基于改进FOCUSS算法的电容层析成像算法研究
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摘要
针对电容层析成像(electrical capacitance tomography,ECT)逆问题求解的病态性和不适定性,在压缩感知(compressed sensing,CS)的基础上,提出一种改进FOCUSS的ECT重建算法。采用离散余弦变换(DCT)基将原始图像灰度信号进行稀疏化处理,在使用正则化FOCUSS算法求解的过程中引入拟牛顿法逼近求解中间稀疏变量,以提高信号重构的准确性。仿真实验结果表明,同LBP、Tikhonov和Landweber和FOCUSS算法相比,改进的FOCUSS算法能够有效区分物场中的不同介质,改善图像过度平滑的问题,减小图像误差至0.23,提高图像相关系数至0.80,具有更好的成像效果,为ECT图像重建算法的研究提供新的思路。
On the basis of compressed sensing,this paper proposed an improved FOCUSS algorithm for the reconstruction of electrical capacitance tomography,which aiming at the ill-conditionedness and ill-posedness of the inverse problem of ECT. The discrete cosine transform(DCT) basis made the grayscale signals of original images sparse. In the process of solving the inverse problem by employing the regularized FOCUSS algorithm,it introduced the quasi-Newton method to approximate and solve the intermediate sparse variables to improve the accuracy of signal reconstruction. Results of the simulation show that compared with LBP,Tikhonov,Landweber and FOCUSS algorithm,the improved FOCUSS algorithm can effectively distinguish the different media in the substance field,alleviate the over-smoothing effect,reduce the image error between the original image and the reconstructed image to 0.23,it increases the correlation coefficient to 0.80,offers better image quality,and provides a new idea for the research on the algorithm for the reconstruction of ECT.
On the basis of compressed sensing,this paper proposed an improved FOCUSS algorithm for the reconstruction of electrical capacitance tomography,which aiming at the ill-conditionedness and ill-posedness of the inverse problem of ECT. The discrete cosine transform(DCT) basis made the grayscale signals of original images sparse. In the process of solving the inverse problem by employing the regularized FOCUSS algorithm,it introduced the quasi-Newton method to approximate and solve the intermediate sparse variables to improve the accuracy of signal reconstruction. Results of the simulation show that compared with LBP,Tikhonov,Landweber and FOCUSS algorithm,the improved FOCUSS algorithm can effectively distinguish the different media in the substance field,alleviate the over-smoothing effect,reduce the image error between the original image and the reconstructed image to 0.23,it increases the correlation coefficient to 0.80,offers better image quality,and provides a new idea for the research on the algorithm for the reconstruction of ECT.
引文
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[9]Bouchhima B,Amara R,Turki Hadj-Alouane M.Perceptual orthogonal matching pursuit for speech sparse modelling[J].Electronics Letters,2017,53(21):1431-1433.
[10]Wang Jing,Zhang Jisheng,Chen Chang,et al.Basic pursuit of an adaptive impulse dictionary for bearing fault diagnosis[C]//Proc of International Conference on Mechatronics and Control.2014.
[11]Zibetti M V W,Helou E S,Pipa D R,et al.accelerating overrelaxed and monotone fast iterative shrinkage-thresholding algorithms with line search for sparse reconstructions[J].IEEE Trans on Image Processing,2017,26(7):3569-3578.
[12]He Xingyu,Tong Ningning,Hu Xiaowei.Two-dimension gradient projection method for sparse matrix reconstruction[J].Electronics Letters,2016,52(17):1493-1495.
[13]Xie Kan,He Zhaoshui,Andrzej Cichocki,et al.Rate of Convergence of the FOCUSS Algorithm[J].IEEE Trans on Neural Networks and Learning Systems,2017,28(6):1276-1289.
[14]Deng Li,Yuan Sanyi,Wang Shangxu.Sparse Bayesian learning-based seismic denoise by using physical wavelet as basis functions[J].IEEEGeoscience and Remote Sensing Letters,2017,14(11):1993-1997.
[15]Gorodnitsky I F,George J S,Rao B D.Sparse signal reconstruction from limited data using FOCUSS:a re-weighted minimum norm algorithm[J].IEEE Trans on Signal Processing,1997,45(3):600-616.
