三维电阻抗成像数值算法和技术基础研究
摘要
电阻抗成像（Electrical Impedance Tomography, EIT）是一种新型的医学成像技术，通过向被测场域施加电激励并测量其表面的电响应来重构其内部的电导率分布。与现有医学影像技术相比，电阻抗成像技术具有功能性成像、设备简单、成本低廉、体积小、对人体无创无害等优点。在临床医学领域，如脑部疾病、消化道疾病、肺部疾病、肿瘤诊断等方面具有良好的应用前景。目前电阻抗成像的研究主要集中在二维成像，现有的三维系统一般采用多层闭合电极的结构，主要应用在肺部、胃部疾病的诊断。而乳腺癌、腹腔内渗血等疾病的诊断，只需要研究皮肤下浅层区域的电导率分布，且乳房等器官不适合使用多层的闭合电极。本文拟在开放式电阻抗成像的基础上，研究三维电阻抗成像激励测量模式、重构算法、系统实现和物理实验等问题，可以应用在乳腺癌普查、前期诊断和腹腔内出血的检测。论文的主要研究内容包括以下几个方面：
1）分析研究国内外现有电阻抗成像系统，针对临床应用提出平板电极加背电极的电阻抗成像结构，该结构可以使电流场分布更加均匀，并能增加探测深度。
2）三维电阻抗成像正问题研究。在研究三维电阻抗成像电极模型的基础上，由麦克斯韦方程组推导全电极模型的有限元方程，在Matlab环境下编写有限元程序，并采用商业电磁场仿真软件Comsol对比程序计算精度。结果表明程序计算结果与Comsol结果误差小于4%，可以作为逆问题计算的基础。采用仿真手段对比研究现有的电阻抗成像激励测量模式，提出区分度和表面投影成像两种评估方法，结果表明背电极电流激励模式区分度高，投影图像效果好，为三维系统设计提供依据。
3）三维电阻抗成像逆问题研究。采用基于牛顿拉弗逊算法的Tikhonov和NOSER正则化算法，首次针对平板电极结构系统开展三维场域的重构计算。提出类似拉普拉斯算子的Tikhonov正则化矩阵选取方法，并使用L曲线确定正则化参数。建立三维圆柱模型对单目标情况进行仿真，结果表明，两种正则化算法存在各自的优缺点。在此基础上提出混合这两种算法的混合正则化算法，通过在同一模型中的仿真，表明混合算法进一步降低条件数，改善逆问题性态，使重建过程趋于稳定，提高目标分辨率。由于三维场域逆问题计算量巨大，计算时间长，借鉴开放式电阻抗成像的方式，提出对二维图像进行线性插值的三维插值成像的思想，通过快速的二维成像以及线性插值，可以得到两层二维图像之间的电导率分布情况。
4）测量系统研制。在深入探讨电阻抗成像激励源、信号测量关键问题基础上，介绍了三维多频电阻抗成像测量硬件系统各个模块设计思路以及实现方式，设计制作出实验样机，并对系统各项性能展开测试。
5）实验研究。为验证样机的性能和重构算法有效性，开展了物理模型实验，包括水槽时差成像实验、琼脂模型时差成像实验、琼脂模型频差成像实验。设计模拟腹腔内出血的血块实验，通过改变血块体积模拟不同出血量。实验结果表明，三维电阻抗成像系统能够重构出深度4cm、大小1cm的目标，分辨不同体积的血块，图像的空间分辨率较高。
最后对研究工作进行了总结，指出目前存在的问题及改进方向。
Electrical Impedance Tomography（EIT） is a new medical imaging modality thatimages by computing electrical properties inside the human body. In the clinicalmedical field it has a good application prospect, such as gastrointestinal disease, lungdisease, cancer diagnosis and brain disease. Compared to the current medical imagingtechnology, EIT has its own advantages, for example, functional imaging, simpleequipment, low-cost and non-invasion. So far the study for EIT has focused on the2-Dmodel. The electrode system of current3D EIT is multilayer closed electrode which isused in the lung, stomach disease diagnosis. While in the breast cancer andintra-abdominal ooze blood disease diagnosis, the conductivity distribution under theskin of the shallow area need to be study. This paper have study the3D EIT include themeasurement system, the stimulatied model, the reconstruction algorithm and physicalexperiment. This system can be used in breast cancer diagnosis and abdominal bleedingdetection. The main contents of the dissertation includethe following parts:
1) The current breast cancer detection equipments, including the domestic andforeign existing EIT systems, were studied and analysed. The structure of plateelectrodes and the back electrode was proposed for clinical application, which makesthe current distribution more uniform, as well as increases the detecting depth.
2) As for the forward problem of3-D EIT, the finite element equations of completeelectrode model were deduced based on the3-D electrode modeling and themathematical model in the electromagnetic problem. Finite element programs werecompiled in Matlab, and commercial electromagnetic field simulation software Comsolwas applied to compare the accuracy of the programs. The results show that the errorbetween Matlab and Comsol is less than4%, which indicate that Matlab programs canbe used as the basis of inverse calculation. The simulations of finite element programswas used to contrast several existing stimulation patterns, then two methods, thedistinguishability and surface projection image methods, were put forward to evaluatethe stimulation pattern. The results show that the back electrode pattern has obviousadvantages in differentiation degree and the projective quality, which provides providereference for the system design.
3) Baesd on the characteristics of the inverse problems of EIT, the Tikhonovregularization algorithm and Newton's One-step Error Reconstructor (NOSER) were used to reconstructed the3D field firstly. The optimal method which is called L-curvemethod was used to select the better Tikhonov regularization parameter. And then theregularization matrix which is similar to the Laplace operator was also given. Then, a3-D cylinder model is set for simulation. The results show that the single regularizationalgorithm has its own merits and demerits, and therefore a hybrid algorithm waspresented based on Tikhonov regularization and the NOSER.Finally, a series ofsimulations were carried out to compare these three algorithms.The encouraging resultsindicate that this proposed algorithm can reduce the number of condition, make thereconstruction process stable and improve the spstial resolution. Owing to the greatamount of calculation in3D inverse problem, based on the2D image reconstruction foropen EIT,3D interpolation imaging algorithm was put forward, and linear interpolationalgorithm was used to get the images between two2D layers.
4) The hardware system was developed. Based on the deep research on the keyproblem of EIT measurement and constant flow source, the principle and realization of3D multi-frequency measurement system were introduced. The experiment prototypewas built and the basic performances had been tested.
5) To test the effectiveness of the performance of the prototype and the combinedreconstruction algorithm, the physical model experiment were carried out, includingtank dynamic imaging experiment, agar dynamic model experiment and the frequencydifference imaging experiments. A simulation experiment of abdominal bleeding wasdesigned, by changing the clot volume to simulate the different blood loss. Theexperimental results show that this3D imaging system can detect the1-cm diametertarget in4-cm-deep and distinguish different volume of blood clots. The spatialresolution of the image and the contrast is better.
The final part is the summary description. This paper summarized the majorresearch achievements, as well as the existing problems and deficiencies. Meanwhile,the further researches on this topic were previewed.
