电容层析成像系统的图像重建算法研究

发布时间：2018-04-24 00:08

本文选题：电容层析成像 + COMSOL　；参考：《中国民航大学》2017年硕士论文

【摘要】：电容层析成像(Electrical Capacitance Tomography,ECT)是一项资源耗费低、快速、安全、廉价的过程层析成像技术,通过对管道中不同物质所对应介电常数的检测,获取管道横截面的相分布状况。近几年,ECT已被广泛应用于气液两相流空隙率测量及流型识别、流化床气固两相流浓度分布可视化、气力输送等多个领域。为了更加全面地学习掌握ECT图像重建算法,主要做了以下几方面的工作:1.阐述ECT技术的基本原理,对正、逆问题进行数学建模,并通过有限差分法对ECT正问题进行求解。2.深入研究目前存在的几种传统图像重建算法,介绍几种典型算法的成像理念,对算法求解过程进行推导与验证,并阐述其优缺点,利用图像评价参数对图像重建结果进行比较。3.针对电容层析成像系统图像重建过程中Tiknonov正则化解过度光滑引起的图像细节信息丢失问题,引入pl,2(?(27)10 p)的混合范数作为正则化算法的数据项和正则化项。该方法利用了欧氏范数2l的光滑性和分数范数pl(?(27)10 p)的稀疏性,不仅比范数2,1l具有更好的联合稀疏性,对噪声的抗干扰性也更强。4.针对电容层析成像图像重建中灵敏度矩阵的病态问题以及消耗主要计算时间的奇异值分解,对部分奇异值分解算法进行改进,该算法在计算大于某一阈值的奇异值及奇异向量时,给出一种新的隐式启动规则,提供了一种直接可以调用的功能,无需对灵敏度矩阵最优基向量组的维度进行预先估算。最后针对雅可比部分奇异值分解算法,提出一套修正的预处理和优化方案。5.针对电容层析成像系统图像重建过程中Tiknonov正则化引起的解的过度光滑和奇异值分解算法引起的数值不稳定,提出了一种更为广义的正则化算法。首先利用正定矩阵对正则化目标函数的惩罚相修正,使其可以对包含非光滑性信息的图像进行更准确重构,进一步在目标函数求解过程中引入对角权值矩阵,对基于2l范数的数据项改进。
[Abstract]:Electrical Capacitance tomography (ECT) is a low cost, fast, safe and cheap process tomography technique. The phase distribution of the cross section of the pipeline can be obtained by detecting the permittivity of different materials in the pipeline. In recent years, ECT has been widely used in voidage measurement and flow pattern identification of gas-liquid two-phase flow, visualization of gas-solid two-phase flow concentration distribution in fluidized bed, pneumatic transport and so on. In order to master the ECT image reconstruction algorithm more comprehensively, we mainly do the following work: 1. This paper expounds the basic principle of ECT technology, models the forward and inverse problems, and solves the forward problem of ECT by finite difference method. In this paper, several traditional image reconstruction algorithms are deeply studied, the imaging concepts of several typical algorithms are introduced, the algorithm solution process is deduced and verified, and its advantages and disadvantages are expounded. The image reconstruction results are compared by using image evaluation parameters. In order to solve the problem of loss of image detail information caused by excessive smoothing of Tiknonov regularization in the process of image reconstruction in electrical capacitance tomography system, the mixed norm of plan 2n / 2710 p) is introduced as the data item and regularization item of the regularization algorithm. This method takes advantage of the smoothness of Euclidean norm 2l and the sparsity of fractional norm pl(?(27)10 p. This method not only has better joint sparsity than norm 2l, but also has stronger anti-jamming to noise. Aiming at the ill-conditioned problem of sensitivity matrix and the singular value decomposition which consumes the main computing time in the reconstruction of electrical capacitance tomography image, the algorithm of partial singular value decomposition is improved. When calculating the singular value and singular vector larger than a certain threshold, the algorithm presents a new implicit start rule, which provides a directly callable function without the need to estimate the dimension of the optimal basis vector group of the sensitivity matrix in advance. Finally, for Jacobian partial singular value decomposition algorithm, a set of modified preprocessing and optimization scheme. In view of the excessive smoothness of solution caused by Tiknonov regularization and the numerical instability caused by singular value decomposition algorithm in image reconstruction of electrical capacitance tomography system, a more generalized regularization algorithm is proposed. Firstly, the penalty phase of regularized objective function is modified by positive definite matrix, which can reconstruct the image containing non-smooth information more accurately, and further introduce diagonal weight matrix in the process of solving objective function. The data item based on 2l norm is improved.
【学位授予单位】：中国民航大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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