ 16 16 ], which has the advantages of anti-noise and high discrimination but requires a very long discrimination time. In 2021, Zuo and Liu et al. compared the performances of three different discrimination methods implemented by four different filtering methods [ 17 17 ]; the intelligent discrimination method they used was the conventional back-propagation neural network (BPNN), which requires the training and prediction sets to be highly similar and processes the dynamic information poorly [ 18 18 ]. Generally, all of the commonly used n- γ discrimination methods mentioned above can be categorized into three categories: time-domain, frequency-domain, and intelligent methods. Although the discrimination time of the time-domain methods is relatively short, their discrimination performances are not satisfactory. In addition, regarding the frequency domain and intelligent methods, although these discrimination methods generally tend to outperform time-domain methods, most require a significant amount of matrix operations; i.e., the algorithm implementation could be relatively cumbersome and time-consuming, which is not conducive to real-time online analysis. These problems raise the question of whether it is possible to find an n- γ discrimination method that is capable of processing the dynamic information contained in the pulse signals, similar to the frequency-domain and intelligent methods while having low computational difficulty and maintaining its time consumption at the same level as the time-domain methods. To solve this problem, we present a novel n- γ discrimination method, which is based on a pulse-coupled neural network (PCNN). Experiments were conducted to verify the performance of the proposed method, in which it was compared with the BPNN method, fractal spectrum method, and charge comparison method, with respect to the figure of merit ( FoM ) and discrimination time. To retrieve the data from the n- γ superposed field, a plastic scintillator (EJ299-33) and a digital oscilloscope were used, which was set with a sampling rate of 1 GS/s, a bandwidth of 200 <math id="M1"><mrow><mtext>MHz</mtext></mrow></math> , and a trigger threshold of 500 mV. The pulse duration was 160 ns, respecting the Shanon criteria, and the bandwidth did not bury the useful signal [ 19 19 ]. The experimental results showed that the proposed method significantly outperformed the others, with an outstanding FoM -value and short discrimination time consumption. The remainder of this paper is organized as follows: the fundamentals of our proposed method and the other three discrimination methods are presented in Sect. 2. The evaluation criteria of n- γ discrimination performance are proposed in Sect. 3. The discrimination results of the different methods are compared and discussed in Sect. 4. The conclusions of the work are presented in Sect. 5. 2 Fundamentals of discrimination methods 1 2.1 Pulse coupled neural network 2 2.1.1 Origin and mathematical expression 3 The pulse-coupled neural network (PCNN) was introduced by Eckhorn and Reitboeck et al. in 1990 [ 20 20 ], which works similarly to real biological neurons, does not require cumbersome work to train the neural network before using it, and, hence, does not require the tested data to be highly similar to the trained data. Based on the neurophysiological findings of the cat’s primary visual cortex [ 21 21 , 22 22 ], they developed a neural network whose central novel principle was abandoning the conventional receptive field and instead introducing a secondary receptive field, the linking field. The integrated input of the aforementioned linking field has an internal cellular circuit, which is capable of modulating the primary feeding receptive field input, influencing the generation of pulse bursts. For a signal fed to the PCNN, which has multiple sampling points — usually, an image [ 23 23 , 24 24 ] — the unique character of the linking field makes it possible to capture the dynamic properties contained in the signal and retrieve the inherent relationships between neighboring sampling points, which is especially crucial for processing signals whose dynamic information is as important as, if not more important than, the information of each sampling point. The model of the PCNN incorporates the accepted, modulation, and pulse generator domains. The accepted domain has two components: feedback input (FI) and link input (LI), which together determine the potential of a neuron. When the potential of a neuron exceeds its dynamic threshold, it is considered activated. The mathematical formulas of the PCNN are as follows [ 25 25 ]: <math display="block" id="M2"><mrow><msub><mi>F</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>α</mi><mtext>F</mtext></msub></mrow></msup><msub><mi>F</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>]</mo></mrow><mo>+</mo><msub><mi>V</mi><mtext>F</mtext></msub><mrow><mo>[</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>]</mo></mrow><mo>+</mo><msub><mi>S</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>,</mo></mrow></math> <math display="block" id="M3"><mrow><msub><mi>L</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>α</mi><mtext>L</mtext></msub></mrow></msup><msub><mi>L</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>]</mo></mrow><mo>+</mo><msub><mi>V</mi><mtext>L</mtext></msub><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mi>k</mi><mi>l</mi></mrow></munder><msub><mi>M</mi><mrow><mi>i</mi><mi>j</mi><mi>k</mi><mi>l</mi></mrow></msub><msub><mi>Y</mi><mrow><mi>k</mi><mi>l</mi></mrow></msub><mrow><mo>[</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>]</mo></mrow><mo>,</mo></mrow></math> <math display="block" id="M4"><mrow><msub><mi>U</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow><mo>=</mo><msub><mi>F</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow><mrow><mo>{</mo><mrow><mn>1</mn><mo>+</mo><mi>β</mi><msub><mi>L</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></mrow><mo>}</mo></mrow><mo>,</mo></mrow></math> <math display="block" id="M5"><mrow><msub><mi>Y</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow><mo>=</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mrow><mn>1</mn><mo>,</mo><mtext>       </mtext><msub><mi>U</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow><mo>></mo><msub><mi>θ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mn>0</mn><mo>,</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>o</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>r</mi><mi>w</mi><mi>i</mi><mi>s</mi><mi>e</mi><mo> </mo></mrow></mtd></mtr></mtable></mrow></mrow><mo>.