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In the thermal infrared (TIR) waveband, solving the target emissivity spectrum and temperature leads to an ill-posed problem in which the number of unknown parameters is larger than that of available measurements. Generally, the approaches developed for solving this kind of problems are called, by a joint name, the TES (temperature and emissivity separation) algorithm. As is shown in the name, the TES algorithm is dedicated to separating the target temperature and emissivity in the calculating procedure. In this paper, a novel method called the new MaxEnt (maximum entropy) TES algorithm is proposed, which is considered as a promotion of the MaxEnt TES algorithm proposed by Barducci. The maximum entropy estimation is utilized as the basic framework in the two preceding algorithms, so that the two algorithms both could make temperature and emissivity separation, independent of experiential information derived by some special data bases. As a result, the two algorithms could be applied to solve the temperature and emissivity spectrum of the targets which are absolutely unknown to us. However, what makes the two algorithms different is that the alpha spectrum derived by the ADE (alpha derived emissivity) method is considered as priori information to be added in the new MaxEnt TES algorithm. Based on the Wien approximation, the ADE method is dedicated to the calculation of the alpha spectrum which has a similar distribution to the true emissivity spectrum. Based on the preceding promotion, the new MaxEnt TES algorithm keeps a simpler mathematical formalism. Without any doubt, the new MaxEnt TES algorithm provides a faster computation for large volumes of data (i.e. hyperspectral images of the Earth). Some numerical simulations have been performed; the data and results show that, the maximum RMSE of emissivity estimation is 0.017, the maximum absolute error of temperature estimation is 0.62 K. Added with Gaussian white noise in which the signal to noise ratio is measured to be 11, the relative RMSE of emissivity estimation is 2.67%, the relative error of temperature estimation is 1.26%. Conclusion shows that the new MaxEnt TES algorithm may achieve high accuracy and fast calculating speed, and also get nice robustness against noise.
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Keywords:
- temperature /
- emissivity /
- alpha spectrum /
- maximum entropy
[1] Liu E C, Zheng X B, Li X, Zhang Y N 2013 Optics and Precision Engineering 21 608 (in Chinese) [刘恩超, 郑小兵, 李新, 张艳娜 2013 光学精密工程 21 608]
[2] Yang C Y, Cao L H, Zhang J P 2014 Optics and Precision Engineering 22 1751 (in Chinese) [杨词银, 曹立华, 张建萍 2014 光学精密工程 22 1751]
[3] Li N, Zhang Y F, Liu C X, Cao L H, Guo L H 2014 Optics and Precision Engineering 22 2054 (in Chinese) [李宁, 张云峰, 刘春香, 曹立华, 郭立红 2014 光学精密工程 22 2054]
[4] Kealy P S, Hook S J 1993 IEEE Trans. Geosci. Remote Sensing 31 1155
[5] Wan Z, Li Z L 1997 IEEE Trans. Geosci. Remote Sensing 35 980
[6] Li Z L, Becker F, Stoll M P, Wang Z 1990 Remote Sensing of Environments 69 197
[7] Gillespie A, Rokugawa S, Matsunaga T, Cothern J S, Hook S, Kahle A B 1998 IEEE Trans. Geosci. Remote Sensing 36 1113
[8] Xu Z, Zhao H J 2009 Acta Optica Sinica 29 394 (in Chinese) [徐州, 赵慧洁 2009 光学学报 29 394]
[9] Yang H, Zhang L F, Zhang X W, Fang C H, Tong Q X 2011 Journal of Remote Sensing 15 1242 (in Chinese) [杨杭, 张立福, 张学文, 房丛卉, 童庆禧 2011 遥感学报 15 1242]
[10] Kahle A B, Madura D P, Soha J M 1980 Applied Optics 19 2279
[11] Wan Z, Dozier J 1989 IEEE Trans. Geosci. Remote Sensing 27 268
