Iterative reconstruction algorithm for the inverse problems in electrical capacitance tomography
The electrical capacitance tomography (ECT) technology is a promising tomography technology that can image the distribution information of permittivity in a measurement region. The imaging algorithms play crucial roles in practical ECT image reconstruction problems. Different from previous numerical...
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| Published in: | Flow measurement and instrumentation Vol. 64; pp. 204 - 212 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
01.12.2018
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| ISSN: | 0955-5986, 1873-6998 |
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| Abstract | The electrical capacitance tomography (ECT) technology is a promising tomography technology that can image the distribution information of permittivity in a measurement region. The imaging algorithms play crucial roles in practical ECT image reconstruction problems. Different from previous numerical methods, this study proposes a novel cost function to model the ECT inverse problem, in which the L1-norm is used as the data fidelity to weaken the influence of the outliers contained in the capacitance data, the L1 regularization is introduced to enhance the sparseness of reconstructed objects, and the second order total variation (STV) regularization is used to weaken the staircasing effects caused by the first order total variation (FTV) regularization. The split Bregman iteration (SBI) algorithm that splits a complicated ECT imaging problem into several simpler sub-problems is developed to solve the proposed cost function effectively. The numerical simulation results show that the imaging algorithm proposed in this paper can reconstruct satisfactory results.
•A new cost function is proposed to model the ECT imaging problem.•A new iterative algorithm is developed to effectively solve the cost function.•The feasibility and effectiveness of the algorithm are numerically validated. |
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| AbstractList | The electrical capacitance tomography (ECT) technology is a promising tomography technology that can image the distribution information of permittivity in a measurement region. The imaging algorithms play crucial roles in practical ECT image reconstruction problems. Different from previous numerical methods, this study proposes a novel cost function to model the ECT inverse problem, in which the L1-norm is used as the data fidelity to weaken the influence of the outliers contained in the capacitance data, the L1 regularization is introduced to enhance the sparseness of reconstructed objects, and the second order total variation (STV) regularization is used to weaken the staircasing effects caused by the first order total variation (FTV) regularization. The split Bregman iteration (SBI) algorithm that splits a complicated ECT imaging problem into several simpler sub-problems is developed to solve the proposed cost function effectively. The numerical simulation results show that the imaging algorithm proposed in this paper can reconstruct satisfactory results.
•A new cost function is proposed to model the ECT imaging problem.•A new iterative algorithm is developed to effectively solve the cost function.•The feasibility and effectiveness of the algorithm are numerically validated. |
| Author | Guo, Ge Tong, Guowei Lu, Lian Liu, Shi |