</mo></mrow></math> <math display="block" id="M6"><mrow><msub><mi>θ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>α</mi><mi>θ</mi></msub></mrow></msup><msub><mi>θ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>]</mo></mrow><mo>+</mo><msub><mi>V</mi><mi>θ</mi></msub><msub><mi>Y</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mrow><mo>[</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mo>]</mo></mrow><mo>,</mo></mrow></math> Where F ij and L ij denote the FI and LI of <math id="M7"><mrow><mrow><mo>(</mo><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow><mo>)</mo></mrow></mrow></math> respectively and coordinate <math id="M8"><mrow><mrow><mo>(</mo><mrow><mi>k</mi><mo>,</mo><mi>l</mi></mrow><mo>)</mo></mrow></mrow></math> represents one of the neighboring neurons of <math id="M9"><mrow><mrow><mo>(</mo><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow><mo>)</mo></mrow></mrow></math> ; n is the iteration count; α F and α L represent the decay times of FI and LI, respectively; V F and V L denote the amplification coefficients of FI and LI, respectively; M is the connection weight matrix, which represents the extent of influence that central neurons received from surrounding neurons; S ij denotes the external input; β is a coefficient influencing the weight of FI and LI in internal activity threshold U ij ; θ ij represents the dynamic threshold, and Y is the timing pulse sequence defined by U ij and θ ij ; V θ and α θ denote the amplification coefficient and decay time of the dynamic threshold θ ij , respectively. Note that the connections of the FI should be slower than those of the LI. Intuitively, as shown in Figs. 1a and 1b Figs. 1a and 1b , the internal activity threshold U ij has a direct influence on the timing pulse sequence Y and Y can further influence the dynamic threshold θ ij . Meanwhile, the change in the dynamic threshold θ ij influences the state of the timing pulse sequence Y because Y is defined by U ij and <math id="M10"><mrow><msub><mi>θ</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow></math> together [ 26 26 ]. Regarding the ignition of a group of closely connected neurons, as shown in Fig. 1-c Fig. 1-c , the internal activity threshold U ij (or could be seen as the total input) and the dynamic threshold θ ij are simultaneously augmented by multiple pulses (external input S ij ). After the stimulation of multiple pulses, the growth rate of U ij begins to slow down while that of θ ij remains, which means that θ ij will eventually exceed U ij and reset occurs. For each neuron, the number of times U ij is greater than θ ij after stimulation by multiple pulses is defined as the ignition time, which is the value of the corresponding location of this neuron in the ignition map. 2.1.2 Implementation on n- γ discrimination 3 PCNN has a tremendous number of applications in image processing [ 26 26 ] but has never been used in the PSD field. Similar to the information contained in an image, the information contained in a pulse signal also has dynamic properties, which are essential to the discrimination process. The distinguished performance of the PCNN in processing dynamic information enables a computer to capture the dynamic characteristics of pulse signals and perform outstanding n- γ discrimination. Specifically, the major difference between neutron and gamma-ray signals is in the falling edge and delayed fluorescence and the detection process of this difference does not only concern the amplitude of each sampling point of the falling edge and afterglow effect peak but is also related to the changing rate of the amplitudes in these locations, which is the aforementioned dynamic information one wants to capture, used to discriminate neutron and gamma-ray signals. When the PCNN is applied in neutron and gamma-ray signal processing, the connection weight matrix M is a one-dimensional vector because the pulse signals of neutrons and gamma rays are one-dimensional. After implementing the PCNN on a pulse signal, an ignition map was obtained, i.e., a matrix with the same dimensions as the original signal. By summing up part of the ignition map that contains the information of a signal’s peak and falling edge, the neutrons and gamma rays can be discriminated. Notice that, unlike other commonly used neural networks, the PCNN requires no training process before the discrimination process, making its computational complexity and time consumption much less than other conventional neural networks. As shown in Fig. 3 Fig. 3 , the difference in the falling edge of neutrons and gamma rays is well detected by PCNN, exhibiting significant differences in the ignition maps of the n- γ signals. For the pulse signal of the gamma ray, the ignition times in the part of the falling edge decrease very quickly, which is attributed to the fast decay time of gamma-ray pulse signals. Conversely, the declining speed of the ignition times in the part of the falling edge is noticeably slower for the neutron signals than that of the gamma-ray pulses and the ignition times surge again when it comes to the part of delayed fluorescence. Consequently, by summing the ignition times of the partial ignition map that incorporates the rising edge, falling edge, and delayed fluorescence, the n- γ pulse signals could be well discriminated, granted that the sum of ignition times of neutron signals is distinctly larger than that of gamma-ray signals. 