Abstract：For the underdetermination of the inverse problem of electrical capacitance tomography (ECT), the improved linear Bregman algorithms based on singular value decomposition (SVD) and second-order iteration were applied to the ECT image reconstruction process. The simulation experiments showed that compared with SVD, Landweber, CG and linear Bregman algorithm, they had the higher image resolution and faster imaging speed. Among the two improved algorithms, the algorithm based on singular value decomposition had fewer image reconstruction artifacts, and the algorithm based on second-order iterations significantly increased the speed.
马敏,孙美娟. 基于改进线性Bregman算法的ECT图像重建算法[J]. 计量学报, 2021, 42(7): 879-884.
MA Min,SUN Mei-juan. Image Reconstruction Algorithms of ECT System Based on the Modified Linearized Bregman Algorithm. Acta Metrologica Sinica, 2021, 42(7): 879-884.
［1］Gunes C, Chowdhury S, Marashdeh Q M, et al. Displacement-current phase tomography and electrical capacitance tomography for air-water flow systems［C］//2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS). IEEE, 2017: 1-3.
［2］温银堂, 曹鹏鹏, 田洪刚, 等. 基于FCM优化的平面阵列电容成像算法［J］. 计量学报, 2020, 41(2): 231-237.
Wen Y T, Cao P P, Tian H G, et al. An Optimized Planar Array Capacitance Imaging Algorithm Based on FCM［J］. Acta Metrologica Sinica, 2020, 41(2): 231-237.
［3］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): 1488-1493.
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): 1488-1493.
［4］Cai J F, Osher S, Shen Z. Linearized Bregman iterations for compressed sensing［J］. Mathematics of Computation, 2009, 78(267): 1515-1536.
［5］Yin W, Osher S, Goldfarb D, et al. Bregman iterative algorithms for l1-minimization with applications to compressed sensing［J］. SIAM J Imaging Sci, 2008, 1(1): 143-168.
［6］马敏, 范广永, 孙颖. 电容成像双共轭梯度图像重建算法改进［J］. 北京航空航天大学学报, 2019, 45(8): 1-7.
Ma M, Fan G Y, Sun Y. Improvement of Capacitance Imaging Double Conjugate Gradient Image Reconstruction Algorithm［J］. Journal of Beijing university of aeronautics and astronautics, 2019, 45(8): 1-7.
［7］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.
［8］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. Application of compressive sensing in capacitance tomography［J］. Journal of Beijing university of aeronautics and astronautics, 2017, 43(11): 2316-2321.
［9］Lunglmayr M, Huemer M. Sparsity-Enabled Step Width Adaption For Linearized Bregman Based Algorithm［C］//2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2018: 608-612.
［10］Zhang H, Cheng L. A linearized Bregman iteration algorithm［J］. Math Numer Sin, 2010, 32(1): 97-104.
［11］Petkovic M D, Stanimirovic P S. Iterative method for computing the Moore-Penrose inverse based on penrose equations［J］. J Comput Appl Math, 2011, 235(6): 1604-1613.
［12］孙涛, 张慧, 成礼智. SVD加速的线性Bregman算法［J］. 计算机应用研究, 2014, 31(7): 2001-2003.
Sun T, Zhang H, Cheng L Z. Linear Bregman algorithm of SVD acceleration［J］. Computer Application Research, 2014, 31(7): 2001-2003.
［13］张彩霞, 电容层析成像系统的图像重建算法研究［D］. 天津:中国民航大学, 2013.
［14］Saha T, Srivastava S, Khare S, et al. An improved algorithm for basis pursuit problem and its applications［J］. Comput Appl Math, 2019, 355: 385-398.
［15］Gebhard A, Lunglmayr M, Huemer M. Investigations on Sparse System Identification with l0-LMS Zero Attracting LMS and Linearized Bregman Iterations［M］. Springer International Publishing, 2018: 1-9.
［16］Cai Y, Donatelli M, Bianchi D, et al. Regularization preconditioners for frame-based image deblurring with reduced boundary artifacts［J］. Siam Sci Compu, 2016, 38(1): B164-B189.
［17］马敏, 范广勇, 王涛. 基于ECT的占空比可调双阵列传感器设计［J］. 计量学报, 2019, 40(6): 1057-1063.
Ma M, Fan G Y, Wang T. Design of EGR Adjustable Dual Array Sensor Based on ECT［J］. Acta Metrologica Sinica, 2019, 40(6): 1057-1063.
2021, Vol. 42 