| Author_xml | – sequence: 1 givenname: Ge surname: Guo fullname: Guo, Ge email: 1724148651@qq.com organization: School of Control and Computer Engineering, North China Electric Power University, Changping District, Beijing 102206, China – sequence: 2 givenname: Guowei surname: Tong fullname: Tong, Guowei organization: School of Control and Computer Engineering, North China Electric Power University, Changping District, Beijing 102206, China – sequence: 3 givenname: Lian surname: Lu fullname: Lu, Lian organization: School of Control and Computer Engineering, North China Electric Power University, Changping District, Beijing 102206, China – sequence: 4 givenname: Shi surname: Liu fullname: Liu, Shi organization: School of Energy, Power and Mechanical Engineering, North China Electric Power University, Changping District, Beijing 102206, China |
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| Cites_doi | 10.2307/2372313 10.1016/S1385-8947(99)00134-5 10.1137/S0036144594276474 10.1137/080716542 10.1109/TIM.2010.2045255 10.1364/OE.18.001854 10.1109/JSEN.2017.2749881 10.1016/j.sigpro.2012.05.027 10.1109/JSEN.2015.2453361 10.1088/1361-6501/aa524e 10.1080/00102202.2010.497420 10.1137/080725891 10.1016/j.flowmeasinst.2014.03.006 10.1088/0957-0233/27/7/074003 10.1088/0957-0233/14/1/201 10.1049/ip-g-2.1992.0015 10.1016/j.cej.2017.07.098 10.5201/ipol.2013.40 10.1088/0031-9155/43/8/032 10.1088/0957-0233/20/10/104027 10.1007/s11263-005-3219-7 10.1049/ip-g-2.1992.0014 10.1109/JSEN.2017.2718593 10.1109/TPAMI.2008.114 10.14257/ijgdc.2016.9.3.11 10.1016/j.flowmeasinst.2017.07.002 10.1137/0911028 10.1007/s10851-013-0445-4 10.1002/1521-4117(200010)17:3<96::AID-PPSC96>3.0.CO;2-8 10.1016/0167-2789(92)90242-F 10.1016/j.na.2006.02.001 10.1016/j.ultramic.2013.07.016 10.3390/app6120403 10.1109/JSEN.2015.2506409 10.1111/j.2517-6161.1996.tb02080.x 10.1093/comjnl/7.2.149 10.1080/00036810903517597 10.3923/itj.2011.1614.1619 |
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| References | Zhang, Xu, Soleimani (bib9) 2017; 17 Neubauer, Hein, Hofmann, Kindermann, Tautenhahn (bib27) 2010; 89 Gao, Zhao (bib23) 2010; 18 Chan, Ng (bib19) 1996; 38 Perera, Pradeep, Mylvaganam, Time (bib5) 2017; 56 Tian, Sun, Ramli, Yang (bib18) 2017; 17 Yang, Peng (bib2) 2003; 14 Lei, Liu, Liu (bib39) 2010; 37 Landweber (bib17) 1951; 73 Papafitsoros, Schönlieb (bib40) 2012; 48 Peng, Henk, Brian (bib3) 2000; 17 Yu, Li, Li, Zhang (bib25) 2016; 9 Shi, Shen (bib31) 2007; 66 Ye, Wang, Yang (bib38) 2016; 27 Zhang, Xu, Fang, Wang (bib16) 2011; 22 Fletcher, Reeves (bib24) 1964; 7 Chen, Zhang, Liu, Chen, Li (bib33) 2017; 28 Su, Zhang, Peng, Yao, Zhang (bib30) 2000; 77 Kwak (bib32) 2008; 30 S.M. Huang, C.G. Xie, R. Thorn, D. Snowden, M.S. Beck, Design of sensor electronics for electrical capacitance tomography, Circuits Devices and Systems IEE Proceedings G. 139 83-88, 1992. Cao, Xu, Wang (bib14) 2009; 20 Wang, Ma, Han, Li (bib44) 2012; 92 Agu, Tokheim, Eikeland, Moldestad (bib8) 2017; 328 Zhang, Xu, Fan, Wang (bib15) 2010; 21 Dodge (bib43) 2002; 6 Hosani, Zhang, Soleimani (bib6) 2015; 15 Yi, Lv, Dang, Xiao (bib35) 2016; 6 Gut, Wolanski (bib7) 2010; 182 Liu, Song, Zhang, Chen, Wang, Cui (bib26) 2016; 9 Hansen (bib12) 1990; 11 Wolf, Lubk, Lichte (bib21) 2014; 136 Yan, Wang, Zhou, Sun (bib28) 2014; 37 Zhang, Xu, Fang, Wang (bib13) 2011; 60 Haddadi, Maddahian (bib37) 2016; 16 Rudin, Osher, Fatemi (bib22) 1992; 60 Guan, Gordon, Zhu (bib20) 1998; 43 Tibshirani (bib42) 2011; 58 C.G. Xie, S.M. Huang, B.S. Hoyle, R. Thorn, C. Lenn, D. Snowden, M.S. Beck, Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors, IEE Proceedings G Circuits, Devices and Systems 139 89-98, 1992. Hao (bib11) 2006; 31 Mueller, Yagel (bib29) 1998; 3 Rasel, Zuccarelli, Marashdeh, Fan, Teixeira (bib4) 2017; 99 Papafitsoros, Schoenlieb, Sengul (bib34) 2013; 3 Goldstein, Osher (bib45) 2009; 2 Li, Cao, Man, Chi (bib10) 2011; 10 Beck, Teboulle (bib46) 2009; 2 Lysaker, Tai (bib41) 2006; 66 Chen (10.1016/j.flowmeasinst.2018.10.010_bib33) 2017; 28 Tibshirani (10.1016/j.flowmeasinst.2018.10.010_bib42) 2011; 58 Liu (10.1016/j.flowmeasinst.2018.10.010_bib26) 2016; 9 Lei (10.1016/j.flowmeasinst.2018.10.010_bib39) 2010; 37 Li (10.1016/j.flowmeasinst.2018.10.010_bib10) 2011; 10 Neubauer (10.1016/j.flowmeasinst.2018.10.010_bib27) 2010; 89 Yi (10.1016/j.flowmeasinst.2018.10.010_bib35) 2016; 6 10.1016/j.flowmeasinst.2018.10.010_bib1 Shi (10.1016/j.flowmeasinst.2018.10.010_bib31) 2007; 66 Agu (10.1016/j.flowmeasinst.2018.10.010_bib8) 2017; 328 Peng (10.1016/j.flowmeasinst.2018.10.010_bib3) 2000; 17 Zhang (10.1016/j.flowmeasinst.2018.10.010_bib16) 2011; 22 Zhang (10.1016/j.flowmeasinst.2018.10.010_bib13) 2011; 60 Lysaker (10.1016/j.flowmeasinst.2018.10.010_bib41) 2006; 66 Perera (10.1016/j.flowmeasinst.2018.10.010_bib5) 2017; 56 Guan (10.1016/j.flowmeasinst.2018.10.010_bib20) 1998; 43 Papafitsoros (10.1016/j.flowmeasinst.2018.10.010_bib34) 2013; 3 Wang (10.1016/j.flowmeasinst.2018.10.010_bib44) 2012; 92 Goldstein (10.1016/j.flowmeasinst.2018.10.010_bib45) 2009; 2 Fletcher (10.1016/j.flowmeasinst.2018.10.010_bib24) 1964; 7 Kwak (10.1016/j.flowmeasinst.2018.10.010_bib32) 2008; 30 Mueller (10.1016/j.flowmeasinst.2018.10.010_bib29) 1998; 3 Gut (10.1016/j.flowmeasinst.2018.10.010_bib7) 2010; 182 Gao (10.1016/j.flowmeasinst.2018.10.010_bib23) 2010; 18 Zhang (10.1016/j.flowmeasinst.2018.10.010_bib15) 2010; 21 Haddadi (10.1016/j.flowmeasinst.2018.10.010_bib37) 2016; 16 Wolf (10.1016/j.flowmeasinst.2018.10.010_bib21) 2014; 136 Hansen (10.1016/j.flowmeasinst.2018.10.010_bib12) 1990; 11 Zhang (10.1016/j.flowmeasinst.2018.10.010_bib9) 2017; 17 Tian (10.1016/j.flowmeasinst.2018.10.010_bib18) 2017; 17 Su (10.1016/j.flowmeasinst.2018.10.010_bib30) 2000; 77 Rasel (10.1016/j.flowmeasinst.2018.10.010_bib4) 2017; 99 Rudin (10.1016/j.flowmeasinst.2018.10.010_bib22) 1992; 60 Cao (10.1016/j.flowmeasinst.2018.10.010_bib14) 2009; 20 Landweber (10.1016/j.flowmeasinst.2018.10.010_bib17) 1951; 73 Yang (10.1016/j.flowmeasinst.2018.10.010_bib2) 2003; 14 Beck (10.1016/j.flowmeasinst.2018.10.010_bib46) 2009; 2 Dodge (10.1016/j.flowmeasinst.2018.10.010_bib43) 2002; 6 Hosani (10.1016/j.flowmeasinst.2018.10.010_bib6) 2015; 15 Chan (10.1016/j.flowmeasinst.2018.10.010_bib19) 1996; 38 Ye (10.1016/j.flowmeasinst.2018.10.010_bib38) 2016; 27 Yu (10.1016/j.flowmeasinst.2018.10.010_bib25) 2016; 9 Hao (10.1016/j.flowmeasinst.2018.10.010_bib11) 2006; 31 10.1016/j.flowmeasinst.2018.10.010_bib36 Papafitsoros (10.1016/j.flowmeasinst.2018.10.010_bib40) 2012; 48 Yan (10.1016/j.flowmeasinst.2018.10.010_bib28) 2014; 37 |
| References_xml | – volume: 37 start-page: 27 year: 2010 end-page: 34 ident: bib39 article-title: A generalized reconstruction algorithm for compressed sensing publication-title: Int. Conf. Intell. Syst. Des. Eng. Appl. – volume: 10 start-page: 269 year: 2011 end-page: 291 ident: bib10 article-title: Image reconstruction algorithm for electrical capacitance tomography publication-title: Inf. Technol. J. – volume: 30 start-page: 1672 year: 2008 end-page: 1692 ident: bib32 article-title: Principal component analysis based on L1-norm maximization publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 18 start-page: 1854 year: 2010 end-page: 1871 ident: bib23 article-title: Multilevel bioluminescence tomography based on radiative transfer equation Part 1: L1 regularization publication-title: Opt. Express – volume: 9 start-page: 91 year: 2016 end-page: 98 ident: bib26 article-title: Improvement of SVM image reconstruction algorithm in ECT system publication-title: Int. J. Grid Distrib. Comput. – volume: 21 start-page: 1 year: 2010 end-page: 6 ident: bib15 article-title: Electrical capacitance tomography with a non-circular sensor using the dbar method publication-title: Meas. Sci. Technol. – volume: 73 start-page: 615 year: 1951 end-page: 624 ident: bib17 article-title: An iteration formula for fredholm integral equations of the first kind publication-title: Am. J. Math. – volume: 99 start-page: 1 year: 2017 end-page: 11 ident: bib4 article-title: Towards