2.2 Back-propagation neural network 2 2.2.1 Model and mathematical expression 3 The back-propagation neural network (BPNN) is a product of artificial intelligence research based on the back-propagation algorithm, which is capable of learning from the examples fed to it [ 27 27 ]. Specifically, adapting the connection weights of the hidden neurons of the BPNN can provide an accurate approximation of the relationship between the training set and corresponding results; sometimes, even the aforementioned relationship is nonlinear [ 28 28 ]. With regard to the BPNN, the mathematical relationships between the inputs and outputs are not specified and the learning process has two steps: forward propagation of the signal and backward propagation of error. Specifically, when the output of the BPNN differentiates from the expected output, defined by the training set, the backward propagation stage begins to adjust the inherent relationships of the hidden node. Mathematically, the hidden node output model and output node output model are denoted as follows: <math display="block" id="M11"><mrow><msub><mi>O</mi><mi>j</mi></msub><mo>=</mo><mtext>h</mtext><mrow><mo>(</mo><mrow><mo>∑</mo><msub><mtext>W</mtext><mrow><mtext>ij</mtext></mrow></msub><mo>×</mo><msub><mtext>X</mtext><mtext>i</mtext></msub><mo>−</mo><msub><mtext>q</mtext><mtext>j</mtext></msub></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> <math display="block" id="M12"><mrow><msub><mtext>Y</mtext><mtext>k</mtext></msub><mo>=</mo><mtext>h</mtext><mrow><mo>(</mo><mrow><mo>∑</mo><msub><mi>T</mi><mrow><mi>j</mi><mi>k</mi></mrow></msub><mo>×</mo><msub><mi>O</mi><mi>j</mi></msub><mo>−</mo><msub><mi>q</mi><mi>k</mi></msub></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> Where X i denotes the input of the BPNN, O j represents the output of the hidden node, Y k denotes the output of the BPNN, h is a nonlinear function, W ij and T ik are weight matrices that are adjusted during backward propagation, and q represents the neural unit threshold. 2.2.2 Implementation on n- γ discrimination 3 In recent decades, back-propagation neural networks have been fully developed to address many civil engineering problems. The final objective of applying n- γ discrimination [ 29 29 , 30 30 ] is to determine the difference between neutron and gamma-ray pulse signals, by which an inherent relationship between a pulse signal and its category can be generalized and further used to discriminate the n- γ pulse signals fed to the BPNN in the future. To realize the aforementioned aim, the BPNN needs to be trained first using two sets of already well-discriminated neutron and gamma-ray pulse signals. In this training step, the BPNN tries to categorize the received pulse signals (the input patterns), with the recursive adjustment aided by the category results of each pulse signal (the output patterns). When the neural network has completed the training step, it can be used to process the test set and discriminate the pulse signals. However, there are a few drawbacks of n- γ discrimination based on BPNN. The training and test sets need to be highly similar and hence these sets cannot use different filtering methods and the pulse signals of these two sets need to be retrieved from the same radiation detection device and come from the same radiation source, with the same average energy. These disadvantages restrict the general application of BPNN for n- γ discrimination. 2.3 Fractal spectrum 2 The fractal spectrum method discriminates n- γ signals using fractal dimensions, which are the power spectra of signals [ 16 16 ]. Specifically, the spectrum of a signal needs to first be calculated and then the frequency of this signal and its spectrum should be presented logarithmically, retrieving an approximate linear relationship between the aforementioned operation results. Finally, a linear regression analysis is implemented to obtain regression coefficients, which can be further used to discriminate the n- γ signals. The mathematical interpretation of the fractal spectrum method is defined as: <math display="block" id="M13"><mrow><msub><mtext>F</mtext><mtext>D</mtext></msub><mrow><mo>(</mo><mtext>k</mtext><mo>)</mo></mrow><mo>=</mo><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mtext>j</mtext><mo>=</mo><mn>1</mn></mrow><mtext>N</mtext></munderover><mtext>D</mtext><mrow><mo>(</mo><mtext>j</mtext><mo>)</mo></mrow><msubsup><mtext>w</mtext><mtext>N</mtext><mrow><mrow><mo>(</mo><mrow><mtext>J</mtext><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mrow><mo>(</mo><mrow><mtext>K</mtext><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow></msubsup><mo>,</mo></mrow></math> <math display="block" id="M14"><mrow><msub><mtext>w</mtext><mtext>N</mtext></msub><mo>=</mo><msup><mtext>e</mtext><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mtext>πi</mtext></mrow><mo>)</mo></mrow><mo>/</mo><mtext>N</mtext></mrow></msup><mo>,</mo></mrow></math> <math display="block" id="M15"><mrow><msub><mtext>P</mtext><mrow><mtext>SS</mtext></mrow></msub><mo>=</mo><mfrac><mrow><msup><mrow><mrow><mo>|</mo><mrow><msub><mtext>F</mtext><mtext>D</mtext></msub><mrow><mo>(</mo><mtext>k</mtext><mo>)</mo></mrow></mrow><mo>|</mo></mrow></mrow><mn>2</mn></msup></mrow><mtext>N</mtext></mfrac><mo>,</mo><mtext> </mtext></mrow></math> <math display="block" id="M16"><mrow><mtext>G</mtext><mrow><mo>(</mo><mtext>w</mtext><mo>)</mo></mrow><mo>=</mo><mtext>G</mtext><mrow><mo>(</mo><mrow><msub><mtext>w</mtext><mn>0</mn></msub></mrow><mo>)</mo></mrow><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mtext>w</mtext><mrow><msub><mtext>w</mtext><mn>0</mn></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mtext>α</mtext></mrow></msup><mo>,</mo></mrow></math> Where D is the input data, N is the calculation length of the Fourier transform, F D is the data processed by the discrete Fourier transform, and P ss represents the power spectrum. Based on Eqs. (8), (9), and (10), the power spectral density function can be calculated. Then, the logarithm of this function is taken and further fitted by formula (11), where G ( w ) denotes the power spectral density of the signal, w 0 is the reference space frequency, w represents the spatial frequency, and G ( w 0 ) denotes the signal conversion coefficient. Finally, the fractal dimension is defined as follows: <math display="block" id="M17"><mrow><mi>D</mi><mi>i</mi><mi>m</mi><mo>=</mo><mn>2.5</mn><mo>−</mo><mi>α</mi><mo>.