基于压缩感知理论的非线性γ谱分析方法

冯丙辰; 方晟; 张立国; 李红; 童节娟; 李文茜

doi:10.7498/aps.62.112901

摘要

γ谱分析是一种重要的放射性核素定量分析方法. 弱峰的检测和重叠峰的分解是γ 谱分析中的难点. 为了解决这两个问题, 基于压缩感知理论, 提出了一种新的γ 谱分析方法. 这一方法从谱仪对γ 谱调制的物理机理出发, 通过数学建模, 将γ 谱分析转化为一个以真实γ 谱为解的求逆问题, 并在压缩感知理论框架下, 运用γ 谱特征峰的稀疏性, 进行逆问题的求解, 直接获得γ 谱的估计结果. 数值模拟结果和蒙特卡洛模拟结果表明: 该方法能在降低统计涨落的同时, 有效减小谱仪调制带来的能谱展宽, 从而提高γ 谱分析精度.

关键词:

Abstract

The gamma-ray spectrum analysis is an important method for quantitative analysis of radionuclide. Although widely used, the weak peak identification and overlapping peaks resolution are still difficult for gamma-ray spectrum analysis. To solve the problem, a new method based on compressed sensing is proposed for improving gamma-ray spectrum analysis in this paper. The proposed method models physical modulation of gamma spectrometer as a linear equation, and formulates the gamma-ray spectrum analysis as a corresponding inverse problem. The true gamma spectrum is obtained by solving the inverse problem by applying sparsity constraint under the framework of compressed sensing. The feasibility of the proposed method is demonstrated by both numerical simulation and Monte Carlo simulation experiments. Results demonstrate that the proposed method can simultaneously resolve overlapped peaks and reduce the fluctuations of gamma-ray spectrum, effectively improving the accuracy of gamma-ray spectrum analysis.

Keywords:

作者及机构信息

1.
清华大学核能与新能源技术研究院, 北京 100084

基金项目: 国家自然科学基金 (批准号: 81101030) 资助的课题.

Authors and contacts

1.
Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 10084, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 81101030).

参考文献

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[6]	Bai X, Li Y Q, Zhao S M 2013 Acta Phys. Sin. 62 044209 (in Chinese) [白旭, 李永强, 赵生妹 2013 物理学报 62 044209]
[7]	Lustig M, Donoho D, Pauly J M 2007 Magnetic Resonance in Medicine 58 1182
[8]	Yu S W, Khwaja A S, Ma J W 2012 Signal Process. 92 357
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[10]	Ma J W 2010 IEEE. T. Instrum. Meas. 59 1600
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[13]	Briesmeister J F 1997 MCNP-A General Monte Carlo N-Particle Transport Code Version 4B, LA-12625-M. Los Alamos National Laboratory
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[19]	Candes E J, Wakin M B 2008 IEEE. Signal Proc. Mag. 25 21
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[21]	Xu H B, Peng X K, Chen C B 2010 Chin. Phys. B 19 062901

施引文献

[1]	Hao F H, Hu G C, Liu S P, Gong J, Xiang Y C, Huang R L 2005 Acta Phys. Sin. 54 3523 (in Chinese) [郝樊华, 胡广春, 刘素萍, 龚建, 向永春, 黄瑞良 2005 物理学报 54 3523]
[2]	Zhao H F, Du L, He L, Bao J L 2011 Acta Phys. Sin. 60 028501 (in Chinese) [赵鸿飞, 杜磊, 何亮, 包军林 2011 物理学报 60 028501]
[3]	Wang C J, Bao D M, Cheng S, Zhang A L 2008 Acta Phys. Sin. 57 5361 (in Chinese) [王崇杰, 包东敏, 程松, 张爱莲 2008 物理学报 57 5361]
[4]	Grenier G, Poussier C 1970 Nuclear Instruments and Methods 89 199
[5]	Sun B, Jiang J J 2011 Acta Phys. Sin. 60 110701 (in Chinese) [孙彪, 江建军 2011 物理学报 60 11701]
[6]	Bai X, Li Y Q, Zhao S M 2013 Acta Phys. Sin. 62 044209 (in Chinese) [白旭, 李永强, 赵生妹 2013 物理学报 62 044209]
[7]	Lustig M, Donoho D, Pauly J M 2007 Magnetic Resonance in Medicine 58 1182
[8]	Yu S W, Khwaja A S, Ma J W 2012 Signal Process. 92 357
[9]	Ma J W, Hussaini M Y 2011 IEEE. T. Instrum. Meas. 60 3128
[10]	Ma J W 2010 IEEE. T. Instrum. Meas. 59 1600
[11]	Ma J W, Plonka G, Hussaini M Y 2012 IEEE. T. Circ. Syst. Vid. 22 1354
[12]	Hou Q W, Cao B Y, Guo Z Y 2009 Acta Phys. Sin. 58 7809 (in Chinese) [侯泉文, 曹炳阳, 过增元 2009 物理学报 58 7809]
[13]	Briesmeister J F 1997 MCNP-A General Monte Carlo N-Particle Transport Code Version 4B, LA-12625-M. Los Alamos National Laboratory
[14]	Candes E J, Tao T 2005 IEEE. T. Inform. Theory. 24 118
[15]	Donoho D L, Elad M, Temlyakov V N 2006 IEEE. T. Inform. Theory. 52 6
[16]	Candes E J, Romberg J, Tao T 2006 IEEE. T. Inform. Theory. 52 489
[17]	Donoho D L 2006 IEEE. T. Inform. Theory. 52 1289
[18]	Candes E J, Romberg J, Tao T 2006 Commun. Pur. Appl. Math. 59 1207
[19]	Candes E J, Wakin M B 2008 IEEE. Signal Proc. Mag. 25 21
[20]	Xu M H, Liang T J, Zhang J 2006 Acta Phys. Sin. 55 2357 (in Chinese) [徐妙华, 梁天骄, 张杰 2006 物理学报 55 2357]
[21]	Xu H B, Peng X K, Chen C B 2010 Chin. Phys. B 19 062901

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