Segment-smoothed Bayesian iterative method to reconstruct pulsed X-ray spectrum
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摘要: 吸收法测量脉冲X射线能谱时，测量数据的微小扰动会引起重建能谱的较大波动，甚至出现不符合物理规律的负值。针对测量数据的噪声对脉冲X射线重建能谱影响较大的问题，构建了重建能谱准确性的评估方法，分析了贝叶斯迭代法对包含不同程度噪声干扰的测量数据重建能谱的准确性。通过在贝叶斯迭代法中加入平滑约束条件的方式，降低了噪声对重建能谱的影响。根据预估待测能谱的特征，提出了以能谱峰值为界分段平滑的方法，比较了整体平滑和分段平滑方法的能谱重建效果。多次求解表明，分段平滑贝叶斯迭代法的重建能谱对噪声的敏感度显著下降。设计了基于吸收法的能谱测量系统，分别利用平滑前后的贝叶斯迭代法依据实验测量数据重建能谱，结果表明，分段平滑的贝叶斯迭代法的重建能谱更接近理论能谱，重建效果更好。Abstract: Minor discrepancies in the measurement data may lead to significant variations in the reconstructed spectrum when measuring and reconstructing the spectrum by the absorption method. In some cases, the reconstructed spectrum may contain negative values that do not conform to the physical law. To address the issue that noise in the measurement data has a significant effect on the reconstructed spectrum, the segment-smoothed Bayesian iterative method is proposed in this paper. The energy spectrum is reconstructed using the Bayesian iteration method under different levels of noise, and the accuracy and noise sensitivity of the reconstructed spectrum are evaluated. An optimization method, which adds smoothing constraints to the Bayesian iterative method, is proposed to reduce noise interference in the reconstructed spectrum. According to the spectrum characteristics, a two-coefficient segment-smoothing method is proposed with the peak value as the dividing line. The spectrum is reconstructed by segmented smoothing and global smoothing Bayesian iterative methods, respectively. The noise sensitivity of the reconstructed spectrum, unfolded by the segment-smoothed Bayesian iterative method, has been significantly reduced. An energy spectrometer based on the absorption method is developed. The spectrum is reconstructed based on the experimental data using the segment-smoothed Bayesian iterative method and the Bayesian iteration method. The spectrum reconstructed using the segment-smoothed Bayesian iterative method is more consistent with the theoretical spectrum, indicating that this method exhibits superior performance.
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图 2 不同能量的光子在探测器上的能量沉积
Figure 2. Energy deposition of different energy photons on the detector
图 3 贝叶斯迭代法在三种初始谱下的重建能谱
Figure 3. X-ray spectra unfolded from three initial spectra by the Bayesian iterative method
图 4 贝叶斯迭代法在三种水平噪声扰动下100次重建能谱（图中每条彩色实线代表1次能谱重建结果）
Figure 4. 100 reconstructed spectra unfolded with the Bayesian iterative method under three noise levels
图 5 平滑前后的贝叶斯迭代法重建能谱误差
Figure 5. Average error of the spectrum reconstructed using smoothed and unsmoothed Bayesian iterative methods
图 6 分段平滑的贝叶斯迭代法对包含3种噪声水平测量数据的100次重建能谱（图中每条彩色实线代表1次能谱重建结果）
Figure 6. 100 reconstructed spectra unfolded with the segmented smoothing Bayesian iterative method under three noise levels
图 8 依据实验波形的重建能谱
Figure 8. Pulsed X-ray spectra reconstructed based on experimental waveforms
表 1 四种噪声扰动下贝叶斯迭代法重建能谱的平均误差
Table 1. Average error of the spectrum reconstructed using the Bayesian iterative method, disturbed by four types of noise
noise type average error of the reconstructed spectrum $ \overline{ \left\| \Delta\mathit{\boldsymbol{\Phi\boldsymbol{ }}} \right\| _2} $ 1% noise level 5% noise level 10% noise level measurement system noise 0.68 1.10 1.53 photon scattering noise 0.68 1.02 1.42 environmental noise 0.65 0.81 1.01 absorption foil thickness error 0.66 0.87 1.31 
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表 2 不同平滑系数在测量系统底噪扰动下重建能谱的平均误差
Table 2. Average error of the spectrum reconstructed with different smoothing coefficients, disturbed by measurement system noise
reconstructed method average error of the reconstructed spectrum $ \overline{ \left\| \Delta\mathit{\boldsymbol{\Phi}} \right\| _2} $ 1% noise level 5% noise level 10% noise level segment smooth 0.748 0.752 0.763 smoothing coefficient s2=0.05 0.777 0.781 0.825 smoothing coefficient s2=0.2 0.740 0.754 0.812
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