</mo></mrow></math> 2.4 Charge comparison 2 The charge comparison method [ 31 31 ] has become one of the most commonly used n- γ discrimination methods, which has a fine n- γ discrimination performance and consumes little time for simultaneous discrimination processing. With regard to its internal principle, owing to the different interaction characteristics between neutrons and gamma rays when they penetrate the plastic scintillator, the ratios of the slow component’s charge to the total charge are different for the pulse signals of neutrons and gamma rays. Based on the aforementioned characteristics, Hawkes et al. calculated the charge ratio R to discriminate n- γ signals [ 32 32 ], defined as follows: <math display="block" id="M18"><mrow><mtext>R</mtext><mo>=</mo><mfrac><mrow><msub><mtext>Q</mtext><mtext>N</mtext></msub></mrow><mrow><msub><mtext>Q</mtext><mtext>M</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> where Q N and Q M represent the summations of the pulse voltage of the slow component and the whole signal, respectively. As a result of the longer decay time and delayed fluorescence of neutrons, the R -value is larger than that of gamma rays. 2.5 Filtering methods 2 Inevitably, the pulse signals detected by the radiation detector always incorporate noise, which makes the difference between the pulse signals of neutrons and gamma rays much less significant. Thus, the performance of direct n- γ discrimination is affected by the useless noise, making the pre-processing of the pulse signals especially important. There are many preprocessing methods, also called filtering methods, which are commonly used in radiation detection, such as the Fourier transform [ 33 33 - 35 35 33-35 ], wavelet transform [ 36 36 - 38 38 36-38 ], Kalman filter [ 39 39 ], and sliding average filter [ 40 40 ]. A discrimination method shows different discrimination effects with different filtering methods; we have demonstrated in our previous work [ 17 17 ] that each discrimination method has the best-matched filtering method, with which it can achieve optimized performance. In the present work, the discussion mainly regards the performance of different discrimination methods; hence, only one is uniformly used as the filtering method for all discrimination methods. In this work, the Fourier transform is selected as the filtering method due to its generally good performance when coupled with most discrimination methods [ 17 17 ] and its common application in radiation detection. After implementing the Fourier transform, the pulse signal is transformed from the time domain to the frequency domain, where the low-amplitude frequency-domain information is the noise component. Filtering is realized by removing the noise component in the frequency domain and further taking the inverse Fourier transform to obtain the pulse signal back to the time domain. As a result of the discrete sampling process being required when the pulse signals are retrieved from the n- γ superposed field, the pulse signals are discrete; hence, a discrete Fourier transform (DFT) is required to filter the n - γ pulse signals. The mathematical transform formulas are as follows: <math display="block" id="M19"><mrow><mtext>G</mtext><mrow><mo>(</mo><mtext>u</mtext><mo>)</mo></mrow><mo>=</mo><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mtext>x</mtext><mo>=</mo><mn>1</mn></mrow><mtext>N</mtext></munderover><mtext>g</mtext><mrow><mo>(</mo><mtext>x</mtext><mo>)</mo></mrow><msup><mtext>e</mtext><mrow><mo>−</mo><mtext>i</mtext><mfrac><mrow><mn>2</mn><mtext>π</mtext></mrow><mtext>N</mtext></mfrac><mtext>xu</mtext></mrow></msup><mo>=</mo><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mtext>x</mtext><mo>=</mo><mn>1</mn></mrow><mtext>N</mtext></munderover><mtext>g</mtext><mrow><mo>(</mo><mtext>x</mtext><mo>)</mo></mrow><msubsup><mtext>ω</mtext><mtext>N</mtext><mrow><mtext>xu</mtext></mrow></msubsup><mtext>  </mtext><mrow><mo>(</mo><mrow><mtext>x</mtext><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mtext>N</mtext></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> <math display="block" id="M20"><mrow><mtext>g</mtext><mrow><mo>(</mo><mtext>x</mtext><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mtext>N</mtext></mfrac><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mtext>x</mtext><mo>=</mo><mn>1</mn></mrow><mtext>N</mtext></munderover><mtext>G</mtext><mrow><mo>(</mo><mtext>u</mtext><mo>)</mo></mrow><msup><mtext>e</mtext><mrow><mtext>i</mtext><mfrac><mrow><mn>2</mn><mtext>π</mtext></mrow><mtext>N</mtext></mfrac><mtext>xu</mtext></mrow></msup><mo>=</mo><mfrac><mn>1</mn><mtext>N</mtext></mfrac><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mrow><mtext>x</mtext><mo>=</mo><mn>1</mn></mrow><mtext>N</mtext></munderover><mtext>G</mtext><mrow><mo>(</mo><mtext>u</mtext><mo>)</mo></mrow><msubsup><mtext>ω</mtext><mtext>N</mtext><mrow><mo>−</mo><mtext>xu</mtext></mrow></msubsup><mtext>   </mtext><mrow><mo>(</mo><mrow><mtext>x</mtext><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mtext>N</mtext></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where Eq. (14) is the positive transform formula for the DFT, Eq. (15) is the inverse transform formula for the DFT, <math id="M21"><mrow><msub><mi>ω</mi><mi>N</mi></msub><mo>=</mo><msup><mi>e</mi><mrow><mrow><mo>(</mo><mrow><mo>−</mo><mn>2</mn><mi>π</mi><mi>i</mi></mrow><mo>)</mo></mrow><mo>/</mo><mi>N</mi></mrow></msup></mrow></math> denotes the frequency, G ( u ) represents the frequency-domain signal, g ( x ) denotes the time-domain signal, and <math id="M22"><mtext>N</mtext></math> is the length of a signal. 