基于稀疏优化的烟羽断层重建方法

钟鸣宇; 奚亮; 司福祺; 周海金; 王煜

doi:10.7498/aps.68.20190268

摘要

烟羽断层重建一般使用两台光谱仪采集数据, 属于典型的不完全角度重建. 为了提高重建结果的稳定性和接近度, 将压缩感知理论引入气体分布重建领域. 提出了一种新的计算机层析算法——低三阶导数全变分法, 用于重建电厂烟囱排放的SO₂截面的二维分布. 使用低三阶导数模型模拟气体扩散, 认为气体浓度对位置的三阶导数是稀疏的. 将重建图像的全变分作为目标函数, 并通过数值最优化方法求得气体浓度分布的最优解. 数值模拟的结果表明, 与传统的低三阶导数法相比, 低三阶导数全变分法将接近度提高了80%以上. 外场实验表明, 重建图像的一致性相关因子达0.9023. 低三阶导数全变分法能有效消除测量误差对图像重建的影响, 提高重建图像的质量.

关键词:

Abstract

In this paper, we present a novel method of computing tomography , i.e. the low third deviation total variation (LTD-TV) method to reconstruct the two-dimensional distribution of SO₂ of stack plume. The path-integral data of the plume are collected by only two imaging differential absorption spectrometers (IDOASs). However, due to the insufficient number of IDOASs, conventional reconstruction methods result in severe streaking artifacts. The traditional low third derivative method is widely used to reconstruct the gas distribution. It suggests a spatial distribution of gas concentrations, which has a low third spatial derivative in every direction and at every point. The derivatives are usually set to be zero. The method improves the reconstructed images by providing extra information which contains the gas concentration in line with the distribution of the second order polynomial, but it also gives rise to the extra artifacts. To address this issue, we further improve the traditional low third deviation (LTD) method by suggesting that the third derivative of gas concentration is sparse. We therefore adopt the compressed sensing (CS) based total variation (TV) optimization framework. In the LTD-TV method, a logarithmic barrier function with TV is used as an objective function. The objective function is then optimized by numerical optimization method, in which the gradient projection is used to determine its descent direction and a Barzilai-Borwein scheme to determine its step-size. The final results are obtained by iterative optimization. Numerical simulations are performed to simulate the reconstruction of gas distribution which is in line with Gaussian distribution. Compared with the conventional LTD method, the LTD-TV method enhances the proximity by 20%—80%, and greatly corrects the artifacts near the edges of images. The result of field campaign suggests that concordance correlation factor between the collected data and reconstructed image is 0.9023. It also shows that it has good noise immunity. In summary, it is the first time that we have introduced the CS theory into the field of gas plume reconstruction. Compared with the existing methods, the LTD-TV method can greatly reduce the artifacts and increase the credibility of the reconstruction.

Keywords:

作者及机构信息

1.
中国科学院安徽光学精密机械研究所, 环境光学与技术重点实验室, 合肥　230031

2.
中国科学技术大学研究生院科学岛分院, 合肥　230031

3.
安徽理工大学电气与信息工程学院, 淮南　232001

通信作者: 司福祺, sifuqi@aiofm.ac.cn

基金项目: 国家重点研发计划(批准号: 2016YFC0200400, 2017YFB0503901)资助的课题.

Authors and contacts

1.
Anhui Institute of Optics and Fine Mechanics,Chinese Academy of Sciences, Hefei 230031, China

2.
University of Science and Technology of China, Hefei 230031, China

3.
College of Electrical and Information enginenering, Anhui University of Science and Technology, Huainan 232001, China

Corresponding author: Si Fu-Qi, sifuqi@aiofm.ac.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFC0200400, 2017YFB0503901).

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参考文献

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施引文献

图 1 扫描区域离散化

Fig. 1. Scanning region discretization.

下载: 全尺寸图片幻灯片

图 2 传统LTD法与LTD-TV法比较　(a), (b), (c)测试图形; (d), (e), (f)传统LTD法重建图形; (g), (h), (i) LTD-TV法20000次迭代重建图形

Fig. 2. Comparison between traditional LTD algorithm and LTD-TV algorithm: (a), (b), (c) Test distribution; (d), (e), (f) reconstruction of distribution using traditional LTD algorithm; (g), (h), (i) reconstruction of distribution using LTD-TV algorithm with 20000 iterations.

下载: 全尺寸图片幻灯片

图 3 接近度随误差系数变化曲线

Fig. 3. Nearness as the functions of error factors.

下载: 全尺寸图片幻灯片

图 4 接近度偏离距离变化曲线

Fig. 4. Nearness as the functions of offset distance.

