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ECT Image Reconstruction Based on Improved Half-threshold Iterative Algorithm |
MA Min,LIU Yi-fei,LIU Ya-nan |
College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China |
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Abstract To solve the problem of ill-posedness and underdetermination for the inverse problem of electrical capacitance tomography, the theory of compressed sensing was applied to the imaging process to alleviate its underdetermination. First, the initial signal was sparsed processing, and then the rows of the sensitivity matrix were rearranged based on the Gaussian random matrix, then the singular value decomposition (SVD) was used to obtain the observation matrix with higher column independence. Finally, the half-threshold iterative algorithm based on l1/2 norm was introduced into the ECT imaging process, and the constraint term of l2 norm was added to the penalty function, and solved by the improved semi-threshold iterative algorithm. The simulation experiment showed that the algorithm effectively reduced the image error and took into account the imaging speed, and had good performance in the ECT imaging process.
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Received: 09 September 2019
Published: 24 May 2021
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[1]王化祥. 电学层析成像技术[J]. 自动化仪表, 2017, 38(5): 1-6.
Wang H X. Electrical Tomography Technology[J]. Process Automation Instrumentation, 2017, 38(5): 1-6.
[2]马敏, 孙美娟, 李明. 基于lp-范数的ECT图像重建算法研究[J]. 计量学报, 2020, 41(9): 1127-1132.
Ma M, Sun M J, Li M. Research on ECT Image Reconstruction Algorithm Based on lp- norm [J]. Acta Metrologica Sinica, 2020, 41(9): 1127-1132.
[3]张立峰, 蒋玉虎. 电容层析成像三维图像重建研究[J]. 计量学报, 2019, 40(3): 462-465.
Zhang L F, Jiang Y H. Study of Three-dimensional Image Reconstruction for Electrical Capacitance Tomography [J]. Acta Metrologica Sinica, 2019, 40(3): 462-465.
[4]陈宇. 电容层析成像反问题求解及图像重建算法研究[D]. 哈尔滨: 哈尔滨理工大学, 2010.
[5]王化祥. 电学层析成像[M]. 北京: 科学出版社, 2013.
[6]Qi C, Shi L. Flame imaging in meso-scale porous media burner using electrical capacitance tomography[J]. Chinese Journal of Chemical Engineering, 2012, 20 (2): 329-336.
[7]Cui Z Q, Wang Q, Xue Q, et al. A review on image reconstruction algorithms for electrical capacitance/resistance tomography[J]. Sensor Review, 2016, 36 (4): 429-445.
[8]Donoho D L. Compressed sensing [J]. IEEE Trans on Information Theory, 2006, 52 (4): 1289-1306.
[9]Candes E, Romberg J. Sparsity and incoherence in compressive sampling[J]. Inverse problems, 2007, 23 (3): 969.
[10]Candes E J, Tao T. Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strateg[J]. IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425.
[11]Candes E J, Tao T. Decoding by linear programming[J]. IEEE transactions on information theory, 2005, 51 (12): 4203-4215.
[12]吴新杰, 黄国兴, 王静文. 压缩感知在电容层析成像流型辨识中的应用[J]. 光学精密工程, 2013, 21(4): 1062-1068.
Wu X J, Huang G X, Wang J W. Application of compressed sensing to flow pattern identification of ECT[J]. Optics and Precision Engineering, 2013, 21(4): 1062-1068.
[13]王琦, 张荣华, 王金海, 等. 基于压缩感知的ECT/CT双模融合系统成像方法[J]. 仪器仪表学报, 2014, 35(6): 1338-1346.
Wang Q, Zhang R H, Wang J H, et al. Image reconstruction method based on compressive sensing for ECT/CT dual modality fusion system[J]. Chinese Journal of Scientific Instrument, 2014, 35(06): 1338-1346.
[14]张立峰. 压缩感知在电容层析成像中的应用[J]. 北京航空航天大学学报, 2017, 43(11): 2316-2321.
Zhang L F. Compressed sensing application to electrical capacitance tomography[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(11): 2316-2321.
[15]吴新杰, 闫诗雨, 徐攀峰, 等. 基于稀疏度自适应压缩感知的电容层析成像图像重建算法[J]. 电子与信息学报, 2018, 40(5): 1250-1257.
Wu X J, Yan S Y, Xu P Y, et al. Image Reconstruction Algorithm for Electrical Capacitance Tomography Based on Sparsity Adaptive Compressed Sensing[J]. Journal of Electronics & Information Technology, 2018, 40(5): 1250-1257.
[16]张勇, 侯之超, 赵永玲. 基于频响函数截断奇异值响应面的有限元模型修正[J]. 振动工程学报, 2017, 30(3): 341-348.
Zhang Y, Hou Z C, Zhao Y L. Finite Element Model Modification for Truncating Singular Response Surface Based on Frequency Response Function[J]. Journal of Vibration Engineering, 2017, 30(3): 341-348.
[17]Xu Z, Zhang H, Wang Y, et al. l1/2regularization[J]. Science China Information Sciences, 2010, 53(6): 1159-1169.
[18]谢林林. 一种快速求解l1/2-正则化问题的新算法[D]. 大连:大连理工大学, 2014.
[19]Xu Z B, Chang X Y, Xu F M, et al. l1/2 regularization: A thresholding representation theory and a fast solver[J]. IEEE Trans Neural Netw Learn Syst, 2012, 23: 1013-1027.
[20]周健, 刘荣敏, 窦云峰, 等. 采用L_(1/2)稀疏约束的梅尔倒谱系数语音重建方法[J]. 声学学报, 2018, 43(6): 991-999.
Zhou J, Liu R M, Dou Y F, et al. Speech reconstruction from Mel-frequencycepstral coefficients via L1/2 sparse constraint[J]. Acta Acustica, 2018, 43(6): 991-999.
[21]张立峰, 朱炎峰. 基于粒子群优化极限学习机及电容层析成像的两相流流型及其参数预测[J]. 计量学报, 2020, 41(12): 1488-1495.
Zhang L F, Zhu Y F. Two-phase Flow Regime and its Parameter Prediction Based on Particle Swarm Optimization Extreme Learning Machine and Electrical Capacitance Tomography[J]. Acta Metrologica Sinica, 2020, 41(12): 1488-1495. |
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