基于卷积稀疏编码的电容层析成像图像重建

针对电容层析成像(ECT)病态性逆问题，提出了一种将卷积稀疏编码模型作为惩罚项嵌入到ECT最小二乘问题的方法，通过预先训练好的滤波器并结合交替方向乘子算法(ADMM)对此模型进行求解，从而完成ECT图像重建。对提出的方法进行了仿真及实验测试，并与LBP、Tikhonov正则化及Landweber迭代算法进行比较。结果表明，提出的方法其重建图像平均相对误差和相关系数分别为0.438 9及0.896 8,均优于其他3种方法，中心物体及多物体分布的重建质量得到显著提升。     

超声层析成像的迭代重建

利用变形Born迭代方法,建立了超声衍射重建算法。在迭代过程中,为了解决超声逆散射问题中的非线性性,需要反复地求解前向散射方程和逆散射方程,以达到全场和未知函数的近似,较好地重建物体内部的断层图象。由于逆散射方程是一个不适定性的方程组,要用正则化方法处理方程的不适定性问题,使迭代方法收敛于问题的真实解,才能成功地应用于较高对比度物体的图象重建问题。用Picard准则对不适定问题进行了分析,给出了通过简单图形．确定模型受噪声污染情况以及正则化方法适用范围的方法。在重建实验中。对建立的图像重建算法进行了实验仿真。达到了较好的效果。     

基于鲁棒正则化极限学习机的电容层析成像图像重建

电容层析成像图像重建是一个非线性及病态性逆问题。基于此,提出了基于迭代重加权最小二乘法的鲁棒正则化极限学习机(RELM-IRLS)算法的电容层析成像图像重建方法,以油/气两相流为研究对象,通过有限元仿真构建随机分布流型,对RELM-IRLS算法完成训练,并与Landweber迭代算法及极限学习机算法进行对比,RELM-IRLS算法的测试集平均误差相比极限学习机算法减小4.6%。仿真及静态实验结果均表明, RELM-IRLS算法所得重建图像质量得到明显提升,且算法具有良好的泛化性能。     

基于l_(2,p)-范数的ECT图像重建算法

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重建图像细节信息丢失问题,引入l_(2,p)(0p≤1)的混合范数作为正则化算法的数据项和正则化项。混合范数l_(2,p)利用了欧氏范数l_2的光滑性和分数范数l_p(0p≤1)的稀疏性,不仅比范数L_(2,1)具有更好的联合稀疏性,对噪声的抗干扰性也更强,进而针对l_(2,p)矩阵范数的非凸、非Lipschitz连续问题提出一种新的电容层析成像图像重建模型。实验结果表明,基于矩阵混合范数l_(2,p)极小化优化模型的正则化算法相比牛顿迭代、奇异值分解、共轭梯度算法具有更强的适应性,更高的图像分辨率及更好的成像质量。     

基于改进SR3模型算法的ECT图像重建研究

针对电容层析成像技术应用于气固两相流检测时,图像重建过程中存在的不适定性问题,提出一种稀疏松弛正则化回归模型(SR3)应用于ECT图像重建。采用软阈值迭代法和梯度下降法为SR3模型求解器,向SR3模型中加入L1、L2惩戒项,并设计滤值环节优化解向量。实验结果表明,改进SR3模型算法相比Tikhonov正则化算法、L1正则化算法及原SR3模型算法,重建图像精度明显提高,图像相对误差显著降低,有较好的成像效果。     

基于自适应步长双参数正则化算法的超声波过程层析成像图像重建

提出了一种新的自适应步长双参数正则化算法,对超声波层析成像系统检测浆体浓度分布进行图像重建。该算法利用转换矩阵将超定解作为先验信息,嵌入到正则化泛函中,避免重建图像被过度平滑,不仅成像速度较快且重建图像具有较高分辨率。仿真实验结果表明,相比于Tikhonov正则化算法以及Landweber算法,自适应步长双参数正则化算法重建图像的相关系数有明显提高并且边界信息更加可靠。     

调和映射约束下的超分辨率图像重建

针对超分辨率图像重建过程中的正则化约束问题,本文提出采用p(x)调和映射进行正则化重建,根据超分辨率图像观察模型及正则约束,给出相应的能量泛函,并采用动态偏微分方程演化来求解能量泛函.该算法在重建的过程中能够根据图像空间特性自适应地采用不同的p(x)范数进行正则化,在图像的平滑区域采用近似2次范数进行正则化,而在图像的边缘区域采用近似1次范数进行正则化.实验结果均表明该算法不仅能有效地重建图像边缘,而且能有效地改善一次范教约束重建的分片常数效应.     