3 Evaluation criteria 1 To evaluate the performance of different n- γ discrimination methods, objective evaluation criteria need to be used, which are the discrimination time (the CPU time required to process all given pulse signals) and the figure of merit ( FoM ) in this work. Regarding calculation of the FoM -value, the histogram of counts of neutrons and gamma rays must be drawn after the discrimination process, as shown in Fig. 2 Fig. 2 . Then, the mathematical formula of FoM [ 41 41 ] is given as follows: <math display="block" id="M23"><mrow><mtext>FoM</mtext><mo>=</mo><mfrac><mtext>S</mtext><mrow><msub><mrow><mtext>FWHM</mtext></mrow><mtext>n</mtext></msub><mo>+</mo><msub><mrow><mtext>FWHM</mtext></mrow><mtext>γ</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> where <math id="M24"><mtext>S</mtext></math> denotes the distance between the neutron count and gamma-ray count peaks, FWHM n and FWHM γ are the half-height widths of the neutron counting peak and gamma-ray counting peak, respectively, estimated by Gaussian fitting. A larger FoM -value corresponds to a better discrimination effect. 4 Experiment 1 4.1 Parameter settings 2 4.1.1 PCNN 3 The parameters of the PCNN are set as: n =180, α F =0.32, α L =0.356, α θ =0.08, V F =0.0005, V L =0.0005, V θ =15, and linking weight M =[0.1409,0,0.1409]. The n- γ signals processed by the PCNN using the aforementioned parameters are shown in Fig. 3b Fig. 3b . The ignition maps of pulse signals between 10 ns before the peak and 20 ns after the peak were selected as the discrimination intervals. 4.1.2 Other methods 3 To train the BPNN, 11,454 well-discriminated and low-noise signals were selected as the training set. There are two hidden layers of the BPNN used in our work, each of which has nine neurons. The entire training process took approximately 0.2 s, which is included in the total time consumption of BPNN in Table 1 Table 1 . With regard to the fractal spectrum method, the pulse signals from 38 – 130 ns after the peak were chosen as the discrimination interval. In the charge comparison method, the total component is composed of pulse signals between 15 ns before the peak and 200 ns after the peak and the slow component incorporates pulse signals between T and 200 ns after the peak. T is delay time, i.e., a parameter between 155 ns and 185 ns that affects the FoM -value of the charge comparison method. The abovementioned parameters of these three methods were optimized in our previous work [ 17 17 ]. 1 1 Discrimination method 1 1 Charge comparison 1 1 BPNN 1 1 Fractal spectrum 1 1 PCNN 1 1 Discrimination time 1 1 1.96 s 1 1 3.65 s 1 1 178.01 s 1 1 2.22 s 1 1 Discrimination effect ( FoM ) 1 1 1.351 1 1 0.989 1 1 1.028 1 1 1.709 4.2 Experimental results and discussions 2 4.2.1 Pulse signals of neutrons and gamma-rays 3 In this work, a 241 Am-Be isotope neutron source was used to generate the n- <math id="M26"><mi>γ</mi></math> superposed field, with an average energy of 4.5 <math id="M27"><mrow><mtext>MeV</mtext></mrow></math> . The detection equipment was composed of two parts: an EJ299-33 plastic scintillator and a digital oscilloscope with a 500 <math id="M28"><mrow><mtext>mV</mtext></mrow></math> trigger threshold (which corresponds to an energy of approximately 1.6 <math id="M29"><mrow><mtext>MeVee</mtext></mrow></math> , where 1 <math id="M30"><mrow><mtext>MeVee</mtext></mrow></math> (i.e., <math id="M31"><mrow><mtext>MeV</mtext></mrow></math> electron equivalent) is defined as the amount of energy converted to light induced by an electron, which deposits 1 <math id="M32"><mrow><mtext>MeV</mtext></mrow></math> in the scintillator), a 200 <math id="M33"><mrow><mtext>MHz</mtext></mrow></math> bandwidth, and a 1 <math id="M34"><mrow><mtext>GS</mtext><mo>/</mo><mtext>s</mtext></mrow></math> sampling rate. Based on this setup, 9414 pulse signals were retrieved. A comparison of the normalized neutron and gamma-ray signals that we retrieved is shown in Fig. 3a Fig. 3a . It can be seen that the rise speeds of both signals are similar, while the luminous attenuation rate of the neutron is noticeably slower than that of gamma rays; this is attributed to its longer decay time and delayed fluorescence [ 42 42 ]. 4.2.2 Discrimination results 3 The 9414 n- γ pulse signals were filtered by the Fourier transform [ 34 34 ] and then discriminated by the aforementioned meth ods (processed on an AMD R9-5900X CPU); the results are shown in Figs. 4 Figs. 4 and 5 5 . Figure 4 Figure 4 shows the scatter plot of pulse signals discriminated by different methods, where the dots above the crossing line are discriminated as neutron signals and the dots below the crossing line are discriminated as gamma-ray signals. For a good discrimination result, the group of neutron dots and the group of gamma-ray dots should be separated and each group should be distributed as centrally as possible while maintaining a good Gaussian distribution at the same time. It can be clearly seen that the PCNN method noticeably outperforms the others, with a clear gap between the neutron and gamma-ray dots. Meanwhile, both groups were centrally distributed, with very few dots located between the two groups or discrete on the outer sides. Figure 5 Figure 5 shows the Gaussian fitting of the histogram of the four methods. The discrimination effect is reflected in two aspects: (i) the length of the gap between the two peaks and (ii) the shape of the two peaks. A wider gap corresponds to better discrimination. The narrower and higher neutron peak (on the right side) and gamma peak (on the left side) represent better discrimination performance. As shown in Fig. 5 Fig. 5 , the fitting curve of the PCNN method exhibits better performance than that of the other methods, with a longer distance between neutrons and gamma-ray counting peaks and has narrower and higher n- γ counting peaks. To quantitatively evaluate the performance of these methods, the FoM -value of their discrimination results were calculated, as presented in Table 1 Table 1 , along with the discrimination time (for the