电磁层析成像图像重建中的修正共轭梯度算法

通过研究共轭梯度算法,推导出适用于电磁层析成像的修正共轭梯度算法,该方法提高了收敛速度,改善了电磁层析成像重建图像的质量。首先以共轭搜索方向充分下降为充分条件,理论推导出修正共轭梯度算法。然后从相对图像误差、相关系数和收敛曲线几个方面出发,评价了Landweber迭代法、单步Tikhonov正则化方法、共轭梯度法和修正共轭梯度法在电磁层析成像图像重建中的结果,得出结论:修正共轭梯度方法的相对图像误差最小,重建图像和原图像的相关系数最高,收敛情况优于共轭梯度算法。     

Fast reconstruction of computerized tomography images based on the cross-entropy method

Computerized tomography (CT) has been applied to multi-phase flow measurement in recent years. Image reconstruction of CT often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive, especially for the case of on-line flow regime identification. In this paper, a minimum cross-entropy (MCE) reconstruction based on wavelet multi-resolution processing, i.e., an MRMCE method, is proposed for fast reconstruction of CT images. Each row of the system’s matrix is transformed by 1-D wavelet decomposition. A regularized MCE solution is obtained using the simultaneous multiplicative algebraic reconstruction technique (SMART) at a coarse resolution level, where important information of the reconstructed image is contained. Then the solution in the finest resolution is obtained by inverse fast wavelet transformation (IFWT). Both computer simulation and experimental work were carried out for oil-gas two-phase flow regimes. Results obtained indicate that the MRMCE method improves the resolution of the reconstructed images and dramatically reduces the computation time compared with the traditional linear back-projection (LBP), MCE and algebraic reconstruction technique (ART) methods. Furthermore, the new method can also be used to accurately estimate the local time-averaged void fraction of dynamic two-phase flow. It is suitable for on-line multi-phase flow measurement.     

基于加权奇异值分解截断共轭梯度的电容层析图像重建

针对电容层析成像技术(ECT)中的"软场"效应和病态问题,提出了一种基于加权奇异值分解(SVD)截断共轭梯度的电容层析(ECT)图像重建算法。阐述了电容层析成像工作原理,提出了12电极ECT系统的测量方法。在分析灵敏度矩阵的奇异值分解理论的基础上,推导出了加权SVD截断共轭梯度的数学模型,并利用Tikhonov方法进行正则化加权处理。最后,分析了算法的收敛性,并将其应用于电容层析成像系统的图像重建中。实验结果表明,对于层流,截断共轭梯度算法的平均误差能达到27.54%,全部流型平均迭代步数达到13步,与LBP、Landweber和CG算法比较,该算法具有成像效果好,成像速度快,易于实现等特点。     

基于改进正则法的ECT图像重建算法

电容层析成像图像重建是一个典型的病态问题,其解是不稳定的。为获得良好的重建效果,需要采用既保证解的稳定性且又能提高重建图像质量的算法。本文提出了一种新的图像重建算法。在分析标准Tikhonov正则法的基础上,针对ECT逆问题的病态性进行改进,并推导出两步图像重建算法：第一步利用标准Tikhonov正则法的计算值获得权矩阵的估计;第二步采用本文所推导的改进Tikhonov正则法获得最终的重建图像。数值实验表明,该算法所获得的图像重建质量得到了明显的提高,且该算法无需迭代,保证了算法实时性。     

A hybrid regularization method combining Tikhonov with total variation for electrical resistance tomography