1）分析研究国内外现有电阻抗成像系统，针对临床应用提出平板电极加背电极的电阻抗成像结构，该结构可以使电流场分布更加均匀，并能增加探测深度。
2）三维电阻抗成像正问题研究。在研究三维电阻抗成像电极模型的基础上，由麦克斯韦方程组推导全电极模型的有限元方程，在Matlab环境下编写有限元程序，并采用商业电磁场仿真软件Comsol对比程序计算精度。结果表明程序计算结果与Comsol结果误差小于4%，可以作为逆问题计算的基础。采用仿真手段对比研究现有的电阻抗成像激励测量模式，提出区分度和表面投影成像两种评估方法，结果表明背电极电流激励模式区分度高，投影图像效果好，为三维系统设计提供依据。
3）三维电阻抗成像逆问题研究。采用基于牛顿拉弗逊算法的Tikhonov和NOSER正则化算法，首次针对平板电极结构系统开展三维场域的重构计算。提出类似拉普拉斯算子的Tikhonov正则化矩阵选取方法，并使用L曲线确定正则化参数。建立三维圆柱模型对单目标情况进行仿真，结果表明，两种正则化算法存在各自的优缺点。在此基础上提出混合这两种算法的混合正则化算法，通过在同一模型中的仿真，表明混合算法进一步降低条件数，改善逆问题性态，使重建过程趋于稳定，提高目标分辨率。由于三维场域逆问题计算量巨大，计算时间长，借鉴开放式电阻抗成像的方式，提出对二维图像进行线性插值的三维插值成像的思想，通过快速的二维成像以及线性插值，可以得到两层二维图像之间的电导率分布情况。
4）测量系统研制。在深入探讨电阻抗成像激励源、信号测量关键问题基础上，介绍了三维多频电阻抗成像测量硬件系统各个模块设计思路以及实现方式，设计制作出实验样机，并对系统各项性能展开测试。
5）实验研究。为验证样机的性能和重构算法有效性，开展了物理模型实验，包括水槽时差成像实验、琼脂模型时差成像实验、琼脂模型频差成像实验。设计模拟腹腔内出血的血块实验，通过改变血块体积模拟不同出血量。实验结果表明，三维电阻抗成像系统能够重构出深度4cm、大小1cm的目标，分辨不同体积的血块，图像的空间分辨率较高。
最后对研究工作进行了总结，指出目前存在的问题及改进方向。
Electrical Impedance Tomography（EIT） is a new medical imaging modality thatimages by computing electrical properties inside the human body. In the clinicalmedical field it has a good application prospect, such as gastrointestinal disease, lungdisease, cancer diagnosis and brain disease. Compared to the current medical imagingtechnology, EIT has its own advantages, for example, functional imaging, simpleequipment, low-cost and non-invasion. So far the study for EIT has focused on the2-Dmodel. The electrode system of current3D EIT is multilayer closed electrode which isused in the lung, stomach disease diagnosis. While in the breast cancer andintra-abdominal ooze blood disease diagnosis, the conductivity distribution under theskin of the shallow area need to be study. This paper have study the3D EIT include themeasurement system, the stimulatied model, the reconstruction algorithm and physicalexperiment. This system can be used in breast cancer diagnosis and abdominal bleedingdetection. The main contents of the dissertation includethe following parts:
1) The current breast cancer detection equipments, including the domestic andforeign existing EIT systems, were studied and analysed. The structure of plateelectrodes and the back electrode was proposed for clinical application, which makesthe current distribution more uniform, as well as increases the detecting depth.
2) As for the forward problem of3-D EIT, the finite element equations of completeelectrode model were deduced based on the3-D electrode modeling and themathematical model in the electromagnetic problem. Finite element programs werecompiled in Matlab, and commercial electromagnetic field simulation software Comsolwas applied to compare the accuracy of the programs. The results show that the errorbetween Matlab and Comsol is less than4%, which indicate that Matlab programs canbe used as the basis of inverse calculation. The simulations of finite element programswas used to contrast several existing stimulation patterns, then two methods, thedistinguishability and surface projection image methods, were put forward to evaluatethe stimulation pattern. The results show that the back electrode pattern has obviousadvantages in differentiation degree and the projective quality, which provides providereference for the system design.
3) Baesd on the characteristics of the inverse problems of EIT, the Tikhonovregularization algorithm and Newton's One-step Error Reconstructor (NOSER) were used to reconstructed the3D field firstly. The optimal method which is called L-curvemethod was used to select the better Tikhonov regularization parameter. And then theregularization matrix which is similar to the Laplace operator was also given. Then, a3-D cylinder model is set for simulation. The results show that the single regularizationalgorithm has its own merits and demerits, and therefore a hybrid algorithm waspresented based on Tikhonov regularization and the NOSER.Finally, a series ofsimulations were carried out to compare these three algorithms.The encouraging resultsindicate that this proposed algorithm can reduce the number of condition, make thereconstruction process stable and improve the spstial resolution. Owing to the greatamount of calculation in3D inverse problem, based on the2D image reconstruction foropen EIT,3D interpolation imaging algorithm was put forward, and linear interpolationalgorithm was used to get the images between two2D layers.
4) The hardware system was developed. Based on the deep research on the keyproblem of EIT measurement and constant flow source, the principle and realization of3D multi-frequency measurement system were introduced. The experiment prototypewas built and the basic performances had been tested.
5) To test the effectiveness of the performance of the prototype and the combinedreconstruction algorithm, the physical model experiment were carried out, includingtank dynamic imaging experiment, agar dynamic model experiment and the frequencydifference imaging experiments. A simulation experiment of abdominal bleeding wasdesigned, by changing the clot volume to simulate the different blood loss. Theexperimental results show that this3D imaging system can detect the1-cm diametertarget in4-cm-deep and distinguish different volume of blood clots. The spatialresolution of the image and the contrast is better.
The final part is the summary description. This paper summarized the majorresearch achievements, as well as the existing problems and deficiencies. Meanwhile,the further researches on this topic were previewed.
引文
[1] A. M. Dijkstra, B. H. Brown, A. D. Leathard, et al. Clinical Applications of ElectricalImpedance Tomography[J], Journal of Medical Engineering&Technology,1993,17(3):89-98.
[2] J. C. Newell, P. M. Edic, X. D. Ren, et al, Assessment of Acute pulmonary Edema in Dogs byElectrical Impedance Imaging[J]. IEEE Transactions on Biomedical Engineering,1996,43(2):133-138.
[3] L. E. Baker, Applications of the Impedance Technique to the Respiratory System[J]. IEEEEngineering in Medicine and Biology Magazine,1989, March:50-52.
[4] I. Frerichs, G. Hahn, G. Hellige, Gravity-dependent Phenomena in Lung VentilationDeterminined by Functional EIT[J], Physiol. Meas.,1996,17(Suppl.4A):149-157.
[5] B. H. Brown, Tissue Impedance Methods [J], Prog. Med. Enviro. Phys.,1983,2:85-110.
[6] Schwan, H. P., Electrical properties of tissue and cell suspensions, in Lawrence, J. H. andTobias, C. A.(eds.) Advances in Biological and Medical Physics [M]. New York: AcademicPress,1957.
[7] S. Gabriel, R. W. Lau and C. Gabriel, The Dielectric Properties of Biological Tissues: II.Measurements in the Frequency Range10Hz to20GHz [J], Phys. Med. Biol.,1996,41:2251–2269.
[8]颜威利,徐桂芝等.生物医学电磁场数值分析[M].机械工业出版社.2007.
[9] Andrzej J. Surowiec, Stanislaw S, et al. Dielectric Properties of Breast Carcinoma and theSurrounding Tissues[J]. IEEE Transactions on Biomedical Engineering,1988,35(4):257-263.