processing time of the 9414 pulse signals) of each method. Table 1 Table 1 demonstrates that our proposed method significantly outperforms the others, with a 26.49% improvement in the FoM -value compared to the charge comparison method, a 72.80% improvement compared to the BPNN, and a 66.24% improvement compared to the fractal spectrum method. This outstanding discrimination performance of the proposed method is because the PCNN is not based on every single point of a fixed vector of the input signal, as in other methods. In contrast, the PCNN not only considers the amplitude of a point but also the amplitudes of points before and after this location; i.e., the PCNN treats the input signal as a whole for analysis and processing, imparting an excellent anti-noise effect and the ability to process the dynamic information contained in a pulse signal. In addition, the discrimination time of our proposed method is quite satisfactory (2.22 s), taking slightly longer than the charge comparison method (1.96 s) and outperforming the BPNN (3.65 s) and fractal spectrum method (178.01 s). As a neural network, the PCNN takes such a short time compared to the BPNN and the fractal spectrum is attributed to its simple computational complexity, with fewer matrix operations compared to the fractal spectrum and without the need for a pre-training step compared to the BPNN. This experimental result shows that the PCNN has the potential to be implemented in real-time applications. 5 Conclusion 1 In this work, a PCNN-based n- γ discrimination method is proposed and compared with the other three methods, including the BPNN, fractal spectrum method, and charge comparison method. Our experiment was conducted on the data of an EJ299-33 plastic scintillator, by which 9414 n- γ pulse signals were retrieved and further processed on an AMD R9-5900X CPU. The experimental results show that our proposed method significantly outperforms the others, with the best FoM -value and short discrimination time. Specifically, the PCNN demonstrates a 26.49% improvement in the FoM -value compared to the charge comparison method, a 72.80% improvement compared to the BPNN, a 66.24% improvement compared to the fractal spectrum method, and the second-fastest discrimination time of 2.22 s. This outstanding performance is because the PCNN treats the input signal as a whole for analysis and processing, imparting an excellent anti-noise effect and the ability to process the dynamic information contained in a pulse signal. This short discrimination time of the PCNN is due to its simple computational complexity, with few matrix operations and without the need for a pre-training step. The distinguished n- γ discrimination effect of the PCNN enables broad application prospects in the radiation detection field and its relatively short discrimination time makes it potentially useful for real-time discrimination. To the best of our knowledge, this is the first report on applying a pulse-coupled neural network for n- γ discrimination. In our future work, we will verify the feasibility of other improved PCNN models, aiming to achieve an even better discrimination effect and shorter discrimination time. References D.D. Zhou , S.M. You , J. Xin et al ., Development of a 4π phoswich detector for measuring radioactive inert gases . Nuclear Techniques 43 , 050401 ( 2020 ). doi: 10.11889/j.0253-3219.2020.hjs.43.050401 http://doi.org/10.11889/j.0253-3219.2020.hjs.43.050401 (in Chinese) Development of a 4π phoswich detector for measuring radioactive inert gases X. Zhang , X. Yuan , X.F. Xie et al ., A digital delay-line-shaping method for pulse shape discrimination in stilbene neutron detector and application to fusion neutron measurement at HL-2A tokamak . Nucl. Instrum. Meth. Phys. A 687 , 7 - 13 ( 2012 ). doi: 10.1016/j.nima.2012.05.077 http://doi.org/10.1016/j.nima.2012.05.077 A digital delay-line-shaping method for pulse shape discrimination in stilbene neutron detector and application to fusion neutron measurement at HL-2A tokamak Y. Sun , G.L. Liu , X.L. Luo , Near space neutron environment and detection . National Defense Science and Technology 35 , 24 - 28 ( 2014 ). doi: 10.3969/j.issn.1671-4547.2014.01.007 http://doi.org/10.3969/j.issn.1671-4547.2014.01.007 (in Chinese) Near space neutron environment and detection M.P. Blakeley , S.C.M. Teixeira , I. Petit-Haertlein et al , Neutron macromolecular crystallography with LADI-III . Acta Cryst. D 66 , 1198 - 1205 ( 2010 ). doi: 10.1107/S0907444910019797 http://doi.org/10.1107/S0907444910019797 Neutron macromolecular crystallography with LADI-III A. El-Taher , Rare earth elements content in geological samples from eastern desert, Egypt, determined by instrumental neutron activation analysis . Appl. Radiat. Isotopes 68 ( 9 ), 1859 - 1863 ( 2010 ). doi: 10.1016/j.apradiso.2010.02.012 http://doi.org/10.1016/j.apradiso.2010.02.012 Rare earth elements content in geological samples from eastern desert, Egypt, determined by instrumental neutron activation analysis G. Tosi , A. Torresin , S. Agosteo et al ., Neutron measurements around medical electron accelerators by active and passive detection techniques . Med. Phys. 18 ( 1 ), 54 ( 1991 ). doi: 10.1118/1.596751 http://doi.org/10.1118/1.596751 Neutron measurements around medical electron accelerators by active and passive detection techniques W.J. Guo , X.M. Wu , J. Wang , Preliminary study of neutron (waterice) detector on moon and mars . Spacecraft Engineering , 19 ( 05 ) 64 - 69 ( 2010 ). https://en.cnki.com.cn/Article_en/CJFDTOTAL-HTGC201005016.htm https://en.cnki.com.cn/Article_en/CJFDTOTAL-HTGC201005016.htm (in Chinese) Preliminary study of neutron (waterice) detector on moon and mars F.D. Brooks , Development of organic scintillators . Nucl. Instrum. Methods , 162 ( 1-3 ) 477 - 505 ( 1979 ). doi: 10.1016/0029-554X(79)90729-8 http://doi.org/10.1016/0029-554X(79)90729-8 Development of organic scintillators D. Cester , M. Lunardon , G. Nebbia et al ., Pulse shape discrimination with fast digitizers . Nucl. Instrum. Meth. Phys. A 