声衍射层析成像研究进展

在计算机层析成像中用声波或电磁波取代X射线照射目标时波长不能再看作无限小,需要将Fourier切片定理修改为Fourier衍射投影定理,基于射线的CT相应地推广为衍射CT。概述了近年来衍射CT的发展,特别是声衍射CT。在理论和算法方面讨论了非均匀Fourier变换算法及其实现、仅根据强度信息的图像重建方法、多频率入射的情况、不完整测量数据条件下的图像重建等问题。此外还扼要介绍了不同领域中衍射CT的研究和应用情况。     

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。     

改进的Tikhonov正则化图像重建算法

Tikhonov正则化法可以解决电容层析成像中图像重建的病态问题,同时能够平衡解的稳定性与精确性,但其有效性和成像质量受到测量数据粗差的影响。改进的Tikhonov正则化法将2范数和M-估计结合,用一个缓慢增长的Cauchy函数代替最小二乘法的平方和函数,提高了估计稳健性和适应性。利用COMSOL和MATLAB软件对方法的有效性进行验证,重建结果表明,改进的Tikhonov正则化法能够有效减少粗差影响,提高重建图像精确度及分辨率。     

一种电容层析成像图像重建优化算法

提出一种电学层析成像(ECT)图像重建优化算法。通过将传统正则化算法转化为最小二乘问题进行求解,结合lp范数逼近正则化最小化问题,利用重新加权的方法进行迭代计算。以油-气两相流模型进行仿真及静态实验,将所提出的优化算法与常用的LBP、Landweber迭代及Tikhonov正则化算法进行对比。结果表明,与常用算法相比,采用该优化算法对管道中心物体及多物体分布流型进行图像重建,其图像相对误差均为最低,且重建图像的形状保真度明显提高。     

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。     

基于改进ICP算法的叶片型线轮廓度误差评定

针对传统最近迭代点(ICP)算法存在配准精度较低的问题进行算法改进。首先,考虑到三坐标测量机测量数据呈现有序排列、且一一对应的特点,使用了一种基于矢量对齐法的型线数据初配准方法进行初配准;其次,在传统ICP算法配准的基础上,对待配准数据进行非均匀有理化B样条(NURBS)曲线拟合,再利用自适应粒子群算法对测量数据进一步精配准;最后,采用基于最小区域的叶片型线轮廓度误差评定方法进行误差评定。实验分析结果表明:改进方法相对于传统ICP算法,可在原有收敛值基础上达到进一步收敛的效果,轮廓度误差相对减小28.57%。该方法有效提高了叶片型线轮廓度误差评定的精确度,可为叶片的加工质量提供可靠判定。     

超声衍射CT及其在不完全投影条件下的实验研究

超声衍射层析成像术是一种利用声波散射数据所携带的信息来反演物体内部结构的技术，具有广泛的应用前景。本文对这一领域的研究现状进行综述，慨述一些典型的超声衍射层析成像重构方法，同时探讨在残缺投影数据下的重构问题，对于不完全投影数据下的图像重构进行了实验研究。最后对实验结果进行讨论。     

A reconstruction algorithm for electrical impedance tomography based on sparsity regularization

This paper develops a novel sparse reconstruction algorithm for the electrical impedance tomography problem of determining a conductivity parameter from boundary measurements. The sparsity of the ‘inhomogeneity’ with respect to a certain basis is a priori assumed. The proposed approach is motivated by a Tikhonov functional incorporating a sparsity‐promoting ?₁‐penalty term, and it allows us to obtain quantitative results when the assumption is valid. A novel iterative algorithm of soft shrinkage type was proposed. Numerical results for several two‐dimensional problems with both single and multiple convex and nonconvex inclusions were presented to illustrate the features of the proposed algorithm and were compared with one conventional approach based on smoothness regularization. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerically robust minimal‐scan reconstruction algorithms for diffraction tomography via radon transform inversion