[10]黄嵩，电阻抗静态成像中正则化算法研究[D]，重庆大学博士学位论文，2005.
[11] Webster J.G, SaKamoto K., Yorkey T.J, Some physical result from an impedance camera [J].Chin. Phy. Physiol. Meas.,1987,8(Suppl A):71-75.
[12] B.H. Brown, A.D. Seagar, The Sheffield Data Collection System [J], Clin. Phys. Physiol.Meas.,1987,8(Suppl A):91-97.
[13] Robert W.M., et al. A real time electrical impedance tomography system for clinical usedesign and preliminary result [J], IEEE BME,1995,42(2):133-140.
[14] Ji Zhenyu, Dong Xiuzhen, Fu Feng, et al. Study of influencing factors on ElectricalImpedance Scanning Imaging. In:Proceedings of the27th Annual Conference, EMBS[C].Shanghai: IEEE2EMBS,2005.2910-2913.
[15] Zheng Xu, Wei He, Haijun Luo, et al. A Multi-channel Magnetic Induction TomographyMeasurement System for Human Brain Model Imaging [J]. Physiol. Meas.2009,30(6):175-186.
[16]徐征.开放式磁感应成像技术基础研究[D].重庆大学博士学位论文.2008.
[17] Woo EJ. Recent development of magnetic resonance electrical impedance tomographytoward high-resolution conductivity imaging. In: Proceedings of2007Joint Meeting of the6thInternational Symposium on Noninvasive Functional Source Imaging of the Brain andHeart and the International Conference on Functional Biomedical Imaging (NFSI&ICFBI2007)[C]. Hangzhou: IEEE,2007:201-204
[18] Chen RX, Wan DR. Further investigation of reliability onimpedance gastrograph forcontinuous measurement of humangastric contractile activity. Peroceedings of the8thinternationalconference on electrical bio-impedance, July,1992, Kupio,Finland:151-152.
[19]任超世，李章勇，王伟等.无创电阻抗胃动力检测与评价[J].中国组织工程研究与临床康复,2010,14(9):1653-1657.
[20] Erol RA, Smallwood. Brown, et al. Detecting oeso-phaseal-related changes using electricalimpedance tomography [J], Physiol. Meas.1995,16:143-152.
[21] R.H. Smallwood, Y.F. Mangnall and A.D. A.D. Leathard, Transport of Gastric Contents [J],Physiol. Meas.,1994,15(Suppl.2A):175-188.
[22] S.P. Devane. Application of EIT to Gastric Emptying in Infants: Validation Against ResidualVolume Method, Clinical and Physiological Applications of Electrical ImpedanceTomography [M], D. Holder (ed). UCL Press, London.1993, Chapter12,113-123.
[23] S.J. Watson, R.H. Smallwood, B.H. Brown, P. Cherian and K.D. Bardhan K.D.,Determination of the Relationship Between the pH and Conductivity of Gastric Juice [J],Physiol. Meas.,1996.17:21-27.
[24] D. S. Holder，Temple，Effectiveness of the Sheffield EIT system in distinguishing patientswith pulmonary pathology from a series of normal subject [M], In: Holder DS, ed. Clinicaland physiological application of electrical impedance tomography. UCL Press, London,1993.
[25]范文茹，王化祥，马雪翠.基于先验信息的肺部电阻抗成像算法[J].中国生物医学工程学报,2009.28(5):680-685.
[26] Jossinet, The Variability of Resistivity in Human Breast Tissue [J], Medical and BiologicalEngineering and Computing,1996, Vol(34):346-350.
[27] DS Holder, Rao A,Hanquan Y.Imaging of physiotogically evoked responses by electricalimpedance tomography with cortical electrodes in the anaesthetised rabbit [J].PhysiolMeas,1996;17(3):179-186.
[28] Schuier FJ, Hossmann KA．Experimental brain infarcts in cats [J]．Ischemic Brain EdemaStroke,1980,11:563-601.
[29]张伟,张鸿毅,保庭毅等.小猪腹腔内出血模型及电阻抗成像监护的初步研究[J].生物医学工程学杂志,2009.26(1):10-13.
[30]李正,董秀珍,尤富生等.电阻抗成像监护家兔腹内出血的实验研究[J].生物医学工程与临床,2006.10(1):5-8.
[31] Watanabe R, Kotoura H, Morishita Y. CT analysis of the use of the electrical impedancetechnique to estimate local oedema in the extremities in patients with lymphatic obstruction[J]. Medicine Biomedical Engineering Compute,1998.36:60-64.
[32] Michel A, Orah L, Dov M, et al. The T-SCANTMtechnology: electrical impedance as adiagnostic tool for breast cancer detection [J]. Physiol. Meas,2001,22(1):1-8.
[33] TransScan T-Scan2000-P970033[E], United States FDA, http://www.fda.gov/cdrh/pdf/p970033.htm,1999-4-16.
[34] Malich A, Fritsch T, Anderson R, et al. Electrical impedance scanning for classifyingsuspicious breast lesions: first results [J]. Eur Radiol,2000.10:1555-1561.
[35] V Cherepenin, A Karpov, A Korjenevsky, et al. A3D electrical impedance tomography (EIT)system for breast cancer detection [J]. Physiol. Meas,2001,22(1):9-18.
[36] Vladimir A C, Alexander Y k, Vladimir N K, et al. Three-Dimensional EIT Imagine of BreastTissues: System Design and Clinical Testing [J]. IEEE Transactions on Medical Imaging,2002,21(6):662-667.
[37] Ryan Halter, Alex Hartov and Keith D Paulsen. Design implementation of a high frequencyelectrical tomography system [J]. Physiol. Meas,2004,25(1):379-390.
[38] Ryan Halter, Alex Hartov and Keith D Paulsen. A Broadband High-Frequency ElectricalImpedance Tomography System for Breast Imaging [J]. IEEE Transactions on BiomedicalEngineering,2008,55(2):650-659.
[39] Z-Tech Breast Scan [E]. http://medgadget.com/2005/04/ztech_breast_sc.html.2005-4-25.
[40] R. D. Cook, G. J. Saulnier, D. G. Gisser, et al. ACT3: a high-speed, high-precision electricalimpedance tomograph [J]. IEEE Trans. Biomed. Eng.,1994,41(8):713-722.
[41] Liu Ning, ACT4: a high-precision, multi-frequency electrical impedance tomograph [D], PhDthesis, Rensselaer Polytechnic Institute,2007.
[42] Myoung Hwan Choi, Tzu-Jen Kao, David Isaacson, et al. A Reconstruction Algorithm forBreast Cancer Imaging With Electrical Impedance Tomography in Mammography Geometry[J]. IEEE Transactions on Biomedical Engineering,2007,54(4):700-710.
[43] Tzu-Jen Kao, G J Saulnier, Hongjun Xia, et al. A compensated radiolucent electrode array forcombined EIT and mammography [J]. Physiol. Meas,2007,28(1):291-299.
[44]殷银锁.电阻抗乳腺扫描(EIS)硬件故障诊断系统的研究及图像后处理[D].第四军医大学硕士学位论文.2008.
[45]张帅.人体胸腔电阻抗成像系统研究[D].河北工业大学博士学位论文.2009.
[46]王平,何为.无创脑水肿检测新技术和临床应用分析[J].重庆大学学报.2003,26(8):83-85.
[47]何为,罗辞勇,张占龙.一种观察脑水肿的新方法:脑电阻抗地形图——原理和临床研究[J].医疗卫生装备,2004,11:5-7.