Electrical resistance tomography (ERT) is a promising measurement technique in industrial process imaging. However, image reconstruction in ERT is an ill-posed inverse problem. Regularization methods have been developed to solve the ill-posed inverse problem. Since the penalty term is a form of L2-norm, Tikhonov regularization method guarantees the stability of the solution, but it always makes the image edge oversmoothed. Total variation (TV) regularization method has good ability of preserving image edges. A hybrid regularization method, which combines Tikhonov with TV regularization method, is proposed to get better reconstructed images. The choice of the adaptive weighted parameter between TV and Tikhonov penalty term has been discussed in detail. In the proposed hybrid regularization method, the function of conductivity gradients is used as the adaptive weighted parameter to control automatically the weighting between the penalty terms from TV and Tikhonov regularization. For the model with sharp edges, the proportion of the penalty term from TV regularization is increased to preserve the edges, while for the model with smooth edges, the proportion of penalty term from Tikhonov regularization is increased to make the solution stable and robust to noise. Both simulation and experimental results of Tikhonov, TV and hybrid regularization method are shown respectively, which indicates that the hybrid regularization method can improve the reconstruction quality with sharp edges and is more robust to noise, and it is applicable for models with different edge characteristic.     

An adaptive Tikhonov regularization parameter choice method for electrical resistance tomography

Electrical resistance tomography (ERT) reconstructs the conductivity distribution from the boundary changes of electrical measurements. The inverse problem of ERT is seriously ill-posed where regularization methods are needed to treat this ill-posedness. A proper choice of regularization parameter which controls the degree of smoothing is very important for these regularization methods. Although have been a variety of methods, such as L-curve method, to choose a reasonable parameter for the problem, these methods usually result in a scalar parameter which cannot distinctly express the spatial characteristic of the conductivity distribution. So a spatially adaptive regularization parameter choice method is proposed for regularizing the inverse problem of ERT based on Tikhonov regularization. Since large regularization parameters can stabilize and smoothen the solution, while small regularization parameters can approximate and sharpen the solution, the proposed method adaptively updates the regularization parameters during the iteration process and provides spatially varying parameter for each pixel of the reconstructed image. When the iteration is stopped, large regularization parameters for the smooth background region and small regularization parameters for the object region can be obtained. The method is discussed using simulated data for some typical conductivity distributions, and further applied to the analysis of real measurement data acquiring from the practical system. The results demonstrate that flexible regularization parameter vectors can be achieved for different distributions and the strength of regularization is adaptively provided for different regions in a specific distribution. The adaptive method achieves an efficient and reliable regularization solution and has outstanding performance in noise immunity especially in smooth background regions.     

基于改进谱投影梯度算法的X射线发光断层成像

X射线发光断层成像(XLCT)是一种可同时获得解剖结构和功能信息的新型分子影像技术,在早期肿瘤检测与放疗方面具有重要应用潜力,但由于测量信息少,成像模型复杂等原因,其断层重建一直是挑战性难题。本文采用非单调Barzilai-Borwein梯度(NBBG)算法来求解重建问题目标函数。每次迭代中,谱投影梯度方法近似为L1范数约束的最小二乘问题。Barzilai-Borwein梯度法获得相应的更新方向,提高算法的收敛速度。采用非单调性线性搜索策略构建最优步长,保证全局收敛性。通过将Barzilai-Borwein梯度法和非单调性搜索结合,在保证全局收敛的同时,克服了选取精确步长带来较大计算量的缺点。数值仿真实验和物理实验得到的基于NBBG算法的单光原重建位置误差分别为0.68和0.94mm,与分裂增广拉格朗日收缩算法(SALSA)相比,本文方法在重建精度、鲁棒性和重建效率等方面都获得了较优的结果。     

基于CT图像的快速成形数据建模方法

针对医学上广泛采用的CT图像数据，提出了基于CT图像的快速成形数据建模方法，通过CT图像滤波，分割，开操作等图像处理方法以及轮廓提取和采样等建模方法，得到快速成形数据接口CLI文件，进而进行原型的快速成形制造。该方法在人体右侧半骨盆置换手术中取得成功，讨论了提高模型精度，构造数据接口文件的有关问题。     

一种基于梯度和零交叉点的图像边缘检测新方法

本文提出了一种基于一阶导数局部极大值和二阶导数零交叉点的图像边缘检测方法。许多传统的边缘检测方法，尤其是一些基于二阶导数零交叉点的方法，对于信号中的噪声比较敏感使得边缘信息不能完全准确地检测出来，而本方法可以较好地解决这些问题。本文提出的算法是先计算出像素一阶导数的局部极大值以及二阶导数对应的零交叉点，将两者进行比较，删除那些二阶导数是零交叉点但一阶导数不是局部极大值的像素点，最后把剩下像素连接起来，即是图像边缘。实验研究结果表明该方法具有良好的边缘检测效果和鲁棒性。     

