基于相位展开和一种新的迭代重建算法的流场莫尔层析术

使用莫尔层析方法测量温度场。设计了一种旋转莫尔偏折仪,该装置可以获取180°范围内的莫尔条纹图。采用傅里叶变换相位展开技术处理莫尔条纹,提取轴向任意截面的投影信息,使用一种新的莫尔层析迭代算法重建温度分布,该迭代算法与已有的代数重建算法不同,它由莫尔偏折基本公式和网格重建技术推导得出,直接使用光线偏折角进行迭代,可以直接实现对非完全投影数据的层析重建。实验中使用8个方向的莫尔条纹图对双峰结构温度场进行重建,得到了截面的温度分布,峰值的重建误差低于5%。测量结果证明这是一种准确、适用性广的层析重建方法。     

光偏折层析重建流场中的两阶段降噪技术

光学层析技术中,包含在投影信息中的噪声会严重影响重建精度。针对偏折层析的关键环节,提出分两阶段对噪声进行抑制的方法。其一是在数据提取阶段使用小波分析技术对偏移量进行降噪,其二是重建时使用偏折角平均修正算法抑制噪声对迭代计算的影响。模拟实验中使用莫尔层析重建技术对三峰温度场进行了重建,结果显示降噪处理能够明显改善噪声对重建造成的不良影响,对误差曲线的分析表明,该处理使得100次迭代后误差的降幅高达45%。结合8邻域求导算法和降噪处理技术,对小型防风喷焰进行实际测量,证实了莫尔偏折层析技术在流场测量领域的实用价值。     

Moiré层析迭代算法改进

应用自开发的Moiré层析算法重建轴对称流场,以检验层析算法的有效性.根据Moiré偏折的光学原理,以及层析的数学、物理意义,研究开发了Moiré偏折层析程序.采用基本代数迭代算法(Algebraic Reconstruction Technique:ART)及自研发的简单自相关代数迭代重建算法(Simple Self-correlative Algebraic Reconstruction Technique:SSART),应用Moiré偏折层析程序模拟重建了轴对称流场.结果发现,本工作开发的Moiré层析程序,采用SSART迭代算法能够较精确地重建正、负向轴对称流场,较采用ART迭代技术有较大的改进.     

基于偏折角修正迭代的层析重建算法族研究

研究非完全数据光偏折层析重建技术,提出了基于偏折角修正迭代的重建算法族,并结合抑制噪声、减弱重建模糊性和边缘效应、优化松弛系数等发展出多种重建迭代形式,使重建精度得到有效提高。在有限角投影、随机噪声数据和无平滑处理等重建条件下,应用该族算法对复杂温度分布进行数值重建,对不同算法的重建效能和重建误差进行对比,分析了各算法与相关的改进代数重建技术在重建性能上的明显差异,并得出最优的偏折层析重建算法。     

预混燃烧火焰的光偏折层析三维动态可视化

使用光偏折层析(CT)方法研究了非稳态预混燃烧流 场的参数测量及火焰结构表征。建立了适用于瞬态流场层 析的叠栅光偏折投影条纹图有序阵列采样系统,实现了单光栅副、单CCD、多方向、同时和 同光路条件的动 态采样。构建适用于少数投影光偏折计算层析的混合正则化重建算法。实验测量中,对C 4H10/空气预混燃烧 流场进行6视角动态采样,使用混合正则化算法对燃烧流场进行截面二维温度分布重建,使 用Sobel梯度 算子进行火焰内外区域温度分布的阈值分割。对4个不同时刻共计150 条莫尔条纹进行信息提取并重建出 20个截面的温度分布,使用移动立方体面绘制算法和光线投射体绘制 算法对三维体数据进行 显示,实现了燃烧流场参量分布及火焰结构的三维动态可视化。     

