摘 要
电阻抗断层成像技术(Electrical Impedance Tomography，简称EIT)是近些年发展起来的一种新兴医学成像技术，它是通过对生物体表面进行电测量来反映生物体内电导率的变化情况。与现有的医学成像技术相比，如X射线成像、计算机断层扫描成像(CT)以及核磁共振(MRI)等，EIT不仅具有功腀@上竦男灾剩一挂蛄邸⑽薮础⑻寤 ⒎奖阈忍氐悖壳耙殉晌苯裆镆窖Чこ痰闹卮笱芯靠翁猓凶殴憷挠τ们熬啊Ⅻbr>论文的重点是研究EIT技术的软件实现过程。首先，通过对二维EIT进行建模， 实现基于Matlab的有限元剖分、推导Laplace方程变分原理和建立EIT正问题的有限元程；其次，对逆问题中的图像重建算法进行研究，推导了修正Newton-Raphson迭代算法的迭代过程，并在此基础上提出一种基于总变差正则化技术的Newton-Raphson迭代算法；再次，利用修正Newton．Raphson迭代算法，基于matlab平台进行图像重建，察单个和两个成像目标情况下图像重建效果，并且对重构图像进行了分析讨论，研究了不同参数对成像结果的影响。 结果表明，应用改进的有限元模型，通过修正Newton-Raphson迭代算法能够得到比较清晰的EIT重构图像，并且正则化参数和迭代步长都对成像结果有着一定的影响。最后采用实测实验数据，通过上述算法，得到重构图像。
关键词：电阻抗断层成像; 正问题，; 逆问题；有限元；正则化
ABSTRACT
Electrical Impedance Tomography(EIT)is a developing technology for medical imaging these years，which is to calculate the changes of conductivityof biomedical issues．Comparedto the current iInaging technology,such as X-ray,Computed Tomography,and MagneticResonanceImaging，EIT has its ownadvantages，e．g．functional imaging，ow-cost,non-invasion and portability．And these features make it become a hot point for study and discussion in biomedical engineering area．.
Paper based on the study of the principle of EIT, the preliminary study on the hardware system, puts forward an improved EIT system. The article focuses on the research of EIT technology software implementation process. First of all, based on 2d EIT modeling, implementation, Laplace equation is derived based on Matlab finite element subdivision EIT is variational principle and establishment of the finite element process; Second, the study of inverse problem of image reconstruction algorithm, modified Newton -- Raphson iteration algorithm was deduced in the iterative process, and based on this, advances a kind of based on total variation regularization techniques of Newton -- Raphson iterative algorithm; . Again, using the modified Newton Raphson iteration algorithm, the image reconstruction based on matlab platform and examine a single case and two imaging target image reconstruction effect, and the reconstructed image are analyzed and discussed, studied the influence of different parameters on the imaging results. Application results show that the improved finite element model, through the modified Newton Raphson iteration algorithm can get clearer EIT reconstruction image, and the regularization parameter and the iteration step length has a certain influence on the imaging results. Then using the measured experimental data, through the above algorithm, reconstruction image is obtained.
Key words：EIT; Forward Problem ; Inverse Problem；Finite Element；Regularization；
目 录
1 绪 论 1
1.1 课题设计的背景和意义 1
1.2 课题研究的内容 2
1.3 国内外研究现状 2
1.4 本文的组织结构 2
2 二维EIT建模 3
2.1 EIT数学模型 4
2.2 EIT的有限元剖分 5
2.3 EIT的Laplace方程的变分原理 5
2.4 EIT正问题的有限元剖分模型 5
3 EIT图像重建算法研究 3
3.1 EIT逆问题基础 6
3.2 最速下降迭代算法 5
3.3 Newton迭代算法 5
3.4 修正的Newton-Rapshon迭代算法 5
4 基于Matlab的EIT图像重建算法仿真实现 6
4.1仿真实现步骤 11
4.2 EIT图像重建 11
4.2.1 单个目标重建 12
4.2.2 两个目标重建 13
4.3参数对结果的影响 14
4.3.1 正则化参数 15
4.3.2 迭代步长 15
5 EIT逆问题总结 20
结 论 10
致 谢 21
参考文献 22
附 录 25
附录一 源代码 25
