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摘要电阻抗断层成像技术（Electrical Impedance Tomography，简称EIT）是一种安全、无放射损伤的功能成像技术。它通过给测量对象施加微弱、安全的电流或电压激励，然后测量对象表面的响应电压或电流来重建其内部的电导率分布或其变化的图像。EIT具有非侵入性、便携性、成本低廉、响应快速等技术优势，因此在工业以及医学领域均具有广阔的应用前景。
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本论文在研究EIT系统构成以及成像算法原理的基础上，对目前常用的静态成像方法Newton-Raphson迭代算法进行了深入地研究。首先，本论文具体阐述了Newton-Raphson迭代算法的原理以及运用Tikhonov正则化对其进行的改进。然后，运用MATLAB对算法的性能进行了仿真验证。仿真结果表明，基于Tikhonov正则化的Newton-Raphson迭代算法可以对多个目标进行有效成像，但算法的抗噪性能较差且对中心目标的成像效果不如边缘目标好。另外，选择适当的迭代参数ε可以有效抑制测量噪声的影响，提高成像的质量。27660
关键词 电阻抗断层成像 静态成像算法 Newton-Raphson迭代算法 MATLAB仿真
毕业论文设计说明书外文摘要
Title Research on the Image Reconstruction Algorithms of Electrical Impedance Tomography and Simulation
Abstract
Electrical Impedance Tomography （EIT）is a functional imaging technology, which is safe and have no radiation injury. It works by giving the object a weak and safe current or voltage, measuring the response voltage or current on the surface of the object. Then, using the data to rebuild the image, which shows the distribution or changes of the electrical impedance in the object. EIT has many technical advantages such as non-invasive, portability, low cost, rapid in response and so on. So it has a broad application prospects in industrial and medical field.
This paper is studying on the composition of the EIT system and the basic principles of EIT imaging algorithms. Because the Newton-Raphson iteration algorithm is a common static electrical impedance imaging methods of EIT, we carry out a deep research on it. Firstly, We specifically expound the principles of the algorithm and use the Tikhonov regularization to improve it. Then, we use MATLAB simulation to verify the performance of the algorithm. The simulation result shows that the Newton-Raphson iteration algorithm which is based on Tikhonov regularization can image in an effective way when there are multiple targets in the imaging field. However, the algorithm has a poor performance when the imaging field has noise and the image quality of the central goal is not as good as the fringe one. Otherwise, it is great to choose a appropriate iterative parameter ε，because it can effectively restrain the influence of the noise and improve the quality of the reconstruction image.
Keywords Electrical Impedance Tomography The Static Imaging Algorithm Methods Newton-Raphson Iteration Algorithm MATLAB Simulation
目 次
1 绪论1
1.1 EIT技术概述1
1.2 EIT图像重构算法概述2
1.3 本论文主要研究内容3
2 EIT系统的构成及工作原理5
2.1 EIT系统的构成5
2.2 EIT系统的工作原理6
2.3 本章小结8
3 EIT图像重构算法研究9
3.1 EIT的数学物理基础9
3.2 EIT正问题算法基础11
3.3 EIT正问题的有限元算法13
3.4 EIT逆问题算法基础18
3.5 基于Tikhonov正则化的Newton-Raphson迭代算法19
3.6 本章小结21
4 基于MATLAB的EIT图像重构算法仿真23
4.1 Newton迭代算法的计算流程23
4.2 基于Tikhonov正则化的Newton-Raphson迭代算法仿真24