multiphase flow decomposition based on electrical capacitance tomography sensors publication-title: IEEE Sens. J. – volume: 7 start-page: 149 year: 1964 end-page: 154 ident: bib24 article-title: Function minimization by conjugate gradients publication-title: Comput. J. – volume: 182 start-page: 1580 year: 2010 end-page: 1585 ident: bib7 article-title: Flame imaging using 3D electrical capacitance tomography publication-title: Combust. Sci. Technol. – volume: 22 start-page: 32 year: 2011 end-page: 33 ident: bib16 article-title: 2D electrical capacitance tomography with sensors of non-circular cross sections using the factorization method publication-title: Meas. Sci. Technol. – volume: 38 start-page: 427 year: 1996 end-page: 482 ident: bib19 article-title: Conjugate gradient methods for toeplitz systems publication-title: Siam Rev. – volume: 6 start-page: 756 year: 2002 end-page: 760 ident: bib43 article-title: Statistical data analysis based on the L1-norm and related methods publication-title: Comput. Stat. Data Anal. – volume: 60 start-page: 900 year: 2011 end-page: 907 ident: bib13 article-title: Electrical capacitance tomography for sensors of square cross sections using Calderon's method publication-title: IEEE Trans. Instrum. Meas. – volume: 66 start-page: 1428 year: 2007 end-page: 1441 ident: bib31 article-title: Convergence of the Polak-Ribiére-Polyak conjugate gradient method publication-title: Nonlinear Anal. Theory Methods Appl. – volume: 28 start-page: 35 year: 2017 end-page: 46 ident: bib33 article-title: Image reconstruction algorithms for electrical capacitance tomography based on ROF model using new numerical techniques publication-title: Meas. Sci. Technol. – volume: 27 start-page: 1 year: 2016 end-page: 12 ident: bib38 article-title: Evaluation of electrical capacitance tomography sensor based on the coupling of fluid field and electrostatic field publication-title: Meas. Sci. Technol. – volume: 3 start-page: 112 year: 2013 end-page: 136 ident: bib34 article-title: Combined first and second order total variation inpainting using Split Bregman publication-title: Image Process. Line – volume: 56 start-page: 23 year: 2017 end-page: 34 ident: bib5 article-title: Imaging of oil-water flow patterns by electrical capacitance tomography publication-title: Flow. Meas. Instrum. – volume: 43 start-page: 2413 year: 1998 end-page: 2421 ident: bib20 article-title: Combining various projection access schemes with the algebraic reconstruction technique for low-contrast detection in computed tomography publication-title: Phys. Med. Biol. – volume: 328 start-page: 997 year: 2017 end-page: 1008 ident: bib8 article-title: Determination of onset of bubbling and slugging in a fluidized bed using a dual-plane electrical capacitance tomography system publication-title: Chem. Eng. J. – reference: S.M. Huang, C.G. Xie, R. Thorn, D. Snowden, M.S. Beck, Design of sensor electronics for electrical capacitance tomography, Circuits Devices and Systems IEE Proceedings G. 139 83-88, 1992. – volume: 48 start-page: 308 year: 2012 end-page: 338 ident: bib40 article-title: A combined first and second order variational approach for image reconstruction publication-title: J. Math. Imaging Vis. – volume: 66 start-page: 5 year: 2006 end-page: 18 ident: bib41 article-title: Iterative image restoration combining total variation minimization and a second-order functional publication-title: Int. J. Comput. Vis. – volume: 20 start-page: 1 year: 2009 end-page: 12 ident: bib14 article-title: Image reconstruction technique of electrical capacitance tomography for low-contrast dielectrics using Calderon's method publication-title: Meas. Sci. Technol. – volume: 11 start-page: 503 year: 1990 end-page: 518 ident: bib12 article-title: Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank publication-title: Siam