It is widely believed that measurements from a full angular range of 2π are generally required to exactly reconstruct a complex‐valued refractive index distribution in diffraction tomography (DT). In this work, we developed a new class of minimal‐scan reconstruction algorithms for DT that utilizes measurements only over the angular range 0 ≤ ? ≤ 3π/2 to perform an exact reconstruction. These algorithms, referred to as minimal‐scan estimate‐combination (MS‐E‐C) reconstruction algorithms, effectively operate by transforming the DT reconstruction problem into a conventional x‐ray CT reconstruction problem that requires inversion of the Radon transform. We performed computer simulations to compare the noise and numerical properties of the MS‐E‐C algorithms against existing filtered backpropagation‐based algorithms. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 84–91, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10014     

New iterative reconstruction methods for fan-beam tomography

In this paper, we present a novel class of iterative reconstruction methods for severely angular undersampled or/and limited-view tomographic problems with fan-beam scanning geometry. The proposed algorithms are based on a new analytical transform which generalizes Fourier-slice theorem to divergent-beam scanning geometries. Using a non-rigid coordinate transform, divergent rays can be reorganized into parallel ones. Therefore, one can employ a simpler parallel-beam projection model instead of more complicated divergent-beam geometries. Various existing iterative reconstruction techniques for divergent-beam geometries can be easily adapted to the proposed framework. The significant advantage of this formulation is the possibility of exploiting efficient Fourier-based recovery methods without rebinning of the projections. In case of highly sparse measurements (few-view data), rebinning methods are not suitable due to error-prone angular interpolation involved. In this work, three new methods based on the novel analytical framework for fan-beam geometry are presented: the Gerchberg-Papoulis algorithm, the Neumann decomposition method and its total variation regularized version. Presented numerical experiments demonstrate that the methods can be competitive in reconstructing from few-view noisy tomographic measurements.     

A new projection-based iterative image reconstruction algorithm for dual-energy computed tomography

Dual-energy CT can be represented as the dual-energy equations by decomposing the linear attenuation coefficient of the X-ray scanned object into two material basis functions of photoelectric absorption and Compton scatter. To solve the dual-energy equations, in this paper, we apply the mean-value theorem for integrals and propose a new projection-based iterative algorithm. We discuss the convergence of the proposed algorithm and carry out various numerical simulations for demonstrating its feasibility.     

一种基于模型的光学层析图像重建方法

光学层析图像重建是个病态问题,测量误差会在重建过程中被放大,对此,提出一种以广义高斯马尔可夫随机场模型为先验信息的光学层析图像重建方法.重建过程是对目标函数的优化过程,目标函数关于光学参数的梯度计算是算法中的难点,因此,提出一种基于梯度树的梯度计算方法.文中分别给出了吸收系数和散射系数的重建结果,并引入三个指标因子衡量重建图像的质量,进而列出不同重建算法下,重建图像的指标值.最后通过对重建结果和指标因子取值的比较,分析基于模型的重建算法的有效性.     

A fast algorithm for three-dimensional electrostatics analysis: fast Fourier transform on multipoles (FFTM)

In this paper, we propose a new fast algorithm for solving large problems using the boundary element method (BEM). Like the fast multipole method (FMM), the speed-up in the solution of the BEM arises from the rapid evaluations of the dense matrix–vector products required in iterative solution methods. This fast algorithm, which we refer to as fast Fourier transform on multipoles (FFTM), uses the fast Fourier transform (FFT) to rapidly evaluate the discrete convolutions in potential calculations via multipole expansions. It is demonstrated that FFTM is an accurate method, and is generally more accurate than FMM for a given order of multipole expansion (up to the second order). It is also shown that the algorithm has approximately linear growth in the computational complexity, implying that FFTM is as efficient as FMM. Copyright © 2004 John Wiley & Sons, Ltd.     

Investigation of smooth basis functions and an approximated projection algorithm for faster tomography

To decrease the calculation time of iterative tomographic reconstruction, this study proposes and investigates the uses of the “dot‐projection” algorithm, which uses smooth basis functions for data representation. Basis functions give an approximation to the basis functions of blobs, which provide a more accurate reconstruction at the same resolution than for traditional “ray‐driven” projection algorithms with voxels. This study evaluates the calculation time decrease and obtained errors from the algorithm for reconstruction, as well as its response to spatial frequencies. Finally, we compare the dot‐projection for several basis functions and the ray‐driven projection with respect to accuracy. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 347–354, 2000