[48]何传红,何为,黄嵩,等,开放式电阻抗成像基本原理和仿真实验研究[J],中国生物医学工程学报,2008,27(5):669-674.
[49]陈民铀，张晓菊，罗辞勇,等.基于开放式场域的EIT模型及仿真[J].重庆大学学报.2009,32(7):731-735.
[50]何传红.开放式电阻抗成像原理和技术研究[D].重庆大学博士学位论文.2009.
[51] M Cheney, D Isaacson. Issues in Electrical Impedance Imaging[J]. IEEE Computational SciEng,1995,2:53-62.
[52] D.C. Barber, B.H. Brown, I.L. Freeston. Imaging Spatial Distributions of Resistivity UsingApplied Potential Tomography[J]. Electron. Lett.,1983,19:933-935.
[53] D.C. Barber and A.D. Seagar. Fast Reconstruction of Resistance Images[J]. Clin. Phys.Physiol. Meas.,1987,8(Suppl. A):47-54.
[54] Gencer N G, Kuzuoglu M, Ider Y Z. Sensitivity matrix approach for image reconstruction forelectrical impedance tomography. Abstracts of the European Community Workshop on ImageReconstruction in Electrical Impedance Tomography[M]. Toulouse,1992,26-27.
[55] Geselowitz D B.1971. An application of electrocardiographic lead theory to impedanceplethysmography[J]. IEEE Trans. Bio med. Eng., BME18(1):28-41
[56] M.Vauhkonen,P.A.Karjalainen and J.P.Kaipio. A Kalman filter approach applied to thetracking of fast movements of organ boundaries[C]. Proceedings of the20th AnnualInternational Conference of the IEEE Engineering in Medicine and Biology Society,1998,Vol.20, No2,1048-1051.
[57] Chen Y M, Liu JQ. An numerical algorithm for remote sensing of thermal conductivity[J].CompPhys,1981,43:315-326
[58] Y Kim, JG Webster, Tompkins WJ. Electrical impedance imaging of the thorax[J]. MicrowavePower,1983,(18):245-257
[59] Nachman A I. Global uniqueness for a two-dimensional inverse boundary value problem[J].Ann. Math.,1993,42:71-96.
[60] Mueller J L,Siltanen S, Isaacson D. A direct reconstruction algorithm for electrical impedancetomography[J]. IEEE Trans. Med. maging,2002,1(6):555-559.
[61] Sung Chan Jun, Jihyeon Kuen, Jeehyun Lee, et al. Frequency-difference EIT (fdEIT) usingweighted difference and equivalent homogeneous admittivity: validation by simulation andtank experiment [J]. Physiol. Meas.,2009,30:1087–1099.
[62] A. P. Calderon. On an inverse boundary value problem [C], Seminar on Numerical Analysisand its Applications to Continuum Physics. Rio de Janeiro, Editors W. H. Meyer and M. A.Raupp, Sociedade Brasileira de Matematica,1980:65-73.
[63] F Kleinermanny, N J Avisy, S K Judah et al. Three-dimensional image reconstruction forelectrical impedance tomography[J]. Physiol. Meas,1996,17:77-83.
[64] Liu yin, Gong lian, Liu ping, et al. An algorithm and simulation of the inverse problem of alow-frequency current field[J]. IEEE Trans on Magnetics,1990,26(2):630-633.
[65]王宏斌.广义反投影方法在三维电阻抗成像中的研究及实现[D].河北工业大学博士学位论文.2011.
[66]张星园.中国乳腺癌发病率呈上升趋势[E], http://news.sina.com.cn/c/2011-03-23/153122167799.shtml,2011-03-23.
[67]东方网.沪女性乳腺癌发病率全国最高,中年女性发病率增长快[E], http://news.ifeng.com/gundong/detail_2011_10/19/9975591_0.shtml,2011-10-19.
[68] Tzu-Jen Kao. A3-D Reconstruction Algorithm for Electrical Impedance Tomography UsingPlanar Electrode Arrays [D], PhD thesis, Rensselaer Polytechnic Institute,2005.
[69]钱英，医学超声设备的新进展，医疗设备信息，2002(11):25-27.
[70] Kwong KK, Belliveau JW, Chesler DA. Dynamic magnetic resonance imaging of humanbrain activity during primary sensory stimulation [J]. Proc Nat Acad Sci USA,1992,89:5675-5679.
[71] Scintimammography [E], http://www.radiologyinfo.org/en/info.cfm?pg=Scintimammo,2010-11-15.
[72] Shepp LA, et al. Maximum likelihood reconstruction in emission tomography [J]. IEEE Trans.Med. Imag.,1982. MI-1:113-122.
[73]王仁平.三维电阻抗成像系统设计与实现[D].河北工业大学硕士学位论文.2006.
[74] Holder D S. Electrical impedance tomography of brain function [C]. Int cof electromagneticfield problems and applications, Chongqing: TSI Press,2008, April:465-470.
[75]刘国强.医学电阻抗成像[M].科学出版社,2006
[76] Cheng K S, Issaacson D, Newell J C, et al, Electrode models for electric current computedtomography[J]. IEEE Trans. Biomed Engr.,1989,36:918-924.
[77]王长清,祝西里.电磁场计算中的时域有限差分法[M].北京大学出版社.1994.
[78]李忠元.电磁场边界元素法[M].北京理工大学出版社.1987.
[79]颜威利,杨庆新,汪友华等.电气工程电磁场数值分析[M].机械工业出版社.2005
[80]龙驭球,新型有限元法引论[M],北京,清华大学出版社,1992
[81] Singiresu S. Rao. The Finite Element Method in Engineering [M]. Elsevier Science&Technology Books.2004.
[82] E Somersalo, M Cheney and D Isaacson, Existence and uniqueness for electrode models forelectric current computed tomography[J]. SIAM J Appl Math,1992,52:1023-1040.
[83] TZU-JEN KAO, J C NEWELL, G J SAULNIER, et al. Distinguishability of inhomogeneitiesusing planar electrode arrays and different patterns of applied excitation [J]. Physiol. Meas.2003,24(1):403-411.
[84] Hadamard J. Lectures on the Cauchy Problem in Linear Partial Differential Equations[M].Yale University Press.1923.
[85]赵翔.概率统计方法在微波生物医学成像和雷电电磁效应评估中的应用[D].四川大学博士学位论文.2005.
[86]黄卡玛,赵翔等.电磁场中的逆问题及应用[M].科学出版社.2005.
[87]穆明凯.3G移动通信无源器件及漏泄电缆技术研究[D].浙江大学博士学位论文.2007.
[88]宋雷鸣.基于相控麦克风阵列的逆向噪声源识别原理与技术研究[D].北京交通大学博士学位论文.2010.
[89]张全升.高速公路路面和路基病害检测理论与方法研究[D].中国地质大学博士学位论文.2007.
[90] E Somersalo, M Cheney and D Isaacson. Layer stripping: a direct numerical method forimpedance imaging[J]. Inverse Prob.1991.7:899-926.
[91] Wexler A, Fry B, Neiman M R. Impedance computed tomography algorithm and system[J].Applied Optics.1985,24:3985-3992.
[92] Woo E J, Hua P, Webster J G, et al. A robust image reconstruction algorithm and its parallelimplementation in electrical impedance tomography[J]. IEEE Trans. Med. Imaging.1993,12(2):137-146.