下载: 全尺寸图片幻灯片

图 5 SO₂柱浓度IDOAS拟合反演实例　(a) SO₂柱浓度; (b)拟合残差

Fig. 5. An example of SO₂ SCD from IDOAS retrieval: (a) SO₂ SCD; (b) fitting residual.

下载: 全尺寸图片幻灯片

图 6 烟囱烟羽SO₂分布重建图

Fig. 6. Reconstruction of SO₂ of stack plume.

下载: 全尺寸图片幻灯片

图 7 测量路径积分浓度与重建路径积分浓度对比　(a) IDOAS #1; (b) IDOAS #2

Fig. 7. Comparison between measured path integrated concentration and reconstructed path integrated concentration: (a) IDOAS #1; (b) IDOAS #2.

下载: 全尺寸图片幻灯片

[1]	Yao L, Garmash O, Bianchi F, Zheng J, Yan C, Kontkanen 2018 Science 361 278 Google Scholar
[2]	饶瑞中 2012 现代大气光学(北京: 科学出版社) 第551页 Rao R Z 2012 Modern Atmospheric Optics (Beijing: Science Press)p551(in Chinese)
[3]	Samanta A, Todd L A 2000 Atmos. Environ. 34 699 Google Scholar
[4]	Todd L A, Ramachandran G 1994 Am. Ind. Hyg. Assoc. J. 55 403 Google Scholar
[5]	韦民红, 童敏明, 李素文, 肖建于 2015 光谱学与光谱分析 35 2252 Google Scholar Wei M H, Tong M M, Li S W, Xiao J Y 2015 Spectrosc. Spect. Anal. 35 2252 Google Scholar
[6]	Drescher A C, Gadgil A J, Price P N, Nazaroff W W 1996 Atmos. Environ. 30 929 Google Scholar
[7]	Price P N, Fischer M L, Gadgil A J, Sextro R G 2001 Atmos. Environ. 35 2827 Google Scholar
[8]	Olaguer E P 2011 Atmos. Environ. 45 6980 Google Scholar
[9]	Olaguer E P, Erickson M H, Wijesinghe A, Neish B S 2016 J. Air Waste Manage. Assoc. 66 164 Google Scholar
[10]	Olaguer E P, Stutz Jochen, Erickson M H, Hurlock S C, Cheung R, Tsai C, Colosimo S F, Festa J, Wijesinghe A, Neish B S 2017 Atmos. Environ. 150 220 Google Scholar
[11]	Johansson M, Bo G, Rivera C, Zhang Y 2009 Bull. Volcanol. 71 1169 Google Scholar
[12]	Kazahaya R, Mori T, Kazahaya K, Hirabayashi J 2008 Geophys. Res. Lett. 35 344
[13]	Casaballe N, Osorio M, Martino M D, Frins E 2017 Earth Space Sci. 4 723 Google Scholar
[14]	杨富强, 张定华, 黄魁东, 王鹍, 徐哲 2014 物理学报 63 058701 Google Scholar Yang F Q, Zhang D H, Huang K D, Wang K, Xu Z 2014 Acta Phys. Sin. 63 058701 Google Scholar
[15]	Sidky E Y, Kao C M, Pan X 2006 J. X-Ray Sci. Technol. 14 119
[16]	Sidky E Y, Pan X C 2008 Phys. Med. Biol. 53 4777 Google Scholar
[17]	Niu T, Zhu L 2012 Med. Phys. 39 4588 Google Scholar
[18]	Barzilai J, Borwein J M 1988 IMA J. Numer. Anal. 8 141 Google Scholar
[19]	司福祺, 谢品华, Heue K P, 刘诚, 彭夫敏, 刘文清 2008 物理学报 57 6018 Google Scholar Si F Q, Xie P H, Heue K P, Liu C, Peng F M, Liu W Q 2008 Acta Phys. Sin. 57 6018 Google Scholar
[20]	周海金 2013 博士学位论文 (合肥: 中国科学技术大学) Zhou H J 2013 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[21]	Wu C F, Chang S Y 2011 Atmos. Environ. 45 1476 Google Scholar
[22]	周斌, 刘文清, 齐锋, 李振璧, 崔延军 2002 光学学报 22 957 Google Scholar Zhou B, Liu W Q, Qi F, Li Z B, Cui Y J 2002 Acta Opt. Sin. 22 957 Google Scholar
[23]	刘世胜魏庆农王峰平詹锴 2009 大气与环境光学学报 4 118 Google Scholar Liu S S, Wei Q N, Wang F P, Zhan K 2009 J. Atmos. Environ. Opt. 4 118 Google Scholar
[24]	Hartl A, Song B C, Pundt I 2006 Atmos. Chem. Phys. 6 847 Google Scholar

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基于稀疏优化的烟羽断层重建方法