广义反投影方法在三维电阻抗成像中的研究及实现
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摘要
电阻抗成像(Electrical Impedance Tomography, EIT)技术作为电学层析成像技术的一种,以无创以及功能成像的特点成为生物电磁成像中的重要研究课题之一。由于其响应速度快、结构简单、成本低廉等特点,在许多领域备受关注,尤其是医学诊断和临床监护等方面。作为一类图像重建的逆问题,电阻抗成像问题具有欠定、非线性以及病态特性,因此重建图像在精确度、稳定性、分辨率等方面距离临床应用的要求还有一定差距。本文以反投影类方法为基础,提出了广义反投影方法,通过建立虚拟节点或虚拟单元拓展计算域,增加了重建图像信息量,降低了问题的欠定性,经仿真及物理模型实验验证了算法的有效性。
本文研究内容得到国家自然科学基金重点项目《人体活性组织介电特性与表征方法研究》(项目编号:50937005)和《参数化重建方法在心脏腔内电阻抗成像中的研究》(项目编号:51077040)的支持和资助。主要研究内容如下:
1.在节点反投影方法的基础上,提出广义反投影方法。通过建立虚拟节点,可以计算区域内任意处信息,使重建图像信息更为丰富。通过仿真实验和物理模型实验,验证了算法在三维重建中的适用性,其重建图像效果较传统反投影方法有明显提高。
2.提出基于线性敏感矩阵的广义反投影方法。通过在区域内建立虚拟单元,可以计算三维区域内任意部分的信息,获取区域内更为详尽的阻抗分布信息。针对算法对电极层间信息重建效果欠佳的问题,进一步提出改进的广义反投影方法。通过建立虚拟平面,使求解区域内的待求点与边界电压分布之间建立空间对应关系,进一步提高投影信息准确性,提高重建图像质量。将算法从二维层析成像推广为真正的三维成像。并由仿真与物理模型实验对算法进行了验证。
3.提出将广义反投影方法和牛顿迭代算法相结合的混合算法。由广义反投影方法结果作为牛顿迭代算法的初始值,使得电阻率初始分布情况接近真实分布。不仅避免了以往通过经验选择初始值,降低了初始误差,而且加快了每步迭代中的误差下降速度,节省了重建时间。
4.提出用于评价EIT重建图像效果的四个量化指标:位置误差、分辨率、形状应变、信息熵,并对成像算法进行了客观评价。通过四个指标量化,广义反投影方法的重建图像效果要优于传统反投影方法和节点反投影方法,而改进的广义反投影方法的重建图像效果又有进一步的提高。混合算法的重建图像比牛顿迭代算法在相同迭代步数下效果更好。
Electrical Impedance Tomography (EIT), as a kind of electrical tomography techniques, is one of the significant research projects with the features of non-invasive and functional imaging. EIT attracts much concern from many areas, especially on medical diagnosis and clinical monitoring, since it has many advantages in response speed, simple structure and cost. However, this inverse problem on image reconstruction processes an underdetermined, non-linear and ill-posed nature. The reconstructed images are far from clinical requirements in the aspects of accuracy, stability and resolution. In this dissertation a novel approach of EIT reconstruction algorithm named generalized back projection algorithm is proposed with the purpose of reducing underdetermined conduction, which establishes imaginary node or imaginary element to extend computation range. The algorithm is verified effectiveness by numerical and real experiments.
This work was supported in part by the National Natural Science Foundation of China under Grant No. 50937005 and No. 51077040. The main works and results are following.
1. Generalized back projection algorithm is proposed based on node back projection algorithm. The information of arbitrary node can be calculated by establishing imaginary node, so that the reconstructed images contain more information. The results of numerical experiments and real experiments verify the applicability of the method for improvement of reconstructed images effect compared with conventional back projection algorithm.
2. Based on linearised sensitivity matrix, generalize back projection algorithm is proposed. The imaginary elements are established in the region, so that the information of arbitrary part can be computed to reconstruct more detailed conductivity distribution information in the region. For the reconstructed images between adjacent electrode sections are less effective, further improved generalize back projection algorithm is proposed, which establishes a mapping of solving projection positions of the inner nodes by boundary voltages through imaginary planes. Since the accuracy of projection information is improved, the reconstructed images get better quality. The method is 3-dimentions reconstruction algorithm rather than 2-dimentions tomography algorithm, and is verified by numerical and real experiments.
3. A mixed method is presented that generalized back projection algorithm and Newton-type iterative algorithm is combined. The initial value of Newton-type iterative algorithm is estimated from generalized back projection algorithm, so that the initial distribution approximate to real condition. The initial selection strategy prevents empirical selection, and reduces initial error and iterative error at every step, so that computation time is saved.