[93] Ye J C, Webb K J. Modified distorted Born iterative method with an approximate Fre'chetderivative for optical diffusion tomography[J]. J. Opt. Soc. Am. A,1999,16(7):1814-1826.
[94] Yang L. Truyen B, Cornelis J. A global optimization approach to electrical impedancetomography[C]. IEEE-EMBS19th Annual International Conference Proceedings, Chicago,1997,1(1):437-444.
[95]侯卫东，莫玉龙.基于遗传算法的电阻抗图像重建[J].生物医学工程学杂志，2003，20(1):107-111.
[96]侯卫东，莫玉龙.基于反向神经网络的阻抗断层图像重建新方法[J].光学学报,2002,22(12):1475-1478.
[97] Tikhonov A. On the solution of incorrectly formulated problems and the regularizationmethod[J]. Soviet Math, Doklady,1963,4:1035-1038.
[98] M.Vauhkonen, D.Vadasz,P.A.Karjalainen, E.Somersalo,etc. Tikhonov regularization and priorinformation in electrical impedance tomography[J]. IEEE Trans. on Med. Img., vol.17, no.2,1998.
[99] Rundnl I, Osher S, Fatem E. Nonlinear total variation based noise removal algorithms[J].Physics D.1992(60):259-268
[100] M. Cheney, D. Isaacson, J. C. Newell, et al, NOSER: An Algorithm for Solving the InverseConductivity Problem [J]. International Journal of Imaging Systems and Technology,1990,2:66-75.
[101] G.H. Golub, P.C. Hansen, D.P. O'Leary. Tikhonov regularization and total least squares [J].SIAM Journal of Matrix Analysis and Applications,1999,1:185-194.
[102] A.N. Tikhonov, V.Y. Arsenin. Soutions of ill-posed problems [M]. Winston,1997.
[103] M.Vauhkonen. Electrical Impedance Tomography and Prior Information[D]. Kupio University,Finland,1997
[104] HANSEN P C, Analysis of discrete ill-posed problems by means of the L-curve[J]. SIAMReview,1992,34(4):561-580.
[105] HANSEN P C,O’LEARY D P.The Use of the L-curve in the regularization of discreteill-posed problems[J].SIAM J.Sci. Comput.,1993,14(6):1487-1503.
[106]陈玉艳,王旭等.基于Tikhonov和变差正则化的磁感应断层成像重建算法[J].东北大学学报,2011,4:460-463
[107]黄嵩,张占龙等.基于混合正则化算法的颅内异物电阻抗成像仿真研究[J].中国生物工程学报,2007,5:695-699.
[108] Hongbin Wang, Guizhi Xu, Shuai Zhang, Ning Yin and Weili Yan, Implementation ofGeneralized back Projection Algorithm in3-D EIT[J], IEEE Transactions on Magnetics,2011,47(5):1466-1469.
[109]庄天戈. CT原理与算法[M].上海交通大学出版社,1992.
[110]缪斌和,邓元木,黄斐增,等.基于对应点匹配的断层图像三维插值方法[J].中国医学物理学杂志,2000,17(1):14-16.
[111] Zhuang Qiao-li, Shen Wei, Sun Qi, et al. Shape-based interpolation of CT image with windowtechnology[C]. International Conference on Computer Application and System Modeling,October22-24, Taiyuan, China.IEEE,2010:536-538
[112] SU C Y, LIN Y S. Colour interpolation using wavelet-based classifiers[J]. ElectronicsLetters,2007,43(12):667-669.
[113]邹鹏程,尹学松.基于断层图像分割的三维匹配插值[J].计算机工程与应用，2004(24)：80-82
[114] Donald J Kalar, Patrick Garrigan, Thomas D Wickens, et al. A unified model of illusory andoccluded contour interpolation[J]. Vision Research,2010,50(3):284-299.
[115] Bat-Sheva Hadad,Daphne Maurer, Terri L Lewis. The development of contour interpolation:Evidence from subjective contours[J]. Journal of Experimental ChildPsychology,2010,106(2-3):163-176.
[116] Albu A B, Beugeling T, Laurendeau D. A morphology-based approach for intersliceinterpolation of anatomical slices from volumetric images[J].2008,55(8):2022–2038.
[117]鞠康.开发式三维多频电阻抗测量系统[D].重庆大学硕士学位论文,2011.
[118]鞠康,何为,何传红,刘斌,李冰.基于数字相敏检波的恒流源输出阻抗检测及补偿技术实现[J].医疗卫生装备.2009,10:5-7.
[119]王守三. PCB的电磁兼容设计技术、技巧和工艺.机械工业出版社.2008年.
[120]白居宪.直接数字频率合成[M].西安:西安交通大学出版社.2007年.
[121]张平，秦嘉川，王茂，刘志言。数字合成正弦信号相位噪声及抑制方法研究。哈尔滨工业大学学报，第31卷第5期，1999：73-78.
[122]王超,郎健,王化祥.用于生物阻抗测量的混频激励电流源[J].计量学报,2006,27(4)：392-396.
[123]董秀珍，史学涛，秦明新等。用于电阻抗参数成像的多频率组合扫频信号源[J]。第四军医大学学报，2000,21（11）：1367-1370.
[124]鞠康,何为,何传红,李冰,罗海军.基于直接数字频率合成的混合频率恒流源设计[J].仪器仪表学报.2010,9:2109-2113.
[125]姜建国,曹建中,高玉明.信号与系统分析基础[M].北京:清华大学出版社.2006年.
[126] Willis J. Tompkins著,林家瑞,徐邦荃译.生物医学数字信号处理[M].华中科技大学出版社.2001
[127]任爱锋,初秀琴,常存,孙肖子.基于FPGA的嵌入式系统设计.西安电子科技大学出版社.2004年.
[128]王晓俊,周杏鹏,王毅.精密阻抗分析仪中数字相敏检波技术研究与实现[J].仪器仪表学报,2006,6:592-595.
[129] N. Liu, G. J. Saulnier, J. C. Newell, A Multichannel Synthesizer and Voltmeter for ElectricalImpedance Tomography [C]. Proc. of25th Annual International Conference of IEEE EMBS,2003:3110-3113.
[130] Tzu-Jen Kao, Gary J. Saulnier, David Isaacson, et. al. A Versatile High-Permittivity Phantomfor EIT [J]. IEEE Transactions on biomedical engineering,2008,55(11):2601-2607.
[131] Eung Je Woo, Impedance Spectroscopy and Multi-Frequency Electrical ImpedanceTomography [J]. International Journal of Bioelectromagnetism,2007,9(2):101-102.
[132]张国鹏,董秀珍,尤富生等.小猪血液的多频电阻抗特性及其等效电路模型的研究[J].航天医学与医学工程,2006,19(1):51-55.
[2] J. C. Newell, P. M. Edic, X. D. Ren, et al, Assessment of Acute pulmonary Edema in Dogs byElectrical Impedance Imaging[J]. IEEE Transactions on Biomedical Engineering,1996,43(2):133-138.
[3] L. E. Baker, Applications of the Impedance Technique to the Respiratory System[J]. IEEEEngineering in Medicine and Biology Magazine,1989, March:50-52.
[4] I. Frerichs, G. Hahn, G. Hellige, Gravity-dependent Phenomena in Lung VentilationDeterminined by Functional EIT[J], Physiol. Meas.,1996,17(Suppl.4A):149-157.
[5] B. H. Brown, Tissue Impedance Methods [J], Prog. Med. Enviro. Phys.,1983,2:85-110.
