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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.
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Keywords:
- spectral absorption by atmospheric gases /
- plume reconstruction /
- low-third-deviation total variational method /
- imaging differential optical absorption spectrometer
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图 1 扫描区域离散化
Figure 1. Scanning region discretization.
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
Figure 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.
图 3 接近度随误差系数变化曲线
Figure 3. Nearness as the functions of error factors.
图 4 接近度偏离距离变化曲线
Figure 4. Nearness as the functions of offset distance.
图 5 SO2柱浓度IDOAS拟合反演实例 (a) SO2柱浓度; (b)拟合残差
Figure 5. An example of SO2 SCD from IDOAS retrieval: (a) SO2 SCD; (b) fitting residual.
图 6 烟囱烟羽SO2分布重建图
Figure 6. Reconstruction of SO2 of stack plume.
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
Figure 7. Comparison between measured path integrated concentration and reconstructed path integrated concentration: (a) IDOAS #1; (b) IDOAS #2.
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[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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