Volume 6 Issue 5
Oct.  2013
Turn off MathJax
Article Contents
YAN Chun-sheng, LIAO Yan-biao, TIAN Qian. Image reconstruction algorithms of computed tomography[J]. Chinese Optics, 2013, 6(5): 617-632. doi: 10.3788/CO.20130605.0617
Citation: YAN Chun-sheng, LIAO Yan-biao, TIAN Qian. Image reconstruction algorithms of computed tomography[J]. Chinese Optics, 2013, 6(5): 617-632. doi: 10.3788/CO.20130605.0617

Image reconstruction algorithms of computed tomography

  • Received Date: 21 Jul 2013
  • Rev Recd Date: 18 Sep 2013
  • Publish Date: 10 Oct 2013
  • The image reconstruction algorithms of tomography are introduced. The characteristics of the various algorithms are compared from the points of view of the forward model simplication and reverse model mapping structure. Studies show that the various conversion methods belonging to linear algorithm have serious distortion, which can be improved by convolution filtering. The various iterative algorithms based on derivative search have strong initial value dependence and slow convergence and are easy to fall into a local optimal solution. The various Fourier transform methods have intrinsic limitation and the wavelet transform can characterize both the time and frequency domain minutiae of the image. The finite element method can simplify the forward model by smart designing pixels of the reconstruction object. With the physical background, the Monte Carlo method, simulated annealing, genetic algorithms, particle filter method and the neural network method are more suitable for complex and nonlinear image reconstruction. Moreover, intelligentization, modeling, parallelization, and integration of various algorithms are the trends for the image reconstruction algorithms of the tomography.

     

  • loading
  • [1] HERMAN G T. Image Reconstruction from Projections[M]. New York:Acdemic Press,1980. [2] 傅鹂,刘石,杨五强. 两相流测量中电容层析成像图像重建的广义逆最小模解与线性反投影和迭代法的比较[J]. 仪器仪表学报,2001,22(1):74-77. FU L,LIU SH,YANG W Q. Comparision of three image reconstruction algorithms for electrical capacitance tomography[J]. Chinese J. Scientific Instrument,2001,22(1): 74-77.(in Chinese) [3] XIE C G,HUANG S M,HOYLE B S,et al. Electrical capacitance tomography for flow imaging: system model for development of image reconstruction algorithms and design of primary sensor[J]. IEE Proceedings G,1992,139(1):89-98. [4] KAUFMAN L. Maximum likelihood, squares, and penalized least squares for PET[J]. IEEE T. Med. Imaging,1993,12(2):200-214. [5] 刘斌,李术才,李树忱,等. 基于不等式约束的最小二乘法三维电阻率反演及其算法优化[J]. 地球物理学报,2012,55(1):260-268. LIU B,LI SH C,LI SH C,et al.. 3D electrical resistivity inversion with least-squares method based on inequality constraint and its computation efficiency optimization[J]. Chinese J. Geophysics,2012,55(1):260-268.(in Chinese) [6] 蔡大用.高等数值分析[M]. 北京:清华大学出版社,1998. CAI D Y. Advanced Numerical Analysis[M]. Beijing:Tinghua University Press,1998.(in Chinese) [7] 陈宇,高宝庆,张立新,等. 基于加权奇异值分解截断共轭梯度的电容层析图像重建[J]. 光学 精密工程,2010,18(3):702-707. CHEN Y,GAO B Q,ZHANG L X,et al.. Image reconstruction based on weighted SVD truncation conjugate gradient algorithm for electrical capacitance tomography[J]. Opt. Precision Eng.,2010,18(3):702-707.(in Chinese) [8] VAUHKONEN M,VAD ASZ D,KARJALAINEN P A,et al.. Tikhonov regularization and prior information in electrical impedance tomography[J]. IEEE T. Med. Imaging,1998,17(2):285-293. [9] FREIBERGER M,CLASON C,SCHARFETTER H. Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach[J]. Appl. Optics,2010,49(19):3741-3747. [10] 王化祥,唐磊,闫勇. 电容层析成像图像重建的总变差正则化算法[J]. 仪器仪表学报,2007,28(11):2014-2018. WANG H X,TANG L,YAN Y. Total variation regularization algorithm for electrical capacitance tomography[J]. Chinese J. Scientific Instrument,2007,28(11):2014-2018.(in Chinese) [11] PENGL H,M ERKUS H,SCARLETT B. Using regularization methods to do image reconstruction of electrical capacitance tomography[J]. Part Syst Charact,2000,17(3):96-104. [12] LIU S,WANG H G,JIANG F,et al.. A new image reconstruction method for tomographic investigation of fluidized beds[J]. AIChE J.,2002,48(8):1631-1638. [13] 苏邦,张以恒,彭黎辉,等. 同步迭代图像重建技术在电容层析成像系统中的应用[J]. 清华大学学报 (自然科学版),2000,40(9):90-92. SU B,ZHANG Y H,PENG L H,et al.. Simultaneous iterative reconstruction technique for electrical capacitance tomography[J]. J Tsinghua University(Science and Technology),2000,40(9):90-92.(in Chinese) [14] 王小璞,张朋,李兴东,等. 一种块迭代的快速代数重建算法[J]. CT理论与应用研究,2000,9(增刊):10-12. WANG X P,ZHANG P,LI X D,et al.. A fast ART algorithm based on block iteration[J]. Computerized Tomography Theory and Appl.,2000,9(supp.):10-12.(in Chinese) [15] DAS R,MAHESH T S,KUMAR A. Efficient quantum-state tomography for quantum-information processing using a two-dimensional Fourier-transform technique[J]. Physical Rev. A,2003,67:062304. [16] JAM A K,AMSARI S. Radon transform theory for random fields and optimum image reconstruction from noisy projections[J]. IEEE International Conference on Ⅰ-CASSP'84,1984,9:495-498. [17] LOHNER R. Translation of Radon[M]. Atlanta:Georgia Institute of Technology,1917. [18] 李世雄,林其彭,李嘉禹. 分区连续函数的Radon变换的高精度反演法[J]. 地球物理学报,1996,39(2):251-264. LI SH X,LIN Q P,LI J Y. High precision reconstruction methods for radon transform of piecewise smooth functions[J]. Geophysics,1996,39(2):251-264.(in Chinese) [19] 张进,王仲,李雅洁,等. 高精度影像测量系统中图像的超分辨率重建[J]. 光学 精密工程,2011,19(1):168-174. ZHANG J,WANG ZH,LI Y J,et al.. Super-resolution reconstruction of image in high accuracy image measuring system[J]. Opt. Precision Eng.,2011,19(1):168-174.(in Chinese) [20] 邓建青,刘晶红,刘铁军. 基于DSP系统的超分辨率图像重建技术研究[J]. 液晶与显示,2012,27(1):114-120. DENG J Q,LIU J H,LIU T J. Super-resolution image reconstruction technology based on dsp system[J]. Chinese J. Liquid Crystals and Displays,2012,27(1):114-120.(in Chinese) [21] 邓建青,刘晶红. 基于Fourier-Mellin变换和Keren算法的改进运动估计算法[J]. 液晶与显示,2011,26(3):364-369. DENG J Q,LIU J H. Improved motion estimation algorithm based on Fourier-Mellin transform and Keren algorithm[J]. Chinese J. Liquid Crystals and Displays,2011,26(3):364-369.