[6] Schwan, H. P., Electrical properties of tissue and cell suspensions, in Lawrence, J. H. andTobias, C. A.(eds.) Advances in Biological and Medical Physics [M]. New York: AcademicPress,1957.
[7] S. Gabriel, R. W. Lau and C. Gabriel, The Dielectric Properties of Biological Tissues: II.Measurements in the Frequency Range10Hz to20GHz [J], Phys. Med. Biol.,1996,41:2251–2269.
[8]颜威利,徐桂芝等.生物医学电磁场数值分析[M].机械工业出版社.2007.
[9] Andrzej J. Surowiec, Stanislaw S, et al. Dielectric Properties of Breast Carcinoma and theSurrounding Tissues[J]. IEEE Transactions on Biomedical Engineering,1988,35(4):257-263.
[10]黄嵩，电阻抗静态成像中正则化算法研究[D]，重庆大学博士学位论文，2005.
[11] Webster J.G, SaKamoto K., Yorkey T.J, Some physical result from an impedance camera [J].Chin. Phy. Physiol. Meas.,1987,8(Suppl A):71-75.
[12] B.H. Brown, A.D. Seagar, The Sheffield Data Collection System [J], Clin. Phys. Physiol.Meas.,1987,8(Suppl A):91-97.
[13] Robert W.M., et al. A real time electrical impedance tomography system for clinical usedesign and preliminary result [J], IEEE BME,1995,42(2):133-140.
[14] Ji Zhenyu, Dong Xiuzhen, Fu Feng, et al. Study of influencing factors on ElectricalImpedance Scanning Imaging. In:Proceedings of the27th Annual Conference, EMBS[C].Shanghai: IEEE2EMBS,2005.2910-2913.
[15] Zheng Xu, Wei He, Haijun Luo, et al. A Multi-channel Magnetic Induction TomographyMeasurement System for Human Brain Model Imaging [J]. Physiol. Meas.2009,30(6):175-186.
[16]徐征.开放式磁感应成像技术基础研究[D].重庆大学博士学位论文.2008.
[17] Woo EJ. Recent development of magnetic resonance electrical impedance tomographytoward high-resolution conductivity imaging. In: Proceedings of2007Joint Meeting of the6thInternational Symposium on Noninvasive Functional Source Imaging of the Brain andHeart and the International Conference on Functional Biomedical Imaging (NFSI&ICFBI2007)[C]. Hangzhou: IEEE,2007:201-204
[18] Chen RX, Wan DR. Further investigation of reliability onimpedance gastrograph forcontinuous measurement of humangastric contractile activity. Peroceedings of the8thinternationalconference on electrical bio-impedance, July,1992, Kupio,Finland:151-152.
[19]任超世，李章勇，王伟等.无创电阻抗胃动力检测与评价[J].中国组织工程研究与临床康复,2010,14(9):1653-1657.
[20] Erol RA, Smallwood. Brown, et al. Detecting oeso-phaseal-related changes using electricalimpedance tomography [J], Physiol. Meas.1995,16:143-152.
[21] R.H. Smallwood, Y.F. Mangnall and A.D. A.D. Leathard, Transport of Gastric Contents [J],Physiol. Meas.,1994,15(Suppl.2A):175-188.
[22] S.P. Devane. Application of EIT to Gastric Emptying in Infants: Validation Against ResidualVolume Method, Clinical and Physiological Applications of Electrical ImpedanceTomography [M], D. Holder (ed). UCL Press, London.1993, Chapter12,113-123.
[23] S.J. Watson, R.H. Smallwood, B.H. Brown, P. Cherian and K.D. Bardhan K.D.,Determination of the Relationship Between the pH and Conductivity of Gastric Juice [J],Physiol. Meas.,1996.17:21-27.
[24] D. S. Holder，Temple，Effectiveness of the Sheffield EIT system in distinguishing patientswith pulmonary pathology from a series of normal subject [M], In: Holder DS, ed. Clinicaland physiological application of electrical impedance tomography. UCL Press, London,1993.
[25]范文茹，王化祥，马雪翠.基于先验信息的肺部电阻抗成像算法[J].中国生物医学工程学报,2009.28(5):680-685.
[26] Jossinet, The Variability of Resistivity in Human Breast Tissue [J], Medical and BiologicalEngineering and Computing,1996, Vol(34):346-350.
[27] DS Holder, Rao A,Hanquan Y.Imaging of physiotogically evoked responses by electricalimpedance tomography with cortical electrodes in the anaesthetised rabbit [J].PhysiolMeas,1996;17(3):179-186.
[28] Schuier FJ, Hossmann KA．Experimental brain infarcts in cats [J]．Ischemic Brain EdemaStroke,1980,11:563-601.
[29]张伟,张鸿毅,保庭毅等.小猪腹腔内出血模型及电阻抗成像监护的初步研究[J].生物医学工程学杂志,2009.26(1):10-13.
[30]李正,董秀珍,尤富生等.电阻抗成像监护家兔腹内出血的实验研究[J].生物医学工程与临床,2006.10(1):5-8.
[31] Watanabe R, Kotoura H, Morishita Y. CT analysis of the use of the electrical impedancetechnique to estimate local oedema in the extremities in patients with lymphatic obstruction[J]. Medicine Biomedical Engineering Compute,1998.36:60-64.
[32] Michel A, Orah L, Dov M, et al. The T-SCANTMtechnology: electrical impedance as adiagnostic tool for breast cancer detection [J]. Physiol. Meas,2001,22(1):1-8.
[33] TransScan T-Scan2000-P970033[E], United States FDA, http://www.fda.gov/cdrh/pdf/p970033.htm,1999-4-16.
[34] Malich A, Fritsch T, Anderson R, et al. Electrical impedance scanning for classifyingsuspicious breast lesions: first results [J]. Eur Radiol,2000.10:1555-1561.
[35] V Cherepenin, A Karpov, A Korjenevsky, et al. A3D electrical impedance tomography (EIT)system for breast cancer detection [J]. Physiol. Meas,2001,22(1):9-18.
[36] Vladimir A C, Alexander Y k, Vladimir N K, et al. Three-Dimensional EIT Imagine of BreastTissues: System Design and Clinical Testing [J]. IEEE Transactions on Medical Imaging,2002,21(6):662-667.
[37] Ryan Halter, Alex Hartov and Keith D Paulsen. Design implementation of a high frequencyelectrical tomography system [J]. Physiol. Meas,2004,25(1):379-390.
[38] Ryan Halter, Alex Hartov and Keith D Paulsen. A Broadband High-Frequency ElectricalImpedance Tomography System for Breast Imaging [J]. IEEE Transactions on BiomedicalEngineering,2008,55(2):650-659.
[39] Z-Tech Breast Scan [E]. http://medgadget.com/2005/04/ztech_breast_sc.html.2005-4-25.
[40] R. D. Cook, G. J. Saulnier, D. G. Gisser, et al. ACT3: a high-speed, high-precision electricalimpedance tomograph [J]. IEEE Trans. Biomed. Eng.,1994,41(8):713-722.
[41] Liu Ning, ACT4: a high-precision, multi-frequency electrical impedance tomograph [D], PhDthesis, Rensselaer Polytechnic Institute,2007.
[42] Myoung Hwan Choi, Tzu-Jen Kao, David Isaacson, et al. A Reconstruction Algorithm forBreast Cancer Imaging With Electrical Impedance Tomography in Mammography Geometry[J]. IEEE Transactions on Biomedical Engineering,2007,54(4):700-710.