748 , 33 - 38 ( 2014 ). doi: 10.1016/j.nima.2014.02.032 http://doi.org/10.1016/j.nima.2014.02.032 Pulse shape discrimination with fast digitizers M.L. Roush , M.A. Wilson , and W.F. Hornyak , Pulse shape discrimination , 31 ( 1 ), 112 - 124 ( 1964 ). doi: 10.1016/0029-554X(64)90333-7 http://doi.org/10.1016/0029-554X(64)90333-7 Pulse shape discrimination C. Frangville , A. Grabowski , J. Dumazert et al ., Nanoparticles-loaded plastic scintillators for fast/thermal neutrons/gamma discrimination: Simulation and results . Nucl. Instrum. Meth. Phys. A 942 , 162370 ( 2019 ). doi: 10.1016/j.nima.2019.162370 http://doi.org/10.1016/j.nima.2019.162370 Nanoparticles-loaded plastic scintillators for fast/thermal neutrons/gamma discrimination: Simulation and results R. Coulon , V. Kondrasovs , Q. Lecomte et al ., Multilayer phoswich scintillators for neutron/gamma discrimination . Radiat. Meas. 117 , 57 - 62 ( 2018 ). doi: 10.1016/j.radmeas.2018.07.011 http://doi.org/10.1016/j.radmeas.2018.07.011 Multilayer phoswich scintillators for neutron/gamma discrimination F.D. Brooks , R.W. Pringle , B.L. Funt , Pulse shape discrimination in a plastic scintillator . IRE T. Nucl. Sci. 7 , 35 - 38 ( 1960 ). doi: 10.1109/TNS2.1960.4315733 http://doi.org/10.1109/TNS2.1960.4315733 Pulse shape discrimination in a plastic scintillator P. Blanc , M. Hamel , L. Rocha et al ., Study and understanding of n/γ discrimination in organic plastic scintillators . in 2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC) , 1978 - 1982 ( 2012 ). doi: 10.1109/nssmic.2012.6551457 http://doi.org/10.1109/nssmic.2012.6551457 Study and understanding of n/γ discrimination in organic plastic scintillators N. Zaitseva , B.L. Rupert , I. PaweŁczak et al ., Plastic scintillators with efficient neutron/gamma pulse shape discrimination . Nucl. Instrum. Meth. Phys. A 668 , 88 - 93 ( 2012 ). doi: 10.1016/j.nima.2011.11.071 http://doi.org/10.1016/j.nima.2011.11.071 Plastic scintillators with efficient neutron/gamma pulse shape discrimination M.Z. Liu , B.Q. Liu , Z. Zuo et al ., Toward a fractal spectrum approach for neutron and gamma pulse shape discrimination . Chinese Phys. C 40 , 066201 ( 2016 ). https://sci-hub.mksa.top/10.1088/1674-1137/40/6/066201 https://sci-hub.mksa.top/10.1088/1674-1137/40/6/066201 Toward a fractal spectrum approach for neutron and gamma pulse shape discrimination Z. Zuo , H.R. Liu , Y.C. Yan et al ., Adaptability of n–γ discrimination and filtering methods based on plastic scintillation . Nucl. Sci. Tech. 32 , 28 ( 2021 ). doi: 10.1007/s41365-021-00865-3 http://doi.org/10.1007/s41365-021-00865-3 Adaptability of n–γ discrimination and filtering methods based on plastic scintillation C.X. Zhang , S.T. Lin , J.L. Zhao et al ., Discrimination of neutrons and γ-rays in liquid scintillator based on Elman neural network . Chinese Physics C , 40 ( 8 ), 086204 ( 2016 ). doi: 10.1088/1674-1137/40/8/086204 http://doi.org/10.1088/1674-1137/40/8/086204 Discrimination of neutrons and γ-rays in liquid scintillator based on Elman neural network J. Iwanowska-Hanke , M. Moszynski , L. Swiderski et al ., Comparative study of large samples (2" × 2") plastic scintillators and EJ309 liquid with pulse shape discrimination (PSD) capabilities . J. Instrum. 9 ( 6 ), P06014 ( 2014 ). doi: 10.1088/1748-0221/9/06/P06014 http://doi.org/10.1088/1748-0221/9/06/P06014 Comparative study of large samples (2" × 2") plastic scintillators and EJ309 liquid with pulse shape discrimination (PSD) capabilities R. Eckhorn , H. J. Reitboeck , M. Arndt et al ., Feature linking via synchronization among distributed assemblies: simulations of results from cat visual cortex . Neural Comput. 2 ( 3 ): 293 - 307 ( 1990 ). doi: 10.1162/neco.1990.2.3.293 http://doi.org/10.1162/neco.1990.2.3.293 Feature linking via synchronization among distributed assemblies: simulations of results from cat visual cortex R. Eckhorn , H.J. Reitbock , M. Arndt et al ., A neural network for feature linking via synchronous activity: Results from cat visual cortex and from simulations . in Rodney M. J. Cotterill (ed.), Models of Brain Function , Cambridge University Press , pp. 255 - 272 ( 1989 ). https://philpapers.org/rec/ECKANN https://philpapers.org/rec/ECKANN A neural network for feature linking via synchronous activity: Results from cat visual cortex and from simulations C.M. Gray , W. Singer , Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex . P. Natl. Acad. Sci. USA 86 ( 5 ), 1698 - 1702 ( 1989 ). doi: 10.1073/pnas.86.5.1698 http://doi.org/10.1073/pnas.86.5.1698 Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex H. J. Reitboeck , R. Eckhorn , M. Arndt et al ., A model of feature linking via correlated neural activity . In: H. Haken , M. Stadler (eds) Synergetics of Cognition . Springer Series in Synergetics , vol 45 . Springer, Berlin, Heidelberg . doi: 10.1007/978-3-642-48779-8_7 http://doi.org/10.1007/978-3-642-48779-8_7 A model of feature linking via correlated neural activity H.S. Ranganath , G. Kuntimad , J.L. Johnson , Pulse coupled neural networks for image processing . Proceedings IEEE Southeastcon '95. Visualize the Future , 1995 , pp. 37 - 43 . doi: 10.1109/SECON.1995.513053 http://doi.org/10.1109/SECON.1995.513053 Pulse coupled neural networks for image processing J.L. Johnson , M.L. Padgett , PCNN models and applications . IEEE T. Neural Networks 10 ( 3 ), 480 - 498 ( 1999 ). doi: 10.1109/72.761706 http://doi.org/10.1109/72.761706 PCNN models and applications J. L. Johnson , H. Ranganath , G. Kuntimad et al , Pulse-coupled neural networks, Neural Networks and Pattern Recognition , O. Omidvar and J. Dayhoff , Eds. San Diego, CA : Academic ( 1998 ). doi: 10.1016/B978-012526420-4/50002-1 http://doi.org/10.1016/B978-012526420-4/50002-1 Pulse-coupled neural networks, Neural Networks and Pattern Recognition A.T.C. Goh , Back-propagation neural networks for modeling complex systems . Artif. Intell. Eng. 9 , 143 - 151 ( 1995 ). doi: 10.1016/0954-1810(94)00011-S http://doi.org/10.1016/0954-1810(94)00011-S Back-propagation