电学成析成像系统模型、算法研究
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摘要
作为一种无损可视化测量手段,电学层析成像技术因其价格低廉、响应快速,在工业和医学领域具有重要的应用价值。目前,电学层析成像大多表现为单模态成像,且成像过程依赖于有限元的数值求解。为深入分析电学层析成像的测量机理,本论文对传感器的数学模型及相应的双模态图像重建算法进行了系统研究。
首先,为实现传感器的标定及进行快速图像重建,讨论了接触式传感器模型,该类传感器属于“计算式”,其电学参数可用几何参数解析表达,且可进行双模态测量。对于电容模态,测量值与理论值的相对偏差小于1.64%;对于电导模态,测量值与理论值的相对偏差小于2.68%。样机上图像重建结果,证实了基于模型的重建算法的有效性。重建过程无需采用有限元求解,降低了图像重建的计算复杂度。根据黎曼定理,基于模型的算法可以推广到任意由Jordan曲线包围的区域。
其次,构建了两种非接触式传感器,其中,导电环式传感器适用于导电介质为连续相的电阻层析成像,配置于导电环上的电极尺寸可以很小,有利于提高电压测量的分辨率,增加电极数目以提高信息获取能力。构建的绝缘环式传感器,在交流电压激励下,可进行双模态电学层析成像,属于非接触式传感器,有望应用于非接触式医学监测领域。在此基础上,设计了两种螺旋式相含率传感器,主要利用了‘软场'效应的全局性质以及螺旋式电极的空间滤波效应。仿真和实验结果表明,螺旋式结构有助于构建较为均匀的灵敏场分布,测量数据和相含率具有较高的线性度。
然后,研究了二端子法测量方式的数学模型及图像重建,获得了对人体/管道分布的重建图像,结果证实了其可行性。由于二端子法测量简化了硬件系统,压缩了测量数据的动态变化范围,对于电学成像系统的小型化设计,较为有利。但同时指出激励和测量模式的改变,仅有利于测量,并不会增加获取的信息量。
最后,讨论了图像重建的线性化方法,提出了一种基于模型的鲁棒算法,对人体肺部活动的数据进行了图像重建。结果表明,基于模型的算法可以通过共形变换灵活推广,且可实现肺部活动的可视化监测。
本工作提出的基于模型的方法,不仅可用于二维的可视化测量,亦可推广到三维情形,可以简化计算,提高成像效率。
As a kind of nondestructive and visible measurement techniques, electrical tomography has found many important applications in both industrial and medical areas, for its low cost and fast response. However, most of the electrical tomography systems are of single modality and using the finite element method in the process of image reconstruction. In order to analyze the measurement mechanism of electrical tomography in depth, the mathematical models of the sensors and associated dual modality image reconstruction algorithms have been investigated systematically in this dissertation.
Firstly, mathematical models of calculable sensors are established, in order to calibrate the sensors and perform fast image reconstruction based on the model. The sensors consist of contact-type electrodes and have standard values determined only by the geometric parameters. Dual modality measurement has been performed on a prototype, and the relative errors between measured and theoretical values are less than 1.64% and 2.68% for capacitive mode and conductive mode, respectively. Images have been reconstructed on the prototype using the model based algorithms. The computation complexity of the image reconstruction has been reduced as the finite element method is not used in the image reconstruction. According to Riemann's theorem, the model based algorithms can be generalized to any region enclosed by a Jordan curve.
Secondly, two kinds of non-contact type sensors have been constructed, i.e. the senor with a conductive ring and the sensor with an insulative ring. The former is suitable to the flow with a conductive continuous phase. It consists of a conductive ring with electrodes mounted on the ring. The small size electrodes are suitable to improve the distinguishabihty of the voltage measurement and the number of the electrodes. The latter is able to capture the dual modality information with the alternating voltage excitation signal. There exists an insulative ring between the electrode array and the measurement region. As its electrode array have no contact with the measurement region, the sensor has a potential application to non-contact monitoring in the medical area. Based on the models of non-contact sensors, associated spiral type sensor have been designed for void fraction measurement. The global property of the 'soft' field and spatial filtering effect of the spiral type electrodes are utilized to generate a homogeneous sensitivity distribution. Experimental and simulation results validate the linear relationship between the measurements and the void fraction ratios.
Thirdly, mathematical models for two-terminal measurement have been established for image reconstruction. Reconstructed images of human body and pipe validate the feasibility of the model based algorithm with the two-terminal measurement. The strategy of the two-terminal measurement simplifies the design of hardware system, reduces the dynamic range of the measurement. And it is useful for smart electrical tomography system. However, different excitation modes can only be used to improve the measurement precision and can not obtain more information.
Finally, the linearization in image reconstruction has been analyzed and a robust algorithm based on the model has been proposed for image reconstruction of the human respiration. Results show that the model based algorithms can be generalized using the conformal transformation and can be used for visible monitoring of the human lung activities.