[43] Tzu-Jen Kao, G J Saulnier, Hongjun Xia, et al. A compensated radiolucent electrode array forcombined EIT and mammography [J]. Physiol. Meas,2007,28(1):291-299.
[44]殷银锁.电阻抗乳腺扫描(EIS)硬件故障诊断系统的研究及图像后处理[D].第四军医大学硕士学位论文.2008.
[45]张帅.人体胸腔电阻抗成像系统研究[D].河北工业大学博士学位论文.2009.
[46]王平,何为.无创脑水肿检测新技术和临床应用分析[J].重庆大学学报.2003,26(8):83-85.
[47]何为,罗辞勇,张占龙.一种观察脑水肿的新方法:脑电阻抗地形图——原理和临床研究[J].医疗卫生装备,2004,11:5-7.
[48]何传红,何为,黄嵩,等,开放式电阻抗成像基本原理和仿真实验研究[J],中国生物医学工程学报,2008,27(5):669-674.
[49]陈民铀，张晓菊，罗辞勇,等.基于开放式场域的EIT模型及仿真[J].重庆大学学报.2009,32(7):731-735.
[50]何传红.开放式电阻抗成像原理和技术研究[D].重庆大学博士学位论文.2009.
[51] M Cheney, D Isaacson. Issues in Electrical Impedance Imaging[J]. IEEE Computational SciEng,1995,2:53-62.
[52] D.C. Barber, B.H. Brown, I.L. Freeston. Imaging Spatial Distributions of Resistivity UsingApplied Potential Tomography[J]. Electron. Lett.,1983,19:933-935.
[53] D.C. Barber and A.D. Seagar. Fast Reconstruction of Resistance Images[J]. Clin. Phys.Physiol. Meas.,1987,8(Suppl. A):47-54.
[54] Gencer N G, Kuzuoglu M, Ider Y Z. Sensitivity matrix approach for image reconstruction forelectrical impedance tomography. Abstracts of the European Community Workshop on ImageReconstruction in Electrical Impedance Tomography[M]. Toulouse,1992,26-27.
[55] Geselowitz D B.1971. An application of electrocardiographic lead theory to impedanceplethysmography[J]. IEEE Trans. Bio med. Eng., BME18(1):28-41
[56] M.Vauhkonen,P.A.Karjalainen and J.P.Kaipio. A Kalman filter approach applied to thetracking of fast movements of organ boundaries[C]. Proceedings of the20th AnnualInternational Conference of the IEEE Engineering in Medicine and Biology Society,1998,Vol.20, No2,1048-1051.
[57] Chen Y M, Liu JQ. An numerical algorithm for remote sensing of thermal conductivity[J].CompPhys,1981,43:315-326
[58] Y Kim, JG Webster, Tompkins WJ. Electrical impedance imaging of the thorax[J]. MicrowavePower,1983,(18):245-257
[59] Nachman A I. Global uniqueness for a two-dimensional inverse boundary value problem[J].Ann. Math.,1993,42:71-96.
[60] Mueller J L,Siltanen S, Isaacson D. A direct reconstruction algorithm for electrical impedancetomography[J]. IEEE Trans. Med. maging,2002,1(6):555-559.
[61] Sung Chan Jun, Jihyeon Kuen, Jeehyun Lee, et al. Frequency-difference EIT (fdEIT) usingweighted difference and equivalent homogeneous admittivity: validation by simulation andtank experiment [J]. Physiol. Meas.,2009,30:1087–1099.
[62] A. P. Calderon. On an inverse boundary value problem [C], Seminar on Numerical Analysisand its Applications to Continuum Physics. Rio de Janeiro, Editors W. H. Meyer and M. A.Raupp, Sociedade Brasileira de Matematica,1980:65-73.
[63] F Kleinermanny, N J Avisy, S K Judah et al. Three-dimensional image reconstruction forelectrical impedance tomography[J]. Physiol. Meas,1996,17:77-83.
[64] Liu yin, Gong lian, Liu ping, et al. An algorithm and simulation of the inverse problem of alow-frequency current field[J]. IEEE Trans on Magnetics,1990,26(2):630-633.
[65]王宏斌.广义反投影方法在三维电阻抗成像中的研究及实现[D].河北工业大学博士学位论文.2011.
[66]张星园.中国乳腺癌发病率呈上升趋势[E], http://news.sina.com.cn/c/2011-03-23/153122167799.shtml,2011-03-23.
[67]东方网.沪女性乳腺癌发病率全国最高,中年女性发病率增长快[E], http://news.ifeng.com/gundong/detail_2011_10/19/9975591_0.shtml,2011-10-19.
[68] Tzu-Jen Kao. A3-D Reconstruction Algorithm for Electrical Impedance Tomography UsingPlanar Electrode Arrays [D], PhD thesis, Rensselaer Polytechnic Institute,2005.
[69]钱英，医学超声设备的新进展，医疗设备信息，2002(11):25-27.
[70] Kwong KK, Belliveau JW, Chesler DA. Dynamic magnetic resonance imaging of humanbrain activity during primary sensory stimulation [J]. Proc Nat Acad Sci USA,1992,89:5675-5679.
[71] Scintimammography [E], http://www.radiologyinfo.org/en/info.cfm?pg=Scintimammo,2010-11-15.
[72] Shepp LA, et al. Maximum likelihood reconstruction in emission tomography [J]. IEEE Trans.Med. Imag.,1982. MI-1:113-122.
[73]王仁平.三维电阻抗成像系统设计与实现[D].河北工业大学硕士学位论文.2006.
[74] Holder D S. Electrical impedance tomography of brain function [C]. Int cof electromagneticfield problems and applications, Chongqing: TSI Press,2008, April:465-470.
[75]刘国强.医学电阻抗成像[M].科学出版社,2006
[76] Cheng K S, Issaacson D, Newell J C, et al, Electrode models for electric current computedtomography[J]. IEEE Trans. Biomed Engr.,1989,36:918-924.
[77]王长清,祝西里.电磁场计算中的时域有限差分法[M].北京大学出版社.1994.
[78]李忠元.电磁场边界元素法[M].北京理工大学出版社.1987.
[79]颜威利,杨庆新,汪友华等.电气工程电磁场数值分析[M].机械工业出版社.2005
[80]龙驭球,新型有限元法引论[M],北京,清华大学出版社,1992
[81] Singiresu S. Rao. The Finite Element Method in Engineering [M]. Elsevier Science&Technology Books.2004.
[82] E Somersalo, M Cheney and D Isaacson, Existence and uniqueness for electrode models forelectric current computed tomography[J]. SIAM J Appl Math,1992,52:1023-1040.
[83] TZU-JEN KAO, J C NEWELL, G J SAULNIER, et al. Distinguishability of inhomogeneitiesusing planar electrode arrays and different patterns of applied excitation [J]. Physiol. Meas.2003,24(1):403-411.
[84] Hadamard J. Lectures on the Cauchy Problem in Linear Partial Differential Equations[M].Yale University Press.1923.
[85]赵翔.概率统计方法在微波生物医学成像和雷电电磁效应评估中的应用[D].四川大学博士学位论文.2005.
[86]黄卡玛,赵翔等.电磁场中的逆问题及应用[M].科学出版社.2005.
[87]穆明凯.3G移动通信无源器件及漏泄电缆技术研究[D].浙江大学博士学位论文.2007.
[88]宋雷鸣.基于相控麦克风阵列的逆向噪声源识别原理与技术研究[D].北京交通大学博士学位论文.2010.