基于改进共轭梯度法的ERT图像重建

针对电阻层析成像(ERT)图像重建中灵敏度矩阵的病态特性导致共轭梯度法的收敛率低的问题,提出了改进的共轭梯度算法,ERT图像重建前先对数据进行归一化预处理,将解空间映射到Krylov子空间中,再通过共轭梯度法求解低维子空间中的反问题。分别利用共轭梯度法、预处理共轭梯度法和改进共轭梯度法对典型的气水两相流模型做了仿真实验。实验结果表明,改进共轭梯度法能够提高重建图像的质量,并且相对于其他算法,降低了计算时间。     

动态电容层析成像图像重建算法

提出了融合ECT测量信息和被测对象动态演化信息的新型图像重建模型;基于Tikhonov正则化方法,建立一个同时考虑了ECT测量信息、被测对象动态演化信息、时间与空间约束的新型图像重建目标泛涵,将图像重建问题转化为最优化问题;提出了集成分裂Bregman迭代法优势的新型算法求解该目标泛涵。数值仿真结果表明,所提出的图像重建算法其图像重建质量均优于OIOR算法、STR算法及PLI算法;同时由于所提出的图像重建算法同时考虑了测量数据和重建模型的不精确性,其抵抗测量噪声的能力得以提高。     

Regularization parameter optimization based on the constraint of Landweber algorithm for electrical capacitance tomography

Image reconstruction algorithms play an important role in practical applications of electrical capacitance tomography. In the present paper, a combined image reconstruction method is proposed, which takes the results of Landweber algorithm as the constraint condition of Tikhonov algorithm's regularization parameter, calculates the regular parameter, inverts the inverse matrix of sensitivity matrix, and finally obtains the dielectric constant distribution; thus, reconstructed images with improved clarity were obtained. Simulation test are carried out to evaluate and analyze the proposed method from image error, correlation coefficient, image reconstruction time, and anti-noise ability. The results revealed that the Tikhonov regularization algorithm had excellent anti-noise ability; thus, it significantly improved the clarity of reconstructed images and clearly distinguished the multi-phase flow pattern and distribution.     

基于 V-ResNet 的电阻抗层析成像方法

电阻抗层析成像技术(EIT)因其非侵入和可视化等特性为人体肺部空间特性的监测提供了一种有效的方法。但是EIT的逆问题具有严重的非线性、病态性和欠定性,使得图像重建结果含有严重的伪影。针对上述问题,提出了一种由预映射、特征提取、深度重建以及残差去噪四个模块构成的V-ResNet的深度网络成像算法,实现对场域空间位置和电导率参数分布的重建。该算法有效地增加了前馈信息的多重传递并解决了深度网络的梯度消失问题,同时残差去噪模块有效地平滑了图像边界。采用相对误差(RE)和结构相似度(SSIM)来衡量成像质量,实验得出RE的平均值为0.14,SSIM平均值为0.96。仿真与实验结果表明,基于V-ResNet的成像算法与传统的成像算法相比,图像重建结果边界清晰,空间分辨率高。     

基于Delaunay三角剖分的多相流射线层析成像

为提高多相流CT系统重建图像质量,提出基于Delaunay三角剖分的射线层析成像方法.根据模型构造点集,对管道截面进行多尺度Delaunay三角剖分,根据三角形重心在探测阵列上的投影到其最近探测阵列元的归一化距离,确定各剖分单元的投影系数,并采用不同的重建算法进行图像重建.仿真与实验结果表明,该方法可利用少量投影数据重建图像,改善了工业多相流检测中投影数据不完整造成的图像失真;与均匀剖分相比,多尺度剖分明显改进了图像精度和实时性.     

Randomized Kaczmarz algorithm for CT reconstruction

The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.     

