电阻抗静态成像中正则化算法研究
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摘要
电阻抗成像技术(Electrical Impedance Tomography，EIT)是一种新兴的计算成像技术，它根据生物体内不同组织导电参数(如电阻率、电容率)的不同，通过对生物体表面电流、电位的施加及测量，来计算重构各组织导电参数的分布情况，进而得到反映生物体内部组织相关信息的图像。EIT技术具有无创、廉价、便携、安全等特点，其重构图像不仅能在一定程度上反映生物体的解剖学结构，更能对生物体组织进行功能性成像，即在组织或器官发生结构性病变之前，就及时检测出该组织或器官的功能性变化，这对疾病的普查、预防与诊治非常有利，因而极具潜在的临床医学应用价值。
论文在阐述EIT技术研究现状、逆问题基本理论的基础上，从提高EIT成像质量和重构速度的角度出发，围绕静态重构中的正则化算法展开研究。首先，为提高EIT正问题的计算精度，采用了计及电极实际尺寸和接触电阻的全电极边界条件模型，并提出用疏、密剖分模型分别作为EIT逆问题和正问题计算模型；继而，在EIT逆问题研究中，针对Tikhonov正则化算法采用连续函数作罚函数，会因其平滑效应引起重构图像质量不高(对比度低、目标区域边界不清)的弊病，提出了两种新的正则化算法：变差正则化算法和混合正则化算法，前者是用离散变差函数作为正则化罚函数而形成的一种算法，它能有效克服连续罚函数的平滑效应，使重构图像对比度、清晰度得到提高；后者则结合了变差罚函数和Tikhonov罚函数的特点，将两种罚函数加权后作为新的正则化罚函数项而形成的一种算法，它在提高重构图像对比度、清晰度的同时，进一步提高了重构算法的收敛精度和抗噪性能；此外，论文还针对Jacobi矩阵计算量大，计算速度慢的问题，提出一种快速微分算法，使该矩阵的计算速度得到极大提高，并用“虚”激励矩阵拓展了该算法的适用范围；然后，论文运用混合正则化算法开展了多种设定情况的仿真研究，特别对颅内异物和人体胸腔进行了重构成像。通过与Tikhonov正则化算法重构结果的对比，显示了该算法能有效克服低电导率颅骨的屏蔽效应，实现对目标区域准确、清晰的重构，所得重构图像更具医用价值。论文还对混合正则化算法进行了噪声分析和实验验证，得到了该算法能接受的噪声程度，对EIT数据采集精度的确定有指导意义，也验证了所提算法的正确性和有效性。
Electrical Impedance Tomography (EIT) is a new type of medical imaging technique. In EIT, an array of electrodes attached around an object, small alternating currents injected via these electrodes, and resulting voltages are measured. With those measurements, an approximation of the spatial impedance (or conductivity) distribution of the object been reconstructed. The advantage of EIT is non-invasive, inexpensive, portable, secure and so on. It has the potential to widespread in medicine. This technique can be used as display not only the anatomical structures, but also the function structures. This is most helpful for preventing and diagnosing disease, prior to disease happed.
In this thesis, on the base of expatiating on fundamental theory of biomedicine, discussed the research status quo of EIT, the regularization algorithm of EIT is focused on. First, the electrode model of EIT in the forward problem is dealed with complete electrode model, which considered the size and the contact resistance of real electrode. Then, an attention put to both sides of speed and precision of EIT problem, and a dense and sparse FEM model is proposed. Secondly, two new regularization algorithms been proposed to research the inverse problem of EIT. The first one is variation regularization algorithm, which imported a variation function as regularization penalty team to improve the contrast of restored image. The second one is mixed regularization algorithm, which imported both variation function and Tikhonov function as the regularization penalty teams, to improve both sides of contrast and precision of restored image. Moreover, a fast algorithm of Jacobi matrix, based on differential principle, is been proposed to improve computational speed and precision of the matrix, which is significative to utilize EIT technique. Further, the mixed regularization algorithm is used to some applications research, especially, the reconstructed of brain hematoma and human breast cases. The comparison with Tikhonov algorithm shows the new algorithm has powerful reconstruction capability and more medical treatment worth. Finally, noise affection for mixed regularization algorithm is studied, and an acceptable noise level be proposed for the algorithm, which is useful to the data collection in EIT, and some laboratory experiments made to validate the mixed regularization algorithm. The result validates the veracity and validity of the proposed algorithm.