neural networks for modeling complex systems K. Hornik , Approximation capabilities of multilayer feedforward networks . Neural Networks , 4 ( 2 ), 251 - 257 ( 1991 ). doi: 10.1016/0893-6080(91)90009-t http://doi.org/10.1016/0893-6080(91)90009-t Approximation capabilities of multilayer feedforward networks B. Esposito , L. Fortuno , A. Rizo , Neural neutron/gamma discrimination in organic scintillators for fusion applications . Proceedings of the 2004 IEEE International Joint Conference on Neural Networks , Budapest, Hungary , July 25-29, 2004 , vol. 4 , pp. 2931 - 2936 ( 2004 ). doi: 10.1109/IJCNN.2004.1381130 http://doi.org/10.1109/IJCNN.2004.1381130 Neural neutron/gamma discrimination in organic scintillators for fusion applications E. Ronchi , P. A. Soderstrom , J. Nyberg et al , An artificial neural network based neutron-gamma discrimination and pile-up rejection framework for the BC-501 scintillation detector . Nucl. Instrum. Meth. Phys. A 610 , 534 - 539 ( 2009 ). doi: 10.1016/j.nima.2009.08.064 http://doi.org/10.1016/j.nima.2009.08.064 An artificial neural network based neutron-gamma discrimination and pile-up rejection framework for the BC-501 scintillation detector D. Wolski , M. Moszyński , T. Ludziejewski et al ., Comparison of n-γ discrimination by zero-crossing and digital charge comparison methods . 360 ( 3 ), 584 - 592 ( 1995 ). doi: 10.1016/0168-9002(95)00037-2 http://doi.org/10.1016/0168-9002(95)00037-2 Comparison of n-γ discrimination by zero-crossing and digital charge comparison methods N.P. Hawkes , K.A.A. Gamage , G.C. Taylor , Digital approaches to field neutron spectrometry . Radiat. Meas. 45 ( 10 ), 1305 - 1308 ( 2010 ). doi: 10.1016/j.radmeas.2010.06.043 http://doi.org/10.1016/j.radmeas.2010.06.043 Digital approaches to field neutron spectrometry K. Yang , P.R. Menge , V. Ouspenski , Enhanced α-γ discrimination in co-doped LaBr3:Ce , 2014 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) , 2014 , pp. 1 - 5 ( 2014 ). doi: 10.1109/NSSMIC.2014.7431223 http://doi.org/10.1109/NSSMIC.2014.7431223 Enhanced α-γ discrimination in co-doped LaBr3:Ce J. Allem , Short term spectral analysis, synthesis, and modification by discrete Fourier transform . 25 ( 3 ), 235 - 238 ( 1997 ). doi: 10.1109/TASSP.1977.1162950 http://doi.org/10.1109/TASSP.1977.1162950 Short term spectral analysis, synthesis, and modification by discrete Fourier transform T.G. Payne , A.D. Southam , T.N. Arvanitis et al ., A signal filtering method for improved quantification and noise discrimination in Fourier transform ion cyclotron resonance mass spectrometry-based metabolomics data . J. Am. Soc. Mass Spectrom. 20 , 1087 - 1095 ( 2009 ). doi: 10.1016/j.jasms.2009.02.001 http://doi.org/10.1016/j.jasms.2009.02.001 A signal filtering method for improved quantification and noise discrimination in Fourier transform ion cyclotron resonance mass spectrometry-based metabolomics data S. Yousefi , L. Lucchese , M.D. Aspinall , Digital discrimination of neutrons and gamma-rays in liquid scintillators using wavelets . Nucl. Instrum. Meth. A 598 , 551 - 555 ( 2009 ). doi: 10.1016/j.nima.2008.09.028 http://doi.org/10.1016/j.nima.2008.09.028 Digital discrimination of neutrons and gamma-rays in liquid scintillators using wavelets S. Hosur , A.H. Tewfik , Wavelet transform domain adaptive FIR filtering . IEEE Trans. Signal Process. 45 , 617 - 630 ( 1997 ). doi: 10.1109/78.558477 http://doi.org/10.1109/78.558477 Wavelet transform domain adaptive FIR filtering H. Singh , R. Mehra , Discrete wavelet transform method for high flux n-c discrimination with liquid scintillators . IEEE Trans. Nucl. Sci. 64 , 1 - 7 ( 2017 ). doi: 10.1109/TNS.2017.2708602 http://doi.org/10.1109/TNS.2017.2708602 Discrete wavelet transform method for high flux n-c discrimination with liquid scintillators J.A. Burns , E.M. Cliff , C. Rautenberg , A distributed parameter control approach to optimal filtering and smoothing with mobile sensor networks . 2009 17th Mediterranean Conference on Control and Automation , 2009 , pp. 181 - 186 . doi: 10.1109/MED.2009.5164536 http://doi.org/10.1109/MED.2009.5164536 A distributed parameter control approach to optimal filtering and smoothing with mobile sensor networks Y. Zheng , S. Chen , W. Tan et al ., Detection of tissue harmonic motion induced by ultrasonic radiation force using pulse-echo ultrasound and a Kalman filter . IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54 , 290 - 300 ( 2007 ). doi: 10.1109/TUFFC.2007.243 http://doi.org/10.1109/TUFFC.2007.243 Detection of tissue harmonic motion induced by ultrasonic radiation force using pulse-echo ultrasound and a Kalman filter R.A. Winyard , J.E. Lutkin , G.W. McBeth , Pulse shape discrimination in inorganic and organic scintillators. I . Nucl. Instrum. Meth. 95 ( 1 ), 141 - 153 ( 1971 ). doi: 10.1016/0029-554X(71)90054-1 http://doi.org/10.1016/0029-554X(71)90054-1 Pulse shape discrimination in inorganic and organic scintillators. I B. D’Mellow , M.D. Aspinall , R.O. Mackin et al ., Digital discrimination of neutrons and γ-rays in liquid scintillators using pulse gradient analysis . Nucl. Instrum. Meth. Phys. A 578 ( 1 ) 191 - 197 ( 2007 ). doi: 10.1016/j.nima.2007.04.174 http://doi.org/10.1016/j.nima.2007.04.174 Digital discrimination of neutrons and γ-rays in liquid scintillators using pulse gradient analysis All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Hao-Ran Liu, Yu-Xin Cheng, Zhuo Zuo, Tian-Tian Sun and Kai-Min Wang. The first draft of the manuscript was written by Hao-Ran Liu, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. 10.1007/s41365-021-00915-w This work was supported by the Key Science and Technology projects of Leshan (No. 19SZD117) and the Sichuan Science and Technology Program (No. 2021JDRC0108). 2021-04-19 2021-05-17 2021-05-22 2021-08-05 2021-08-01 2021-09-07 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2021 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-021-00915-w http://dx.doi.org/10.1007/s41365-021-00915-w . 2021 Nuclear Science and Techniques 08 32