基于高斯锐化法的重叠峰分解方法研究

在放射性能谱测量中，由于探测器分辨率较低、待测样品中原子能级相近，往往会出现全能峰的重叠现象，对放射性核素的定性或定量检测带来较大的困难；常规的分离算法一般需要复杂的谱变换或大量的标准谱样本，不适用于现场测量中重叠峰的实时分解。因此，提出一种基于高斯锐化法的能谱重叠峰解析方法(GSM)，结合峰锐化法的分辨率增强能力和褶积滑动变换法的平滑特性，可快速地识别、定位和解析γ能谱中的重叠峰。该方法首先对高斯函数进行锐化并做归一化处理，并以此作为变换算子，选择合适的高斯参数及窗宽度，通过对原始γ能谱数据进行褶积滑动变换，达到滤波和提高重叠峰分离度的目的；然后求解GSM成形处理后的谱线近似函数作为目标函数，并选取峰位中心附近若干点作为初始参数，最后以非线性拟合的方法进行重叠峰特征峰参数的解析。实验中，首先验证了该方法变换前后峰位、峰面积特征值的不变性，其次分别对重叠峰能谱段以及MCNP模拟的131I，137Cs，214Bi，206Bi和26Al混合放射源γ能谱进行方法验证。实验结果表明，该方法对于分离度大于0.375、信噪比大于40 dB的重叠峰具有较好分解效果，分解前后的峰位和峰面积的相对误差分别在1%和4.5%以内；对于γ能谱进行全谱解析后，重叠峰的峰位分离相对误差在1%以内，单峰的分离相对误差约为0.1%以内，且当变换算子的半宽度接近探测器能量分辨率时，重叠峰的分解结果更准确。该方法具备较好的噪声抑制性能，在全谱解析中无需进行能谱光滑及本底扣除等谱线预处理操作，且计算资源耗费少，分解精确度较高，便于能谱测量系统的嵌入式实时解谱应用，对放射性测量中能谱的现场快速解析具有实用性。

Research on a Decomposing Method of Energy Spectrum Overlapping Peaks Based on Gaussian Sharpening Method

In the measurement of the radioactivity energy spectrum, due to the low resolution of the detector, the similarity of the atomic energy level in the sample to be tested, and the limitation of the instrument stripping technology, the overlapping phenomenon of full energy peak often occurs, which brings great difficulties to the qualitative or quantitative detection of radionuclides. Conventional separation algorithms generally require complex spectrum transformation or a large number of standard spectrum samples and are not suitable for real-time decomposition of overlapping peaks at on-site of measurement. Therefore, a decomposition method of energy spectrum overlapping peaks based on the Gaussian sharpening method (GSM) is proposed, combining the resolution enhancement capability of the peak sharpening method and the smoothing characteristics of the convolution sliding transformation method, which can quickly identify, locate and resolve overlapping peaks in the γ energy spectrum. Firstly, the Gaussian function is sharpened and normalized and selected the appropriate Gaussian parameters and window width, used as a transformation operator to filter and improve the separation of overlapping peaks through convolution and sliding transformation of the original γ energy spectrum data. Then, the approximate function of the energy spectrum after GSM shaping is solved as the objective function, and several points near the center of the peak position are selected as initial parameters. Finally, the analysis of the characteristic peak parameters of the overlapping peaks is carried out by the method of nonlinear fitting. In the experiment, we first verified the invariance of the peak position and peak area eigenvalues before and after GSM shaping, and then the GSM was verified in the overlapping peak energy spectrum and the MCNP simulated131I, 137Cs, 214Bi, 206Bi and 26Al mixed radioactive source γ energy spectrum. The experimental results show that GSM has great decomposition ability for the overlapping peak with the resolution better than 0.375 and the SNR better than 40 dB, the relative errors of the peak position and peak area before and after decomposition are within 1% and 4.5%, respectively; For the GSM-processed energy spectrum of γ-ray, the relative error of the position of the overlapping peak is within 1% and that of the single peak is within 0.1%, furthermore, the decomposition result will be more accurate if the half-width in the transformation operator is set close to the energy resolution of the detector. GSM is noise-immune and does not require pre-processing operations such as spectrum smoothing and background subtraction in full-spectrum analysis. Besides, it consumes less computing resources and has high-resolution accuracy, which is convenient for embedded real-time spectrum analysis of energy spectrum measurement system and has practicability for quick on-site analysis of energy spectrum in radioactive measurement.