论文在阐述EIT技术研究现状、逆问题基本理论的基础上，从提高EIT成像质量和重构速度的角度出发，围绕静态重构中的正则化算法展开研究。首先，为提高EIT正问题的计算精度，采用了计及电极实际尺寸和接触电阻的全电极边界条件模型，并提出用疏、密剖分模型分别作为EIT逆问题和正问题计算模型；继而，在EIT逆问题研究中，针对Tikhonov正则化算法采用连续函数作罚函数，会因其平滑效应引起重构图像质量不高(对比度低、目标区域边界不清)的弊病，提出了两种新的正则化算法：变差正则化算法和混合正则化算法，前者是用离散变差函数作为正则化罚函数而形成的一种算法，它能有效克服连续罚函数的平滑效应，使重构图像对比度、清晰度得到提高；后者则结合了变差罚函数和Tikhonov罚函数的特点，将两种罚函数加权后作为新的正则化罚函数项而形成的一种算法，它在提高重构图像对比度、清晰度的同时，进一步提高了重构算法的收敛精度和抗噪性能；此外，论文还针对Jacobi矩阵计算量大，计算速度慢的问题，提出一种快速微分算法，使该矩阵的计算速度得到极大提高，并用“虚”激励矩阵拓展了该算法的适用范围；然后，论文运用混合正则化算法开展了多种设定情况的仿真研究，特别对颅内异物和人体胸腔进行了重构成像。通过与Tikhonov正则化算法重构结果的对比，显示了该算法能有效克服低电导率颅骨的屏蔽效应，实现对目标区域准确、清晰的重构，所得重构图像更具医用价值。论文还对混合正则化算法进行了噪声分析和实验验证，得到了该算法能接受的噪声程度，对EIT数据采集精度的确定有指导意义，也验证了所提算法的正确性和有效性。
Electrical Impedance Tomography (EIT) is a new type of medical imaging technique. In EIT, an array of electrodes attached around an object, small alternating currents injected via these electrodes, and resulting voltages are measured. With those measurements, an approximation of the spatial impedance (or conductivity) distribution of the object been reconstructed. The advantage of EIT is non-invasive, inexpensive, portable, secure and so on. It has the potential to widespread in medicine. This technique can be used as display not only the anatomical structures, but also the function structures. This is most helpful for preventing and diagnosing disease, prior to disease happed.
In this thesis, on the base of expatiating on fundamental theory of biomedicine, discussed the research status quo of EIT, the regularization algorithm of EIT is focused on. First, the electrode model of EIT in the forward problem is dealed with complete electrode model, which considered the size and the contact resistance of real electrode. Then, an attention put to both sides of speed and precision of EIT problem, and a dense and sparse FEM model is proposed. Secondly, two new regularization algorithms been proposed to research the inverse problem of EIT. The first one is variation regularization algorithm, which imported a variation function as regularization penalty team to improve the contrast of restored image. The second one is mixed regularization algorithm, which imported both variation function and Tikhonov function as the regularization penalty teams, to improve both sides of contrast and precision of restored image. Moreover, a fast algorithm of Jacobi matrix, based on differential principle, is been proposed to improve computational speed and precision of the matrix, which is significative to utilize EIT technique. Further, the mixed regularization algorithm is used to some applications research, especially, the reconstructed of brain hematoma and human breast cases. The comparison with Tikhonov algorithm shows the new algorithm has powerful reconstruction capability and more medical treatment worth. Finally, noise affection for mixed regularization algorithm is studied, and an acceptable noise level be proposed for the algorithm, which is useful to the data collection in EIT, and some laboratory experiments made to validate the mixed regularization algorithm. The result validates the veracity and validity of the proposed algorithm.
引文
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[3]．沙洪，任超世 等生物电阻抗分析在临床监测中的应用进展与前景 中国医疗器械信息，2001，7(5)，PP9-11
[4]．任超世，崔云莉 医学电阻抗技术的问题和发展与应用前景 中国医学物理学杂志，1997，14(1)，pp 59-61
[5]. Erol, Smallwood, Brown et al, Detecting oeso-phaseal-related changes using electrical impedance tomography. PhysiologicalMeasurement, 1995, 16, pp 143-152
[6]. Baxter A. J. Mangnall Y. E. Brown et al, Evaluation of applied potential tomography as a new non-invasive gastric secretion test. GUT, 1988, 30, pp 1730-1735
[7]. Holder, Temple, Effectiveness of the Sheffield EIT system in distinguishing patients with pulmonary pathology from a series of normal subject. In: Holder DS, ed. Clinical and Physiological Application of electrical impedance tomography. UCL Press, London, 1993
[8]．李增煌，牛汝辑 电阻抗呼吸图仪在慢阻肺患者膈肌疲劳检测上的应用研究 临床内科杂志，1992，9(3)，pp27-29
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