J. Sci. Stat. Comput. – volume: 77 start-page: 37 year: 2000 end-page: 41 ident: bib30 article-title: The use of simultaneous iterative reconstruction technique for electrical capacitance tomography publication-title: Chem. Eng. J. – volume: 3 start-page: 1552 year: 1998 end-page: 1559 ident: bib29 article-title: Rapid 3D cone-beam reconstruction with the Algebraic Reconstruction technique (art) by utilizing texture mapping graphics hardware publication-title: Nucl. Sci. Symp – volume: 31 start-page: 283 year: 2006 end-page: 289 ident: bib11 article-title: Tikhonov regularization algorithm for pseudomonotone variational inequalities publication-title: Acta Math. Vietnam. – volume: 89 start-page: 1729 year: 2010 end-page: 1743 ident: bib27 article-title: Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces publication-title: Appl. Anal. – volume: 136 start-page: 15 year: 2014 end-page: 25 ident: bib21 article-title: Weighted simultaneous iterative reconstruction technique for single-axis tomography publication-title: Ultramicroscopy – volume: 37 start-page: 92 year: 2014 end-page: 98 ident: bib28 article-title: 3D ECT reconstruction by an improved Landweber iteration algorithm publication-title: Flow. Meas. Instrum. – volume: 6 start-page: 403 year: 2016 end-page: 418 ident: bib35 article-title: A novel mechanical fault diagnosis scheme based on the convex 1-D second-order total variation denoising algorithm publication-title: Appl. Sci. – volume: 17 start-page: 7029 year: 2017 end-page: 7042 ident: bib18 article-title: Adaptive selection of relaxation factor in Landweber iterative algorithm publication-title: IEEE Sens. J. – volume: 2 start-page: 323 year: 2009 end-page: 343 ident: bib45 article-title: The split Bregman method for L1-regularized problems publication-title: SIAM J. Imaging Sci. – volume: 2 start-page: 183 year: 2009 end-page: 202 ident: bib46 article-title: A fast iterative shrinkage-thresholding algorithm for linear inverse problems publication-title: Siam J. Imaging Sci. – volume: 60 start-page: 259 year: 1992 end-page: 268 ident: bib22 article-title: Nonlinear total variation based noise removal algorithms publication-title: Phys. D Nonlinear Phenom. – volume: 9 start-page: 243 year: 2016 end-page: 252 ident: bib25 article-title: Research and application of NSSN neural network in electrical capacitance tomography image reconstruction publication-title: Int. J. Signal Process. – volume: 17 start-page: 96 year: 2000 end-page: 104 ident: bib3 article-title: Using regularization methods for image reconstruction of electrical capacitance tomography publication-title: Part. Part. Syst. Charact. – volume: 92 start-page: 2952 year: 2012 end-page: 2961 ident: bib44 article-title: Split Bregman iterative algorithm for sparse reconstruction of electrical impedance tomography publication-title: Signal Process. – volume: 15 start-page: 6089 year: 2015 end-page: 6099 ident: bib6 article-title: A limited region electrical capacitance tomography for detection of deposits in pipelines publication-title: IEEE Sens. J. – volume: 17 start-page: 8263 year: 2017 end-page: 8270 ident: bib9 article-title: Quantitative reconstruction of the exterior boundary shape of metallic inclusions using electrical capacitance tomography publication-title: IEEE Sens. J. – volume: 58 start-page: 267 year: 2011 end-page: 288 ident: bib42 article-title: Regression shrinkage and selection via the Lasso publication-title: J. R. Stat. Soc. – volume: 16 start-page: 1786 year: 2016 end-page: 1794 ident: bib37 article-title: A new algorithm for image reconstruction of electrical capacitance tomography based on inverse heat conduction problems publication-title: IEEE Sens. J. – volume: 14 start-page: 1 year: 2003 end-page: 13 ident: bib2 article-title: Image reconstruction algorithms for electrical capacitance