The model based methods proposed in this dissertation is not only suitable to visible measurement in two dimensions, but also can be used to simplify the image reconstruction in three dimensions.
首先,为实现传感器的标定及进行快速图像重建,讨论了接触式传感器模型,该类传感器属于“计算式”,其电学参数可用几何参数解析表达,且可进行双模态测量。对于电容模态,测量值与理论值的相对偏差小于1.64%;对于电导模态,测量值与理论值的相对偏差小于2.68%。样机上图像重建结果,证实了基于模型的重建算法的有效性。重建过程无需采用有限元求解,降低了图像重建的计算复杂度。根据黎曼定理,基于模型的算法可以推广到任意由Jordan曲线包围的区域。
其次,构建了两种非接触式传感器,其中,导电环式传感器适用于导电介质为连续相的电阻层析成像,配置于导电环上的电极尺寸可以很小,有利于提高电压测量的分辨率,增加电极数目以提高信息获取能力。构建的绝缘环式传感器,在交流电压激励下,可进行双模态电学层析成像,属于非接触式传感器,有望应用于非接触式医学监测领域。在此基础上,设计了两种螺旋式相含率传感器,主要利用了‘软场'效应的全局性质以及螺旋式电极的空间滤波效应。仿真和实验结果表明,螺旋式结构有助于构建较为均匀的灵敏场分布,测量数据和相含率具有较高的线性度。
然后,研究了二端子法测量方式的数学模型及图像重建,获得了对人体/管道分布的重建图像,结果证实了其可行性。由于二端子法测量简化了硬件系统,压缩了测量数据的动态变化范围,对于电学成像系统的小型化设计,较为有利。但同时指出激励和测量模式的改变,仅有利于测量,并不会增加获取的信息量。
最后,讨论了图像重建的线性化方法,提出了一种基于模型的鲁棒算法,对人体肺部活动的数据进行了图像重建。结果表明,基于模型的算法可以通过共形变换灵活推广,且可实现肺部活动的可视化监测。
本工作提出的基于模型的方法,不仅可用于二维的可视化测量,亦可推广到三维情形,可以简化计算,提高成像效率。
As a kind of nondestructive and visible measurement techniques, electrical tomography has found many important applications in both industrial and medical areas, for its low cost and fast response. However, most of the electrical tomography systems are of single modality and using the finite element method in the process of image reconstruction. In order to analyze the measurement mechanism of electrical tomography in depth, the mathematical models of the sensors and associated dual modality image reconstruction algorithms have been investigated systematically in this dissertation.
Firstly, mathematical models of calculable sensors are established, in order to calibrate the sensors and perform fast image reconstruction based on the model. The sensors consist of contact-type electrodes and have standard values determined only by the geometric parameters. Dual modality measurement has been performed on a prototype, and the relative errors between measured and theoretical values are less than 1.64% and 2.68% for capacitive mode and conductive mode, respectively. Images have been reconstructed on the prototype using the model based algorithms. The computation complexity of the image reconstruction has been reduced as the finite element method is not used in the image reconstruction. According to Riemann's theorem, the model based algorithms can be generalized to any region enclosed by a Jordan curve.
Secondly, two kinds of non-contact type sensors have been constructed, i.e. the senor with a conductive ring and the sensor with an insulative ring. The former is suitable to the flow with a conductive continuous phase. It consists of a conductive ring with electrodes mounted on the ring. The small size electrodes are suitable to improve the distinguishabihty of the voltage measurement and the number of the electrodes. The latter is able to capture the dual modality information with the alternating voltage excitation signal. There exists an insulative ring between the electrode array and the measurement region. As its electrode array have no contact with the measurement region, the sensor has a potential application to non-contact monitoring in the medical area. Based on the models of non-contact sensors, associated spiral type sensor have been designed for void fraction measurement. The global property of the 'soft' field and spatial filtering effect of the spiral type electrodes are utilized to generate a homogeneous sensitivity distribution. Experimental and simulation results validate the linear relationship between the measurements and the void fraction ratios.
Thirdly, mathematical models for two-terminal measurement have been established for image reconstruction. Reconstructed images of human body and pipe validate the feasibility of the model based algorithm with the two-terminal measurement. The strategy of the two-terminal measurement simplifies the design of hardware system, reduces the dynamic range of the measurement. And it is useful for smart electrical tomography system. However, different excitation modes can only be used to improve the measurement precision and can not obtain more information.
Finally, the linearization in image reconstruction has been analyzed and a robust algorithm based on the model has been proposed for image reconstruction of the human respiration. Results show that the model based algorithms can be generalized using the conformal transformation and can be used for visible monitoring of the human lung activities.
The model based methods proposed in this dissertation is not only suitable to visible measurement in two dimensions, but also can be used to simplify the image reconstruction in three dimensions.
引文
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