(in Chinese) [22] 李志国. 基于特征点匹配的图像配准算法精度提升方法研究[J]. 光学与光电技术,2012,10(6):103-106. LI ZH G. Research on precision improvement method of image registration algorithm based on feature points matching[J]. Opt. Optoelectronic Technology,2012,10(6):103-106.(in Chinese) [23] 章东,龚秀芬. |ω|滤波器对卷积滤波法进行非线性参量B/A成像的影响[J]. 声学学报,1995,20(4):271-279. ZHANG D,GONG X F. The influence of |ω| filter function on nonlinear parameter imaging using filtered convolution method[J]. Acta Acustica,1995,20(4):271-279.(in Chinese) [24] RAMACHANDRAN G N,LAKSHMINARAYANAN A V. Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transform[J]. Proc. National Acadmey Sci.,1971,68(9):2236-2240. [25] SHEPP L A,LOGAN B F. Reconstruction interior head tissue from X-ray transmissions[J],IEEE Trans,Nucl. Sci.,1974,21(1):228-236. [26] 姚姚.蒙特卡罗非线性反演方法及应用[M]. 北京:冶金工业出版社,1997. YAO Y. Monte Carlo Nonlinear Inversion Method and Its Application[M]. Beijing:Metallurgical Industry Press,1997.(in Chinese) [27] FLOCK S T,PATTERSON M S,WILSON B C,et al.. Monte Carlo modeling of light propagation in highly scattering tissues-I:model predictions and comparison with diffusion theory[J]. IEEE T. Bio-Med. Eng.,1989,36(12):1162-1168. [28] WALKER C,GOMATI M E. Monte carlo simulations of low energy electrons in solids. http:[C]//www.elec.york.ac.uk/research/projects/Monte_Carlo_simulations_of_low_energy_electrons_in_solids.html,2006. [29] NIEMZ M H.激光与生物组织的相互作用: 原理及应用[M]. 西安: 西安交通大学出版社, 1999. NIEMZ M H. Laser-tissue interactions:Principles and Applications[M]. Xi'an:Xi'an Jiaotong University Press,1999.(in Chinese) [30] 吴新杰,黄国兴,王静文. 粒子滤波算法在ECT图像重建中的应用[J]. 光学 精密工程,2012,20(8):1824-1830. WU X J,HUANG G X,WANG J W. Application of particle filtering algorithm to image reconstruction of ECT[J]. Opt. Precision Eng.,2012,20(8):1824-1830.(in Chinese) [31] 李军科,张串,吴建军. 基于蒙特卡洛方法的粒子滤波算法研究[J]. 电脑与信息技术,2008,16(1):49-53. LI J K,ZHANG C,WU J J. Study of particle filter algorithm based on Monte Carlo methods[J]. Computer and Information Technology,2008,16(1):49-53.(in Chinese) [32] WEBB S. The physical basis of IMRT and inverse planning[J]. The British J. Radiology,2003,76:678-689. [33] KIRKPATRICK S,GELATT C D,VECCHI M P. Optimization bysimulated annealing[J]. Science,1983,220(4 598):671-680. [34] BLACKOWIAK A D AND RAJAN S D. Multi-Path arrival estimates using simulated annealing:application to crosshole tomography experiment[J]. IEEE J. Ocanic Eng.,1995,20(3):157-165. [35] 王芳,陈生昌. 解非线性反演问题的新策略[J]. 石油物探,1999,38(3):76-84. WANG F,CHEN SH CH. New strategy to solute nonlinear inverse problem[J]. Geophysical Prospecting for Petroleum,1999,38(3):76-84.(in Chinese) [36] 阎春生. 光纤过程层析成像技术研究[D]. 北京:清华大学电子工程系,2003. YAN CH SH. Study on optical fiber process tomography [D]. Beijing:Department of Electronic Engineering,Tsinghua University,2003.(in Chinese) [37] SHI C Z,CHAN C C,JIN W. Improving the performance of a FBG sensor network using a genetic algorithm[J]. Sens. Actuators A.,2003,107:57-61. [38] 杜平安,甘娥忠,于亚婷.