窄角锥束CT的改进扫描方式

基于圆形扫描轨道的FDK算法因其机械实现简单、算法效率高，已成为目前主要使用的三维锥束CT重建算法。但在工业CT（ICT）中，当探测器面阵的尺寸较小、射线束的水平张角较小，而待检测的工件较大时，单圆扫描的FDK重建算法受到限制。为解决小尺寸探测器检测大尺寸工件问题，本文研究了一种大步距平移加小分度旋转的扫描方式。与Ⅱ代锥束CT比，这种改进的扫描方式既可以节省扫描时间，数据的冗余量也比较少。仿真实验结果表明，这种改进的扫描方式具有良好的空间分辨率和密度分辨率。     

应用投影收缩的压缩感知锥束CT短扫描重建

由于锥束CT成像系统在短扫描方式下无法获得完全投影数据,从而限制了图像重建的质量,本文提出了一种基于投影收缩的压缩感知锥束CT短扫描重建算法。考虑BB(Barzilai-Borwen)梯度投影算法的非单调收敛,分析了投影收缩法的预测校正特性,并将校正过程引入到压缩感知图像重建算法中。结合目标函数下降方向和凸集投影下降方向,校正BB梯度投影算法,改善BB梯度投影算法的非单调特性。应用该算法对模拟投影数据和仿体扫描数据分别进行了重建试验。模拟试验结果表明,在25个采样角度下,用提出算法重建图像的信噪比值比自适应最速下降-凸集投影算法、投影收缩算法和BB梯度投影算法的重建结果分别高出9.487 0、9.802 7、3.615 9dB。仿真试验结果表明:在少量投影角度下该算法重建结果有效抑制了条状伪影,清晰重建出边缘细节,极大提高了少量投影数据重建图像的质量。     

一种皮鞋内腔尺寸CT测量仪

针对目前皮鞋内腔尺寸测量尚无有效的测量方法，致使制鞋业的产品设计生产落后、皮鞋的档次低及品种少的实际情况，本文研究开发了一种基于CT技术的皮鞋内腔尺寸自动测量仪。皮鞋内腔尺寸CT测量仪由6个部分组成，即X射线源与前准直器、探测系统、机械扫描及控制系统、主计算机系统、图像重建与处理系统及尺寸测量分析系统。研究结果表明，重建出的皮鞋内腔CT图像清晰，尺寸误差〈0．4mm，达到了设计使用的要求，为皮鞋内腔尺寸的无损测量提供了一种新的检测手段。     

CT图像表面重建技术中的边缘轮廓提取方法

论述了 CT图像表面重建技术中的边缘轮廓提取方法。采用该方法 ,得到了 CT图像的截面数据 ,进而利用CAD软件实现了 CT图像表面的三维重建。最后给出了儿童股骨三维表面重建的实例     

A second-order time-accurate finite element method for analysis of conjugate heat transfer between solid and unsteady viscous flow

A fractional four-step finite element method for analyzing conjugate heat transfer between solid and unsteady viscous flow is presented. The second-order semi-implicit Crank-Nicolson scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. The streamline upwind Petrov-Galerkin method (SUPG) is applied for the weighted formulation of the Navier-Stokes equations. The method uses a three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the method presented is to consistently couple heat transfer along the fluid-solid interface. Five test cases, which are the lid-driven cavity flow, natural convection in a square cavity, transient flow over a heated circular cylinder, forced convection cooling across rectangular blocks, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the method presented. This paper was recommended for publication in revised form by Associate Editor Kyung-Soo Yang Atipong Malatip received his B.S. degree in Mechanical Engineering from King Mongkut’s University of Technology North Bangkok, Thailand, in 2002. He then received his M.S. degree in Mechanical Engineering Chulalongkorn University, Thailand, in 2005. He is currently pursuing a Ph.D. degree in Mechanical Engineering at Chulalongkorn University. His research interests include computational fluid dynamics and fluid-thermal-structural interaction. Niphon Wansophark received his B.S., M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 1996, 2000, and 2007, respectively. He is an Assistant Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods and finite element method. Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chula-longkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis.