In order to improve the sampling rate and the quality of the reconstructed images of electrical capacitance tomography (ECT) system,a new ECT image reconstruction algorithm based on compressed sensing theory was proposed.Firstly,using the orthogonal basis of Discrete Fourier Transformation,the gray signals of original images can be transformed into sparse signals.Then,14 electrodes randomly selected from the 16 electrodes ECT system were excited randomly and the capacitance values between different electrode pairs were also measured in a random order.By this way,the capacitance signals and the corresponding observation matrix were obtained.Finally,using L1 regularization model and primal dual interior point method,the gray signals of original images were achieved.The simulation results showed that the quality of the reconstructed images were better than the corresponding images obtained by the Landweber iterative algorithm.Therefore,the algorithm proposed can reconstruct high precision images with less observation data,which provides a new method for ECT image reconstruction.
[1] 王化祥,等.电学层析成像[M].北京:科学出版社,2013.4-6. Wang Huaxiang,et al.Electrical Tomography[M].Beijing:Science Press,2013.4-6.(in Chinese)
[2] 郭红星,余胜生,保宗悌,王延平.电容层析成像的电场分布与反演[J].电子学报,2002,30(1):62-65. Guo Hongxing,Yu Shengsheng,Bao Zongti,Wang Yanping.Electric field distributions and inversions for electrical capacitance tomography[J].Acta Electronica Sinica,2002,30(1):62-65.(in Chinese)
[3] 陈德运,陈宇,王莉莉,于晓洋.基于改进Gauss-Newton 的电容层析成像图像重建算法[J].电子学报,2009,37(4):739-743. Chen Deyun,Chen Yu,Wang Lili,Yu Xiaoyang.A novel gauss-newton image reconstruction algorithm for electrical capacitance tomography system[J].Acta Electronica Sinica,2009,37(4):739-743.(in Chinese)
[4] Donoho D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[5] Yeyang Yu,Mingjian Hong,Feng Liu,Hua Wang,Crozier S.Compressed sensing MRI using Singular Value Decompositionbased sparsity basis[A].Annual International Conference of the IEEE Engineering in Medicine and Biology Society[C].Milano,Italy:IEEE,2011.5734-5737.
[6] 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 Xinjie,Huang Guoxing,Wang jingwen.Application of compressed sensing to flow pattern identification of ECT[J].Optics and Precision Engineering,2013,21(4):1062-1068.(in Chinese)
[7] 马坚伟,徐杰,鲍跃全,等.压缩感知及其应用:从稀疏约束到低秩约束优化[J].信号处理,2012,28(5):609-623. Ma Jianwei,Xu Jie,Pao Yuequan,et al.Compressive sensing and its application:from sparse to low-rank regularized optimization[J].Signal Processing,2012,28(5):609-623.(in Chinese)
[8] Candès E J.Robust uncertainty principles and signal recovery[A].The 2nd Int Conf Computational Harmonic Anaysis[C].Nashville,TN,2004.
[9] 戴琼海,付长军,季向阳.压缩感知研究[J].计算机学报,2011,34(3):3425-3434. Dai Qionghai,Fu Changjun,Ji Xiangyang.Research on compressed sensing[J].Chinese Journal of Computers,2011,34(3):3425-3434.(in Chinese)
[10] Baraniuk R G.Compressive sensing[Lecture Notes] [J].IEEE Trans on Signal Processing Magazine,2007,24(4):118-121.
[11] 石光明,刘丹华,高大化,等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081. Shi Guangming,Liu Danhua,Gao Dahua,et al.Advances in theory and application of compressed sensing[J].Acta Electronica Sinica,2009,37(5):1070-1081.(in Chinese)
[12] Natarajan B K.Sparse approximate solutions to linear systems[J].SIAM Journal on Computing,1995,24(2):227-234.
[13] Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].SIAM Review,2001,43(1):129-159.
[14] 李然,干宗良,崔子冠,等.压缩感知图像重建算法的研究现状及其展望[J].电视技术,2013,37(19):7-14. Li Ran,Gan Zongliang,Cui Ziguan,Zhu Xiuchang,et al.Study status and prospective of compressive sensing image reconstruction[J].Video Engineering,2013,37(19):7-14.(in Chinese)
[15] Seung-Jean Kim,K Koh,M Lustig,Stephen Boyd,Dimitry Gorinevsky.An interior-point method for large-scale l1-regularized least squares[J].IEEE Journal of Selected Topics in Signal Processing,2007,1(4),606-617.
[16] 黎胜亮,刘昆,张峰,等.基于压缩感知在线稀疏的红外视频遥感凝视成像[J].电子学报,2015,43(3):518-522. Li Shengliang,Liu Kun,Zhang Feng,et al.Infrared remote sensing video staring imagery based on compressed sensing online sparse[J].Acta Electronica Sinica,2015,43(3):518-522.(in Chinese)
[17] Figueiredo M A T,Nowak R D,Wright S J.Gradient projection for sparse reconstruction:applicationto compressed sensing and other inverse problem[J].IEEE Journal of Selected Topics in Signal Processing,2007,1(4):586-597.
[18] 余恺,李元实,王智,等.基于压缩感知的新型声信号采集方法[J].仪器仪表学报,2012,33(1):105-112. Yu Kai,Li Yuanshi,Wang Zhi,et al.New method for acoustic signal collection based on compressed sampling[J].Chinese Journal of Scientific Instrument,2012,33(1):105-112.(in Chinese)
[19] 熊元新,陈允平.离散傅里叶变换的定义研究[J].武汉大学学报(工学版),2006,39(1):89-91,142. Xiong Yuanxin,Chen Yunping.Research on definition of discrete Fourier transform[J].Engineering Journal of Wuhan University,2006,39(1):89-91,142.(in Chinese)
[20] Geselowitz D B,An application of electrocardiographic lead theory to impedance plethysmography[J].IEEE Trans Biomed Eng,1971,18(1):38-41.
[21] 张立峰,王化祥.一种新的电容层析成像电极组合激励测量模式[J].化工学报,2012,63(3):860-865. Zhang Lifeng,Wang Huaxiang.A new combined-electrode exciting-measuring mode for electrical capacitance tomography[J].Ciesc Journal,2012,63(3):860-865.(in Chinese)
[22] 王琦,张荣华,王金海,王化祥.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 Qi,Zhang Ronghua,Wang Jinhai,Wang Huaxiang.Image reconstruction method based on compressive sensing for ECT/CT dual modality fusion system[J].Chinese Journal of Scientific Instrument,2014,35(6):1338-1346.(in Chinese)