[89]张全升.高速公路路面和路基病害检测理论与方法研究[D].中国地质大学博士学位论文.2007.
[90] E Somersalo, M Cheney and D Isaacson. Layer stripping: a direct numerical method forimpedance imaging[J]. Inverse Prob.1991.7:899-926.
[91] Wexler A, Fry B, Neiman M R. Impedance computed tomography algorithm and system[J].Applied Optics.1985,24:3985-3992.
[92] Woo E J, Hua P, Webster J G, et al. A robust image reconstruction algorithm and its parallelimplementation in electrical impedance tomography[J]. IEEE Trans. Med. Imaging.1993,12(2):137-146.
[93] Ye J C, Webb K J. Modified distorted Born iterative method with an approximate Fre'chetderivative for optical diffusion tomography[J]. J. Opt. Soc. Am. A,1999,16(7):1814-1826.
[94] Yang L. Truyen B, Cornelis J. A global optimization approach to electrical impedancetomography[C]. IEEE-EMBS19th Annual International Conference Proceedings, Chicago,1997,1(1):437-444.
[95]侯卫东，莫玉龙.基于遗传算法的电阻抗图像重建[J].生物医学工程学杂志，2003，20(1):107-111.
[96]侯卫东，莫玉龙.基于反向神经网络的阻抗断层图像重建新方法[J].光学学报,2002,22(12):1475-1478.
[97] Tikhonov A. On the solution of incorrectly formulated problems and the regularizationmethod[J]. Soviet Math, Doklady,1963,4:1035-1038.
[98] M.Vauhkonen, D.Vadasz,P.A.Karjalainen, E.Somersalo,etc. Tikhonov regularization and priorinformation in electrical impedance tomography[J]. IEEE Trans. on Med. Img., vol.17, no.2,1998.
[99] Rundnl I, Osher S, Fatem E. Nonlinear total variation based noise removal algorithms[J].Physics D.1992(60):259-268
[100] M. Cheney, D. Isaacson, J. C. Newell, et al, NOSER: An Algorithm for Solving the InverseConductivity Problem [J]. International Journal of Imaging Systems and Technology,1990,2:66-75.
[101] G.H. Golub, P.C. Hansen, D.P. O'Leary. Tikhonov regularization and total least squares [J].SIAM Journal of Matrix Analysis and Applications,1999,1:185-194.
[102] A.N. Tikhonov, V.Y. Arsenin. Soutions of ill-posed problems [M]. Winston,1997.
[103] M.Vauhkonen. Electrical Impedance Tomography and Prior Information[D]. Kupio University,Finland,1997
[104] HANSEN P C, Analysis of discrete ill-posed problems by means of the L-curve[J]. SIAMReview,1992,34(4):561-580.
[105] HANSEN P C,O’LEARY D P.The Use of the L-curve in the regularization of discreteill-posed problems[J].SIAM J.Sci. Comput.,1993,14(6):1487-1503.
[106]陈玉艳,王旭等.基于Tikhonov和变差正则化的磁感应断层成像重建算法[J].东北大学学报,2011,4:460-463
[107]黄嵩,张占龙等.基于混合正则化算法的颅内异物电阻抗成像仿真研究[J].中国生物工程学报,2007,5:695-699.
[108] Hongbin Wang, Guizhi Xu, Shuai Zhang, Ning Yin and Weili Yan, Implementation ofGeneralized back Projection Algorithm in3-D EIT[J], IEEE Transactions on Magnetics,2011,47(5):1466-1469.
[109]庄天戈. CT原理与算法[M].上海交通大学出版社,1992.
[110]缪斌和,邓元木,黄斐增,等.基于对应点匹配的断层图像三维插值方法[J].中国医学物理学杂志,2000,17(1):14-16.
[111] Zhuang Qiao-li, Shen Wei, Sun Qi, et al. Shape-based interpolation of CT image with windowtechnology[C]. International Conference on Computer Application and System Modeling,October22-24, Taiyuan, China.IEEE,2010:536-538
[112] SU C Y, LIN Y S. Colour interpolation using wavelet-based classifiers[J]. ElectronicsLetters,2007,43(12):667-669.
[113]邹鹏程,尹学松.基于断层图像分割的三维匹配插值[J].计算机工程与应用，2004(24)：80-82
[114] Donald J Kalar, Patrick Garrigan, Thomas D Wickens, et al. A unified model of illusory andoccluded contour interpolation[J]. Vision Research,2010,50(3):284-299.
[115] Bat-Sheva Hadad,Daphne Maurer, Terri L Lewis. The development of contour interpolation:Evidence from subjective contours[J]. Journal of Experimental ChildPsychology,2010,106(2-3):163-176.
[116] Albu A B, Beugeling T, Laurendeau D. A morphology-based approach for intersliceinterpolation of anatomical slices from volumetric images[J].2008,55(8):2022–2038.
[117]鞠康.开发式三维多频电阻抗测量系统[D].重庆大学硕士学位论文,2011.
[118]鞠康,何为,何传红,刘斌,李冰.基于数字相敏检波的恒流源输出阻抗检测及补偿技术实现[J].医疗卫生装备.2009,10:5-7.
[119]王守三. PCB的电磁兼容设计技术、技巧和工艺.机械工业出版社.2008年.
[120]白居宪.直接数字频率合成[M].西安:西安交通大学出版社.2007年.
[121]张平，秦嘉川，王茂，刘志言。数字合成正弦信号相位噪声及抑制方法研究。哈尔滨工业大学学报，第31卷第5期，1999：73-78.
[122]王超,郎健,王化祥.用于生物阻抗测量的混频激励电流源[J].计量学报,2006,27(4)：392-396.
[123]董秀珍，史学涛，秦明新等。用于电阻抗参数成像的多频率组合扫频信号源[J]。第四军医大学学报，2000,21（11）：1367-1370.
[124]鞠康,何为,何传红,李冰,罗海军.基于直接数字频率合成的混合频率恒流源设计[J].仪器仪表学报.2010,9:2109-2113.
[125]姜建国,曹建中,高玉明.信号与系统分析基础[M].北京:清华大学出版社.2006年.
[126] Willis J. Tompkins著,林家瑞,徐邦荃译.生物医学数字信号处理[M].华中科技大学出版社.2001
[127]任爱锋,初秀琴,常存,孙肖子.基于FPGA的嵌入式系统设计.西安电子科技大学出版社.2004年.
[128]王晓俊,周杏鹏,王毅.精密阻抗分析仪中数字相敏检波技术研究与实现[J].仪器仪表学报,2006,6:592-595.
[129] N. Liu, G. J. Saulnier, J. C. Newell, A Multichannel Synthesizer and Voltmeter for ElectricalImpedance Tomography [C]. Proc. of25th Annual International Conference of IEEE EMBS,2003:3110-3113.
[130] Tzu-Jen Kao, Gary J. Saulnier, David Isaacson, et. al. A Versatile High-Permittivity Phantomfor EIT [J]. IEEE Transactions on biomedical engineering,2008,55(11):2601-2607.
[131] Eung Je Woo, Impedance Spectroscopy and Multi-Frequency Electrical ImpedanceTomography [J]. International Journal of Bioelectromagnetism,2007,9(2):101-102.
[132]张国鹏,董秀珍,尤富生等.小猪血液的多频电阻抗特性及其等效电路模型的研究[J].航天医学与医学工程,2006,19(1):51-55.
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