电学层析成像图像重建算法研究及软件系统设计
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摘要
电学层析成像(Electrical Tomography,ET)技术是近年来发展起来的一种新型检测技术,由于其具有无辐射、非侵入、响应速度快和价格低廉等优势,在工业过程成像和医学成像等领域都有良好的应用前景。电容层析成像(Electrical Capacitance Tomography , ECT )和电阻层析成像( Electrical Resistance Tomography,ERT)是基于不同原理的两种ET技术。
在过去二十多年中,ET技术得到了迅速的发展,但由于ET反问题的求解具有非线性、欠定性和病态性等难点,使得重建图像质量并不理想。同时,软件系统设计相对滞后,功能不够完善。针对目前存在的问题,本文研究了常用图像重建算法的原理,提出了Tikhonov预迭代算法和基于卡尔曼滤波的快速图像重建算法,并开发了一套电学层析成像软件系统,主要工作和结论如下:
1.分析了ET技术的反问题,总结了灵敏度系数算法、Landweber迭代算法、Tikhonov正则化算法、牛顿-拉夫逊算法及共轭梯度算法等五种常用图像重建算法的原理。在此基础上,对Tikhonov迭代算法进行改进,提出了Tikhonov预迭代算法,明显提高了成像速度。
2.对各种常用图像重建算法从重建图像质量和成像速度两方面进行了仿真和实验评价。
3.提出了基于卡尔曼滤波的快速图像重建算法,并通过仿真和实验验证其有效性。结果表明,基于卡尔曼滤波的快速图像重建算法是一种重建图像质量好,成像速度快,而且对噪声干扰有很好鲁棒性的图像重建算法。
4.使用Visual C++编程环境下的MFC和OpenGL开发了一套可用于在线检测和离线分析的电学层析成像软件系统TJU-ET-IV。该软件系统集成了五种快速图像重建算法,可用于对双截面12/16电极ECT/ERT系统进行高速成像,同时实现了USB高速通讯、纵截面显示、截面含气率实时显示、相关速度测量、数据存储及回放等功能。
5.分析了相关速度测量原理,提出了基于截面含气率的气/液两相流相关速度测量方法,利用TJU-ET-IV软件系统具有的数据存储及回放功能对该相关速度测量方法进行了评定实验。实验结果表明,该方法测速精度较高且稳定可靠。
Electrical Tomography (ET) is a new detection technique developed in recent years. Due to the advantages of being non-radiant, non-intrusive, rapid response and low cost, ET should have a good application prospect in many fields such as industrial process imaging, medical imaging and so on. Electrical Capacitance Tomography (ECT) and Electrical Resistance Tomography (ERT) based on different principle are two categories of ET.
Although great progress has been made in ET technique in the past two decades, satisfactory reconstructed images in terms of good quality haven’t been achieved because the reconstruction problem of ET is a nonlinear, underdetermined and ill-conditioned inverse problem. Meanwhile, the development of the software system has lagged behind leading to deficient functions. To solve the problems existed, the principles of some commonly used image reconstruction algorithms were studied, the Tikhonov pre-iteration algorithm and a fast image reconstruction algorithm based on Kalman filtering were proposed, and a software system for ET was developed in this thesis. The main work and results are as follows:
1. The inverse problem of ET was analyzed. Five commonly used image reconstruction algorithms were reviewed, including sensitivity coefficient, Landweber iteration, Tikhonov regularization, Newton-Raphson and conjugate gradient method. Based on them, the Tikhonov pre-iteration algorithm which can markedly improve the reconstruction speed of Tikhonov iteration algorithm was proposed.
2. The commonly used image reconstruction algorithms were evaluated in terms of the quality of reconstructed images and the reconstruction speed through simulation and experiment respectively.
3. A fast image reconstruction algorithm based on Kalman filtering was proposed. And its effectiveness was verified through simulation and experiment. The results show that the proposed algorithm has the characteristic of good quality of reconstructed images, high reconstruction speed and good robustness to noise.
4. TJU-ET-IV, a software system for ET which can be used for online testing and offline analysis, was developed using MFC and OpenGL under the programming environment of Visual C++. This software system containing five fast image reconstruction algorithms can carry out the image reconstruction for 12/16 electrode ECT/ERT system on two different cross sections at the same time. Also, it implements the functions of high-speed communication via USB, inspection of the longitudinal section, real-time display of void fraction, measurement of the cross-correlation velocity, history data storage and playback, and the like.