4. To evaluate EIT reconstructed images, four quantitative metrics is presented: position error, resolution, shape deformation and information entropy. The four metrics conduct to evaluate reconstruction algorithms objectively. Compared with conventional back projection algorithm and node back projection algorithm, the images reconstructed by generalized back projection algorithm are more accurate in terms of the four metrics, and the results of improved generalized back projection algorithm are further raised. Compared with conventional Newton-type iterative algorithm, the combination method provides reconstructed images with better effect at the same iterative step.
本文研究内容得到国家自然科学基金重点项目《人体活性组织介电特性与表征方法研究》(项目编号:50937005)和《参数化重建方法在心脏腔内电阻抗成像中的研究》(项目编号:51077040)的支持和资助。主要研究内容如下:
1.在节点反投影方法的基础上,提出广义反投影方法。通过建立虚拟节点,可以计算区域内任意处信息,使重建图像信息更为丰富。通过仿真实验和物理模型实验,验证了算法在三维重建中的适用性,其重建图像效果较传统反投影方法有明显提高。
2.提出基于线性敏感矩阵的广义反投影方法。通过在区域内建立虚拟单元,可以计算三维区域内任意部分的信息,获取区域内更为详尽的阻抗分布信息。针对算法对电极层间信息重建效果欠佳的问题,进一步提出改进的广义反投影方法。通过建立虚拟平面,使求解区域内的待求点与边界电压分布之间建立空间对应关系,进一步提高投影信息准确性,提高重建图像质量。将算法从二维层析成像推广为真正的三维成像。并由仿真与物理模型实验对算法进行了验证。
3.提出将广义反投影方法和牛顿迭代算法相结合的混合算法。由广义反投影方法结果作为牛顿迭代算法的初始值,使得电阻率初始分布情况接近真实分布。不仅避免了以往通过经验选择初始值,降低了初始误差,而且加快了每步迭代中的误差下降速度,节省了重建时间。
4.提出用于评价EIT重建图像效果的四个量化指标:位置误差、分辨率、形状应变、信息熵,并对成像算法进行了客观评价。通过四个指标量化,广义反投影方法的重建图像效果要优于传统反投影方法和节点反投影方法,而改进的广义反投影方法的重建图像效果又有进一步的提高。混合算法的重建图像比牛顿迭代算法在相同迭代步数下效果更好。
Electrical Impedance Tomography (EIT), as a kind of electrical tomography techniques, is one of the significant research projects with the features of non-invasive and functional imaging. EIT attracts much concern from many areas, especially on medical diagnosis and clinical monitoring, since it has many advantages in response speed, simple structure and cost. However, this inverse problem on image reconstruction processes an underdetermined, non-linear and ill-posed nature. The reconstructed images are far from clinical requirements in the aspects of accuracy, stability and resolution. In this dissertation a novel approach of EIT reconstruction algorithm named generalized back projection algorithm is proposed with the purpose of reducing underdetermined conduction, which establishes imaginary node or imaginary element to extend computation range. The algorithm is verified effectiveness by numerical and real experiments.
This work was supported in part by the National Natural Science Foundation of China under Grant No. 50937005 and No. 51077040. The main works and results are following.
1. Generalized back projection algorithm is proposed based on node back projection algorithm. The information of arbitrary node can be calculated by establishing imaginary node, so that the reconstructed images contain more information. The results of numerical experiments and real experiments verify the applicability of the method for improvement of reconstructed images effect compared with conventional back projection algorithm.
2. Based on linearised sensitivity matrix, generalize back projection algorithm is proposed. The imaginary elements are established in the region, so that the information of arbitrary part can be computed to reconstruct more detailed conductivity distribution information in the region. For the reconstructed images between adjacent electrode sections are less effective, further improved generalize back projection algorithm is proposed, which establishes a mapping of solving projection positions of the inner nodes by boundary voltages through imaginary planes. Since the accuracy of projection information is improved, the reconstructed images get better quality. The method is 3-dimentions reconstruction algorithm rather than 2-dimentions tomography algorithm, and is verified by numerical and real experiments.
3. A mixed method is presented that generalized back projection algorithm and Newton-type iterative algorithm is combined. The initial value of Newton-type iterative algorithm is estimated from generalized back projection algorithm, so that the initial distribution approximate to real condition. The initial selection strategy prevents empirical selection, and reduces initial error and iterative error at every step, so that computation time is saved.
4. To evaluate EIT reconstructed images, four quantitative metrics is presented: position error, resolution, shape deformation and information entropy. The four metrics conduct to evaluate reconstruction algorithms objectively. Compared with conventional back projection algorithm and node back projection algorithm, the images reconstructed by generalized back projection algorithm are more accurate in terms of the four metrics, and the results of improved generalized back projection algorithm are further raised. Compared with conventional Newton-type iterative algorithm, the combination method provides reconstructed images with better effect at the same iterative step.
引文
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