改进的共轭梯度算法的图像重建算法

针对电容层析成像图像重建问题的病态性,在Tikhonov正则化的基础上,以正则化解决方案的规模和给定数据的质量为理论依据,引入一个数学变换,提出了一种新的正则化方法,该方法克服了常规正则化方法扰乱原系统的缺陷。同时,将ECT物理模型进行规范化,并对共轭梯度算法进行改进。仿真实验表明,改进的共轭梯度算法的成像质量高于LBP算法、 Tikhonov正则化算法和共轭梯度算法,并利用相关系数进行了验证。     

超声逆散射成像问题中正则化参数研究

研究了二维理想情况下,基于精确场描述的超声逆散射成像问题,先用矩量法将波动方程化为离散形式,分别用BI和DBI算法进行迭代重建。影响整个算法的一个关键因素是散射场方程的正则化求解,具有明显的不适定性。文章基于L曲线法,提出以解的范数和残差变化量的加权形式作为确定正则化参数的依据,在迭代过程根据问题不适定性程度,自适应地调整搜索范围。仿真结果表明,该算法可快速地找到最优正则化参数。     

基于电容层析的LN2-VN2两相流成像经典算法比较研究

针对低温流体液气介电常数接近1的特点,基于八电极电容层析成像(ECT)传感器,通过定量对比图像误差和相关性系数,系统分析了线性反投影算法、Tikhonov正则化算法、Landweber迭代算法、迭代Tikhonov正则化算法、代数重建技术和同步代数重建技术等传统用于室温流体的线性算法,用于LN₂-VN₂两相流的反演图像精度,并指出了各算法优缺点。通过对比水-空气的反演图像,发现LN₂-VN₂反演过程ECT线性化误差较小,从而有更好的反演结果。     

Image deconvolution using incomplete Fourier measurements

In this article, we propose a new deconvolution algorithm, which is based on image reconstruction from incomplete measurements in Fourier domain. Our algorithm has two steps. First, an initial estimator is obtained using Fourier regularized inverse operator. Second, parts of the estimator's Fourier coefficients are saved, and the others are removed to suppress noise energy, then the remaining coefficients are used to recover image based on the sparse constraints. This image reconstruction problem is an optimization problem that is solved by a fast algorithm named split Bregman iteration. Different from other deconvolution algorithms, our algorithm only uses parts of Fourier components to restore the blurred image and combines two different regularization strategies efficiently by applying a selection matrix. The experiment shows that our method gives better performance than many other competitive deconvolution methods. © 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 233–240, 2012     

Application of electrical capacitance tomography to the void fraction measurement of two-phase flow

Based on the electrical capacitance tomography technique, a new method for the void fraction measurement of two-phase flow is proposed. A 12-electrode void fraction measurement system is established. A mathematical model of image reconstruction of electrical capacitance tomography is developed. To obtain the quantitative information of two-phase flow, combining the Tikhonov regularization principle and the algebraic reconstruction technique algorithm, a new image reconstruction algorithm is presented. The experimental results show that the accuracy of void fraction measurement is satisfactory. The proposed method is suitable for the void fraction measurement of many kinds of two-phase flow.     

Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography

In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method presented here, a potential function with edge-preserving properties is introduced as a regularized term in an objective function. With the minimization of this proposed objective function, an iterative method to solve this optimization problem is presented in which half-quadratic regularization is introduced to simplify the minimization task. Both numerical and experimental data are employed to justify the proposed technique. The reconstruction results indicate that edge-preserving regularization provides a superior performance over Tikhonov regularization.     

A three-dimensional inverse finite-element method applied to experimental eddy-current imaging data

Eddy-current techniques can be used to create electrical conductivity mapping of an object. The eddy-current imaging system in this paper is a magnetic induction tomography (MIT) system. MIT images the electrical conductivity of the target based on impedance measurements from pairs of excitation and detection coils. The inverse problem here is ill-posed and nonlinear. Current state-of-the-art image reconstruction methods in MIT are generally based on linear algorithms. In this paper, a regularized Gauss-Newton scheme has been implemented based on an edge finite-element forward solver and an efficient formula for the Jacobian matrix. Applications of Tikhonov and total variation regularization have been studied. Results are presented from experimental data collected from a newly developed MIT system. The paper also presents further progress in using an MIT system for molten metal flow visualization in continuous casting by applying the proposed algorithm in a real experiment in a continuous casting pilot plant of Corus RD&T, Teesside Technology Centre.