tomography publication-title: Meas. Sci. Technol. – reference: C.G. Xie, S.M. Huang, B.S. Hoyle, R. Thorn, C. Lenn, D. Snowden, M.S. Beck, Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors, IEE Proceedings G Circuits, Devices and Systems 139 89-98, 1992. – volume: 73 start-page: 615 year: 1951 ident: 10.1016/j.flowmeasinst.2018.10.010_bib17 article-title: An iteration formula for fredholm integral equations of the first kind publication-title: Am. J. Math. doi: 10.2307/2372313 – volume: 77 start-page: 37 year: 2000 ident: 10.1016/j.flowmeasinst.2018.10.010_bib30 article-title: The use of simultaneous iterative reconstruction technique for electrical capacitance tomography publication-title: Chem. Eng. J. doi: 10.1016/S1385-8947(99)00134-5 – volume: 38 start-page: 427 year: 1996 ident: 10.1016/j.flowmeasinst.2018.10.010_bib19 article-title: Conjugate gradient methods for toeplitz systems publication-title: Siam Rev. doi: 10.1137/S0036144594276474 – volume: 2 start-page: 183 year: 2009 ident: 10.1016/j.flowmeasinst.2018.10.010_bib46 article-title: A fast iterative shrinkage-thresholding algorithm for linear inverse problems publication-title: Siam J. Imaging Sci. doi: 10.1137/080716542 – volume: 60 start-page: 900 year: 2011 ident: 10.1016/j.flowmeasinst.2018.10.010_bib13 article-title: Electrical capacitance tomography for sensors of square cross sections using Calderon's method publication-title: IEEE Trans. Instrum. Meas. doi: 10.1109/TIM.2010.2045255 – volume: 18 start-page: 1854 year: 2010 ident: 10.1016/j.flowmeasinst.2018.10.010_bib23 article-title: Multilevel bioluminescence tomography based on radiative transfer equation Part 1: L1 regularization publication-title: Opt. Express doi: 10.1364/OE.18.001854 – volume: 17 start-page: 7029 year: 2017 ident: 10.1016/j.flowmeasinst.2018.10.010_bib18 article-title: Adaptive selection of relaxation factor in Landweber iterative algorithm publication-title: IEEE Sens. J. doi: 10.1109/JSEN.2017.2749881 – volume: 92 start-page: 2952 year: 2012 ident: 10.1016/j.flowmeasinst.2018.10.010_bib44 article-title: Split Bregman iterative algorithm for sparse reconstruction of electrical impedance tomography publication-title: Signal Process. doi: 10.1016/j.sigpro.2012.05.027 – volume: 15 start-page: 6089 year: 2015 ident: 10.1016/j.flowmeasinst.2018.10.010_bib6 article-title: A limited region electrical capacitance tomography for detection of deposits in pipelines publication-title: IEEE Sens. J. doi: 10.1109/JSEN.2015.2453361 – volume: 28 start-page: 35 year: 2017 ident: 10.1016/j.flowmeasinst.2018.10.010_bib33 article-title: Image reconstruction algorithms for electrical capacitance tomography based on ROF model using new numerical techniques publication-title: Meas. Sci. Technol. doi: 10.1088/1361-6501/aa524e – volume: 182 start-page: 1580 year: 2010 ident: 10.1016/j.flowmeasinst.2018.10.010_bib7 article-title: Flame imaging using 3D electrical capacitance tomography publication-title: Combust. Sci. Technol. doi: 10.1080/00102202.2010.497420 – volume: 2 start-page: 323 year: 2009 ident: 10.1016/j.flowmeasinst.2018.10.010_bib45 article-title: The split Bregman method for L1-regularized problems publication-title: SIAM J. Imaging Sci. doi: 10.1137/080725891 – volume: 31 start-page: 283 year: 2006 ident: 10.1016/j.flowmeasinst.2018.10.010_bib11 article-title: Tikhonov regularization algorithm for pseudomonotone variational inequalities publication-title: Acta Math. Vietnam. – volume: 37 start-page: 92 year: 2014 ident: 10.1016/j.flowmeasinst.2018.10.010_bib28 article-title: 3D ECT reconstruction by an improved Landweber iteration algorithm publication-title: Flow. Meas. Instrum. doi: 10.1016/j.flowmeasinst.2014.03.006 – volume: 27 start-page: 1 year: 2016 ident: 10.1016/j.flowmeasinst.2018.10.010_bib38 article-title: Evaluation of