5. The principle of cross-correlation velocity measurement was analyzed. A gas-liquid two-phase flow cross-correlation velocity measurement method based on void fraction was proposed. Taking advantage of the history data storage and playback function of TJU-ET-IV software system, the proposed cross-correlation velocity measurement method was evaluated. Experiment results show that the proposed method has good stability and high precision.
在过去二十多年中,ET技术得到了迅速的发展,但由于ET反问题的求解具有非线性、欠定性和病态性等难点,使得重建图像质量并不理想。同时,软件系统设计相对滞后,功能不够完善。针对目前存在的问题,本文研究了常用图像重建算法的原理,提出了Tikhonov预迭代算法和基于卡尔曼滤波的快速图像重建算法,并开发了一套电学层析成像软件系统,主要工作和结论如下:
1.分析了ET技术的反问题,总结了灵敏度系数算法、Landweber迭代算法、Tikhonov正则化算法、牛顿-拉夫逊算法及共轭梯度算法等五种常用图像重建算法的原理。在此基础上,对Tikhonov迭代算法进行改进,提出了Tikhonov预迭代算法,明显提高了成像速度。
2.对各种常用图像重建算法从重建图像质量和成像速度两方面进行了仿真和实验评价。
3.提出了基于卡尔曼滤波的快速图像重建算法,并通过仿真和实验验证其有效性。结果表明,基于卡尔曼滤波的快速图像重建算法是一种重建图像质量好,成像速度快,而且对噪声干扰有很好鲁棒性的图像重建算法。
4.使用Visual C++编程环境下的MFC和OpenGL开发了一套可用于在线检测和离线分析的电学层析成像软件系统TJU-ET-IV。该软件系统集成了五种快速图像重建算法,可用于对双截面12/16电极ECT/ERT系统进行高速成像,同时实现了USB高速通讯、纵截面显示、截面含气率实时显示、相关速度测量、数据存储及回放等功能。
5.分析了相关速度测量原理,提出了基于截面含气率的气/液两相流相关速度测量方法,利用TJU-ET-IV软件系统具有的数据存储及回放功能对该相关速度测量方法进行了评定实验。实验结果表明,该方法测速精度较高且稳定可靠。
Electrical Tomography (ET) is a new detection technique developed in recent years. Due to the advantages of being non-radiant, non-intrusive, rapid response and low cost, ET should have a good application prospect in many fields such as industrial process imaging, medical imaging and so on. Electrical Capacitance Tomography (ECT) and Electrical Resistance Tomography (ERT) based on different principle are two categories of ET.
Although great progress has been made in ET technique in the past two decades, satisfactory reconstructed images in terms of good quality haven’t been achieved because the reconstruction problem of ET is a nonlinear, underdetermined and ill-conditioned inverse problem. Meanwhile, the development of the software system has lagged behind leading to deficient functions. To solve the problems existed, the principles of some commonly used image reconstruction algorithms were studied, the Tikhonov pre-iteration algorithm and a fast image reconstruction algorithm based on Kalman filtering were proposed, and a software system for ET was developed in this thesis. The main work and results are as follows:
1. The inverse problem of ET was analyzed. Five commonly used image reconstruction algorithms were reviewed, including sensitivity coefficient, Landweber iteration, Tikhonov regularization, Newton-Raphson and conjugate gradient method. Based on them, the Tikhonov pre-iteration algorithm which can markedly improve the reconstruction speed of Tikhonov iteration algorithm was proposed.
2. The commonly used image reconstruction algorithms were evaluated in terms of the quality of reconstructed images and the reconstruction speed through simulation and experiment respectively.
3. A fast image reconstruction algorithm based on Kalman filtering was proposed. And its effectiveness was verified through simulation and experiment. The results show that the proposed algorithm has the characteristic of good quality of reconstructed images, high reconstruction speed and good robustness to noise.
4. TJU-ET-IV, a software system for ET which can be used for online testing and offline analysis, was developed using MFC and OpenGL under the programming environment of Visual C++. This software system containing five fast image reconstruction algorithms can carry out the image reconstruction for 12/16 electrode ECT/ERT system on two different cross sections at the same time. Also, it implements the functions of high-speed communication via USB, inspection of the longitudinal section, real-time display of void fraction, measurement of the cross-correlation velocity, history data storage and playback, and the like.
5. The principle of cross-correlation velocity measurement was analyzed. A gas-liquid two-phase flow cross-correlation velocity measurement method based on void fraction was proposed. Taking advantage of the history data storage and playback function of TJU-ET-IV software system, the proposed cross-correlation velocity measurement method was evaluated. Experiment results show that the proposed method has good stability and high precision.
引文
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