[12] Tang S H, Zhu Q J, Su L H 2005 J. Infrared Millim. Waves 24 286 (in Chinese) [唐世浩, 朱启疆, 苏理宏 2005 红外与毫米波学报 24 286]
[13] Price J C 1984 J. Geophys. Res. 89 7231
[14] Morgan J A 2005 IEEE Trans. Geosci. Remote Sensing 43 1279
[15] Liu Y J, Yang Z D 2001 Principle and Algorithm of Remote Sensing Information Processing for MODIS (Beijing: Sciences Press) p232 (in Chinese) [刘玉洁, 杨忠东 2001 MODIS遥感信息处理原理与算法(北京: 科学出版社) 第232页]
[16] Barducci A, Pippi I 1996 IEEE Trans. Geosci. Remote Sensing 34 681
[17] Barducci A, Guzzi D, Lastri C, Marcoionni P, Nardino V, Pippi I 2014 IEEE Trans. Geosci. Remote Sensing 53 738
[18] Barducci A, Guzzi D, Lastri C, Marcoionni P, Nardino V, Pippi I 2013 Infrared Physics & Technology 56 12
[19] Kealy P S, Gabell A R 1990 Proc. 2nd TIMS Workshop JPL Pub 90-55 11-15
[20] Jiang X K, Zhang Q C, Shi H T, Mao L, Cheng T, Wu X P 2011 Acta Phys. Sin. 60 054401 (in Chinese) [蒋兴凯, 张青川, 史海涛, 毛亮, 程腾, 伍小平 2011 物理学报 60 054401]
[21] Zhou Y P, Li F J, Che C, Tan L Y, Ran Q W, Yu S Y, Ma J 2014 Acta Phys. Sin. 63 148501 (in Chinese) [周彦平, 黎发军, 车驰, 谭立英, 冉启文, 于思源, 马晶 2014 物理学报 63 148501]
[22] Sun C M, Yuan Y, Zhang X B 2010 Acta Phys. Sin. 59 7523 (in Chinese) [孙成明, 袁艳, 张修宝 2010 物理学报 59 7523]
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[1] Liu E C, Zheng X B, Li X, Zhang Y N 2013 Optics and Precision Engineering 21 608 (in Chinese) [刘恩超, 郑小兵, 李新, 张艳娜 2013 光学精密工程 21 608]
[2] Yang C Y, Cao L H, Zhang J P 2014 Optics and Precision Engineering 22 1751 (in Chinese) [杨词银, 曹立华, 张建萍 2014 光学精密工程 22 1751]
[3] Li N, Zhang Y F, Liu C X, Cao L H, Guo L H 2014 Optics and Precision Engineering 22 2054 (in Chinese) [李宁, 张云峰, 刘春香, 曹立华, 郭立红 2014 光学精密工程 22 2054]
[4] Kealy P S, Hook S J 1993 IEEE Trans. Geosci. Remote Sensing 31 1155
[5] Wan Z, Li Z L 1997 IEEE Trans. Geosci. Remote Sensing 35 980
[6] Li Z L, Becker F, Stoll M P, Wang Z 1990 Remote Sensing of Environments 69 197
[7] Gillespie A, Rokugawa S, Matsunaga T, Cothern J S, Hook S, Kahle A B 1998 IEEE Trans. Geosci. Remote Sensing 36 1113
[8] Xu Z, Zhao H J 2009 Acta Optica Sinica 29 394 (in Chinese) [徐州, 赵慧洁 2009 光学学报 29 394]
[9] Yang H, Zhang L F, Zhang X W, Fang C H, Tong Q X 2011 Journal of Remote Sensing 15 1242 (in Chinese) [杨杭, 张立福, 张学文, 房丛卉, 童庆禧 2011 遥感学报 15 1242]
[10] Kahle A B, Madura D P, Soha J M 1980 Applied Optics 19 2279
[11] Wan Z, Dozier J 1989 IEEE Trans. Geosci. Remote Sensing 27 268
[12] Tang S H, Zhu Q J, Su L H 2005 J. Infrared Millim. Waves 24 286 (in Chinese) [唐世浩, 朱启疆, 苏理宏 2005 红外与毫米波学报 24 286]
[13] Price J C 1984 J. Geophys. Res. 89 7231
[14] Morgan J A 2005 IEEE Trans. Geosci. Remote Sensing 43 1279
[15] Liu Y J, Yang Z D 2001 Principle and Algorithm of Remote Sensing Information Processing for MODIS (Beijing: Sciences Press) p232 (in Chinese) [刘玉洁, 杨忠东 2001 MODIS遥感信息处理原理与算法(北京: 科学出版社) 第232页]
[16] Barducci A, Pippi I 1996 IEEE Trans. Geosci. Remote Sensing 34 681
[17] Barducci A, Guzzi D, Lastri C, Marcoionni P, Nardino V, Pippi I 2014 IEEE Trans. Geosci. Remote Sensing 53 738
[18] Barducci A, Guzzi D, Lastri C, Marcoionni P, Nardino V, Pippi I 2013 Infrared Physics & Technology 56 12
[19] Kealy P S, Gabell A R 1990 Proc. 2nd TIMS Workshop JPL Pub 90-55 11-15
[20] Jiang X K, Zhang Q C, Shi H T, Mao L, Cheng T, Wu X P 2011 Acta Phys. Sin. 60 054401 (in Chinese) [蒋兴凯, 张青川, 史海涛, 毛亮, 程腾, 伍小平 2011 物理学报 60 054401]
[21] Zhou Y P, Li F J, Che C, Tan L Y, Ran Q W, Yu S Y, Ma J 2014 Acta Phys. Sin. 63 148501 (in Chinese) [周彦平, 黎发军, 车驰, 谭立英, 冉启文, 于思源, 马晶 2014 物理学报 63 148501]
[22] Sun C M, Yuan Y, Zhang X B 2010 Acta Phys. Sin. 59 7523 (in Chinese) [孙成明, 袁艳, 张修宝 2010 物理学报 59 7523]
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