有限元法-原理、建模及应用[M]. 北京:国防工业出版社,2004. DU P A,GAN E ZH,YU Y T. Finite Element Method-principle, Modeling and Application[M]. Beijing:National Defense Industry Press,2004.(in Chinese) [39] 肖化,严杰,保宗悌. 有限元在电容层析中的应用研究[J]. 应用科学学报,1998,16(2):171-175. XIAO H,YAN J,BAO Z T. Application research of finite element in electrical capacitance tomography[J]. J. Appl. Sciences,1998,16(2):171-175.(in Chinese) [40] JOSHI A,BANGERTH W,SEVICK-MURACA E M. Adaptive finite element based tomography for fluorescence optical imaging in tissue[J]. Opt. Express,2004,12(22):5402-5417. [41] 蔡自兴,徐光佑.人工智能及其应用[M]. 3版.北京:清华大学出版社,2004. CAI Z X,XU G Y. Artificial Intelligence and Its Application[M]. 3nd ed. Beijing:Tsinghua University Press,2004.(in Chinese) [42] 李扬,汪仁煌,郑莹娜. 用线性神经网络映射光学过程层析成像的逆问题[J]. 中国图像图形学报,2003,8(7):738-743. LI Y,WANG R H,ZHENG Y N. Inverse problem of optic process tomography solved by using linear neural networks[J]. J. Image and Graphics,2003,8(7):738-743.(in Chinese) [43] 宋建中. 图像处理智能化的发展趋势[J]. 中国光学,2011,4(5):431-440. SONG J ZH. Development trend of image processing intelligence[J]. Chinese Optics,2011,4(5):431-440.(in Chinese) [44] OSBORN J,JUEZ F J D C,GUZMAN D,et al.. Using artificial neural networks for open-loop tomography[J]. Opt. Express,2012,20(3):2420-34. [45] 李岩,冯莉,朱艳丹,等. 类支集神经网络在ECT图像重建巾的研究与应用[J]. 计算机工程与应用,2011,47(25):205-211. LI Y,FENG L,ZHU Y D,et al.. Image reconstruction algorithm based on NSSN for Electrical Capacitance Tomography[J]. Computer Eng. Appl.,2011,47(25):205-211.(in Chinese) [46] 张彦俊,陈德运. 代数神经网络电阻层析成像图像重建算法[J]. 计算机工程与应用,2009,45(32):19-21. ZHANG Y J,CHEN D Y. Algebraic neural network image reconstruction algorithm for electrical resistance tomography[J]. Computer Eng. and Appl.,2009,45(32):19-21.(in Chinese) [47] 李岩,曹帅,冯莉,等. Chebyshev神经网络在ECT图像重建中的研究与应用[J]. 计算机工程与应用,2011,47(32):198-200. LI Y,CAO SH,FENG L,et al.. Research and application of image reconstruction algorithm based on Chebyshev for ECT[J]. Computer Eng. Appl.,2011,47(32):198-200.(in Chinese) [48] 唐远炎,王玲.小波分析与文本文字识别[M]. 北京:科学出版社,2004. TANG Y Y,WANG L. Wavelet Analysis and Text Character Recognition[M]. Beijing:Science Press,2004.(in Chinese) [49] DAUBECHIES I. Ten Lectures on Wavelets[M]. Philadelphia:Society for Industrial and Applied Mathematics,1992. [50] MALLAT S G. A theory of multiresolution signal decomposition:the wavelet representation[J]. IEEE Trans Pattern Anal. Machine Intel,1989,11(7):674-693. [51] ZHU W W,WANG Y,DENG Y N,et al.. A wavelet-based multiresolution regularized least squares reconstruction approach for optical tomography[J]. IEEE T. Med. Imaging,1997,16(2):210-217. [52] 陶李,王珏,邹永宁,等. 改进的Zernike矩工业CT图像边缘检测[J]. 中国光学,2012,5(1):48-56. DAO L,WANG J,ZOU Y N,et al.. Improved Zernike moment method for industrial CT image edge detection[J]. Chinese Optics,2012,5(1):48-56.(in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Article views(3193) PDF downloads(961) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return