electrical capacitance tomography sensor based on the coupling of fluid field and electrostatic field publication-title: Meas. Sci. Technol. doi: 10.1088/0957-0233/27/7/074003 – volume: 37 start-page: 27 year: 2010 ident: 10.1016/j.flowmeasinst.2018.10.010_bib39 article-title: A generalized reconstruction algorithm for compressed sensing publication-title: Int. Conf. Intell. Syst. Des. Eng. Appl. – volume: 14 start-page: 1 year: 2003 ident: 10.1016/j.flowmeasinst.2018.10.010_bib2 article-title: Image reconstruction algorithms for electrical capacitance tomography publication-title: Meas. Sci. Technol. doi: 10.1088/0957-0233/14/1/201 – ident: 10.1016/j.flowmeasinst.2018.10.010_bib1 doi: 10.1049/ip-g-2.1992.0015 – volume: 328 start-page: 997 year: 2017 ident: 10.1016/j.flowmeasinst.2018.10.010_bib8 article-title: Determination of onset of bubbling and slugging in a fluidized bed using a dual-plane electrical capacitance tomography system publication-title: Chem. Eng. J. doi: 10.1016/j.cej.2017.07.098 – volume: 3 start-page: 112 year: 2013 ident: 10.1016/j.flowmeasinst.2018.10.010_bib34 article-title: Combined first and second order total variation inpainting using Split Bregman publication-title: Image Process. Line doi: 10.5201/ipol.2013.40 – volume: 43 start-page: 2413 year: 1998 ident: 10.1016/j.flowmeasinst.2018.10.010_bib20 article-title: Combining various projection access schemes with the algebraic reconstruction technique for low-contrast detection in computed tomography publication-title: Phys. Med. Biol. doi: 10.1088/0031-9155/43/8/032 – volume: 20 start-page: 1 year: 2009 ident: 10.1016/j.flowmeasinst.2018.10.010_bib14 article-title: Image reconstruction technique of electrical capacitance tomography for low-contrast dielectrics using Calderon's method publication-title: Meas. Sci. Technol. doi: 10.1088/0957-0233/20/10/104027 – volume: 66 start-page: 5 year: 2006 ident: 10.1016/j.flowmeasinst.2018.10.010_bib41 article-title: Iterative image restoration combining total variation minimization and a second-order functional publication-title: Int. J. Comput. Vis. doi: 10.1007/s11263-005-3219-7 – ident: 10.1016/j.flowmeasinst.2018.10.010_bib36 doi: 10.1049/ip-g-2.1992.0014 – volume: 22 start-page: 32 year: 2011 ident: 10.1016/j.flowmeasinst.2018.10.010_bib16 article-title: 2D electrical capacitance tomography with sensors of non-circular cross sections using the factorization method publication-title: Meas. Sci. Technol. – volume: 6 start-page: 756 year: 2002 ident: 10.1016/j.flowmeasinst.2018.10.010_bib43 article-title: Statistical data analysis based on the L1-norm and related methods publication-title: Comput. Stat. Data Anal. – volume: 17 start-page: 8263 year: 2017 ident: 10.1016/j.flowmeasinst.2018.10.010_bib9 article-title: Quantitative reconstruction of the exterior boundary shape of metallic inclusions using electrical capacitance tomography publication-title: IEEE Sens. J. doi: 10.1109/JSEN.2017.2718593 – volume: 99 start-page: 1 year: 2017 ident: 10.1016/j.flowmeasinst.2018.10.010_bib4 article-title: Towards multiphase flow decomposition based on electrical capacitance tomography sensors publication-title: IEEE Sens. J. – volume: 3 start-page: 1552 year: 1998 ident: 10.1016/j.flowmeasinst.2018.10.010_bib29 article-title: Rapid 3D cone-beam reconstruction with the Algebraic Reconstruction technique (art) by utilizing texture mapping graphics hardware publication-title: Nucl. Sci. Symp – volume: 9 start-page: 243 year: 2016 ident: 10.1016/j.flowmeasinst.2018.10.010_bib25 article-title: Research and application of NSSN neural network in electrical capacitance tomography image reconstruction publication-title: Int. J. Signal Process. – volume: 30 start-page: 1672 year: 2008 ident: 10.1016/j.flowmeasinst.2018.10.010_bib32 article-title: Principal component analysis based on