[16]张立峰,刘昭麟,田沛.基于压缩感知的电容层析成像图像重建算法[J].电子学报,2017,45(2):353-358.(Zhang Lifeng,Liu Zhaolin,Tian Pei.Image reconstruction algorithm for electrical capacitance tomography based on compressed sensing[J].Acta Electronica Sinica,2017,45(2):353-358.)
[17]Zhen Ren,Yang W Q.A simulation study of a miniature parallel ECTsensor[C]//Proc of IEEE International Conference on Imaging Systems and Techniques.Piscataway,NJ:IEEE Press,2014:144-147.
[2]赵玉磊.电容层析成像的图像重建算法研究与半物理仿真平台设计[D].西安:西安电子科技大学,2016.(Zhao Yulei.Research on image reconstruction algorithms and design of semi-physical simulation system for electrical capacitance tomography[D].Xi’an:Xidian University,2016.)
[3]薛倩,马敏,王化祥.基于电场中心线的ECT灵敏度矩阵计算[J].中南大学学报:自然科学版,2016,47(11):3929-3934.(Xue Qian,Ma Min,Wang Huaxiang.Sensitivity matrix generation for electrical capacitance tomography based on electrical field center lines[J].Journal of Central South University:Science and Technology,2016,47(11):3929-3934.)
[4]Cui Ziqiang,Wang Qi,Xue Qian,et al.A review on image reconstruction algorithms for electrical capacitance/resistance tomography[J].Sensor Review,2016,36(4):429-445.
[5]Donoho D L.Compressed sensing[J].IEEE Trans on Information Theory,2006,52(4):1289-1306.
[6]Candes E J,Romberg J,Tao T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J].IEEE Trans on Information Theory,2006,52(2):489-509.
[7]任越美,张艳宁,李映.压缩感知及其图像处理应用研究进展与展望[J].自动化学报,2014,40(8):1563-1575.(Ren Yuemei,Zhang Yanning,Li Ying.Advances and perspective on compressed sensing and application on image processing[J].Acta Automatica Sinica,2014,40(8):1563-1575.)
[8]Wang Lin,Cai Gaigai,You Wei,et al.Transients extraction based on averaged random orthogonal matching pursuit algorithm for machinery fault diagnosis[J].IEEE Trans on Instrumentation and Measurement,2017,66(12):3237-3248.
[9]Bouchhima B,Amara R,Turki Hadj-Alouane M.Perceptual orthogonal matching pursuit for speech sparse modelling[J].Electronics Letters,2017,53(21):1431-1433.
[10]Wang Jing,Zhang Jisheng,Chen Chang,et al.Basic pursuit of an adaptive impulse dictionary for bearing fault diagnosis[C]//Proc of International Conference on Mechatronics and Control.2014.
[11]Zibetti M V W,Helou E S,Pipa D R,et al.accelerating overrelaxed and monotone fast iterative shrinkage-thresholding algorithms with line search for sparse reconstructions[J].IEEE Trans on Image Processing,2017,26(7):3569-3578.
[12]He Xingyu,Tong Ningning,Hu Xiaowei.Two-dimension gradient projection method for sparse matrix reconstruction[J].Electronics Letters,2016,52(17):1493-1495.
[13]Xie Kan,He Zhaoshui,Andrzej Cichocki,et al.Rate of Convergence of the FOCUSS Algorithm[J].IEEE Trans on Neural Networks and Learning Systems,2017,28(6):1276-1289.
[14]Deng Li,Yuan Sanyi,Wang Shangxu.Sparse Bayesian learning-based seismic denoise by using physical wavelet as basis functions[J].IEEEGeoscience and Remote Sensing Letters,2017,14(11):1993-1997.
[15]Gorodnitsky I F,George J S,Rao B D.Sparse signal reconstruction from limited data using FOCUSS:a re-weighted minimum norm algorithm[J].IEEE Trans on Signal Processing,1997,45(3):600-616.
[16]张立峰,刘昭麟,田沛.基于压缩感知的电容层析成像图像重建算法[J].电子学报,2017,45(2):353-358.(Zhang Lifeng,Liu Zhaolin,Tian Pei.Image reconstruction algorithm for electrical capacitance tomography based on compressed sensing[J].Acta Electronica Sinica,2017,45(2):353-358.)
[17]Zhen Ren,Yang W Q.A simulation study of a miniature parallel ECTsensor[C]//Proc of IEEE International Conference on Imaging Systems and Techniques.Piscataway,NJ:IEEE Press,2014:144-147.