L1-norm maximization publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2008.114 – volume: 9 start-page: 91 year: 2016 ident: 10.1016/j.flowmeasinst.2018.10.010_bib26 article-title: Improvement of SVM image reconstruction algorithm in ECT system publication-title: Int. J. Grid Distrib. Comput. doi: 10.14257/ijgdc.2016.9.3.11 – volume: 56 start-page: 23 year: 2017 ident: 10.1016/j.flowmeasinst.2018.10.010_bib5 article-title: Imaging of oil-water flow patterns by electrical capacitance tomography publication-title: Flow. Meas. Instrum. doi: 10.1016/j.flowmeasinst.2017.07.002 – volume: 11 start-page: 503 year: 1990 ident: 10.1016/j.flowmeasinst.2018.10.010_bib12 article-title: Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank publication-title: Siam J. Sci. Stat. Comput. doi: 10.1137/0911028 – volume: 48 start-page: 308 year: 2012 ident: 10.1016/j.flowmeasinst.2018.10.010_bib40 article-title: A combined first and second order variational approach for image reconstruction publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-013-0445-4 – volume: 17 start-page: 96 year: 2000 ident: 10.1016/j.flowmeasinst.2018.10.010_bib3 article-title: Using regularization methods for image reconstruction of electrical capacitance tomography publication-title: Part. Part. Syst. Charact. doi: 10.1002/1521-4117(200010)17:3<96::AID-PPSC96>3.0.CO;2-8 – volume: 60 start-page: 259 year: 1992 ident: 10.1016/j.flowmeasinst.2018.10.010_bib22 article-title: Nonlinear total variation based noise removal algorithms publication-title: Phys. D Nonlinear Phenom. doi: 10.1016/0167-2789(92)90242-F – volume: 66 start-page: 1428 year: 2007 ident: 10.1016/j.flowmeasinst.2018.10.010_bib31 article-title: Convergence of the Polak-Ribiére-Polyak conjugate gradient method publication-title: Nonlinear Anal. Theory Methods Appl. doi: 10.1016/j.na.2006.02.001 – volume: 136 start-page: 15 year: 2014 ident: 10.1016/j.flowmeasinst.2018.10.010_bib21 article-title: Weighted simultaneous iterative reconstruction technique for single-axis tomography publication-title: Ultramicroscopy doi: 10.1016/j.ultramic.2013.07.016 – volume: 6 start-page: 403 year: 2016 ident: 10.1016/j.flowmeasinst.2018.10.010_bib35 article-title: A novel mechanical fault diagnosis scheme based on the convex 1-D second-order total variation denoising algorithm publication-title: Appl. Sci. doi: 10.3390/app6120403 – volume: 16 start-page: 1786 year: 2016 ident: 10.1016/j.flowmeasinst.2018.10.010_bib37 article-title: A new algorithm for image reconstruction of electrical capacitance tomography based on inverse heat conduction problems publication-title: IEEE Sens. J. doi: 10.1109/JSEN.2015.2506409 – volume: 58 start-page: 267 year: 2011 ident: 10.1016/j.flowmeasinst.2018.10.010_bib42 article-title: Regression shrinkage and selection via the Lasso publication-title: J. R. Stat. Soc. doi: 10.1111/j.2517-6161.1996.tb02080.x – volume: 7 start-page: 149 year: 1964 ident: 10.1016/j.flowmeasinst.2018.10.010_bib24 article-title: Function minimization by conjugate gradients publication-title: Comput. J. doi: 10.1093/comjnl/7.2.149 – volume: 89 start-page: 1729 year: 2010 ident: 10.1016/j.flowmeasinst.2018.10.010_bib27 article-title: Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces publication-title: Appl. Anal. doi: 10.1080/00036810903517597 – volume: 10 start-page: 269 year: 2011 ident: 10.1016/j.flowmeasinst.2018.10.010_bib10 article-title: Image reconstruction algorithm for electrical capacitance tomography publication-title: Inf. Technol. J. doi: 10.3923/itj.2011.1614.1619 – volume: 21 start-page: 1 year: 2010 ident: 10.1016/j.flowmeasinst.2018.10.010_bib15 article-title: Electrical capacitance tomography with a non-circular sensor using the dbar method publication-title: Meas. Sci. Technol. |
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