应用非线性自适应迭代重建算法层析热流场

为了提高光学计算层析技术(OCT)对热流场的诊断能力,采用非线性自适应迭代重建算法(NAIRT)重建热流场的截面温度分布。应用准直激光束扫描待测热流场,应用双光栅衍射获得莫尔条纹。为了获得层析投影数据,对莫尔条纹进行了包括傅立叶变换、数字滤波、逆傅立叶变换、相位分析和截面提取,最终获得扫描光线偏折角信息,即层析投影。应用NAIRT对偏折角迭代重建热流场的折射率分布,应用G_D变换进一步转换为温度分布,从而获得热流场的截面温度层析信息。结果表明,NAIRT不仅能精确重建实验热流场的截面温度分布,还可以层析热流场的任意截面。所以,NAIRT能够有效诊断热流场。     

极少方向投影光偏折CT的偏折角压缩传感修正重建

将压缩传感理论与偏折角修正迭代技术相结合解决光偏折层析极少方向的投影重建,提出了一种新的偏折角压缩传感修正重建算法。该算法以待测场梯度的l1范数为稀疏性先验模型,结合最速下降法进行全变差调整,并引入压缩传感权重因子对迭代过程进行优化。在极少方向投影条件下对双峰温度场进行模拟重建,并在相同条件下与已有算法进行比较。结果表明,在6方向投影数据条件下,新算法在峰值构建和重建平滑度方面均表现出显著的优越性,新算法的峰值误差和标准距离误差分别比现有算法降低了18.32%和46.67%。通过对喷焰温度分布的实验测量证明了该算法的有效性。     

包含遮挡物的三维流场莫尔层析重建

为了研究复杂流场环境下的包含遮挡物的非完全数据层析重建问题,从莫尔层析的基本理论出发,提出了一种将包含先验知识的属性矩阵融入迭代过程的全新的基于级数展开类的莫尔层析迭代算法。在此基础上,通过数值模拟,重建了包含遮挡物的三峰高斯分布的温度场,取得了理想的重建结果,并在相同条件下与层析变换类算法中滤波反投影算法进行了对比。结果表明,将先验知识以属性矩阵的形式融入迭代过程后,新算法与滤波反投影算法相比,能有效地处理包含遮挡物的非完全数据重建问题,为莫尔层析应用于实际测量奠定基础。     

瞬态三维温度场的莫尔偏折层析

本文讨论了莫尔偏折法层析三维温度场的原理;提出了一种多通道(多方向)莫尔偏折的方法来获得多方向光线经过温度场后偏折的数据,然后利用计算机层析再现三维温度扬的方法;并分析了最佳通道采样角间隔的选取问题,得到了角间隔与角频率之间的关系。采用YAG脉冲激光光源,测量了非对称火焰的三维空间温度分布,并与干涉法测量的结果比较,得到一致的结果。     

瞬态三维温度场的莫尔偏折层析

本文讨论了莫尔偏折法层析三维温度场的原理;提出了一种多通道(多方向)莫尔偏折的方法来获得多方向光线经过温度场后偏折的数据,然后利用计算机层析再现三维温度扬的方法;并分析了最佳通道采样角间隔的选取问题,得到了角间隔与角频率之间的关系。采用YAG脉冲激光光源,测量了非对称火焰的三维空间温度分布,并与干涉法测量的结果比较,得到一致的结果。     

Attraction-Repulsion Expectation-Maximization Algorithm for Image Reconstruction and Sensor Field Estimation

In this paper, we propose an attraction-repulsion expectation-maximization (AREM) algorithm for image reconstruction and sensor field estimation. We rely on a new method for density estimation to address the problems of image reconstruction from limited samples and sensor field estimation from randomly scattered sensors. Density estimation methods often suffer from undesirable phenomena such as over-fitting and over-smoothing. Specifically, various density estimation techniques based on a Gaussian mixture model (GMM) tend to cluster the Gaussian functions together, thus resulting in over-fitting. On the other hand, other approaches repel the Gaussian functions and yield over-smooth density estimates. We propose a method that seeks an equilibrium between over-fitting and over-smoothing in density estimation by incorporating attraction and repulsion forces among the Gaussian functions and determining the optimal balance between the competing forces experimentally. We model the attractive and repulsive forces by introducing the Gibbs and inverse Gibbs distributions, respectively. The maximization of the likelihood function augmented by the Gibbs density mixture is solved under the expectation-maximization (EM) method. Computer simulation results are provided to demonstrate the effectiveness of the proposed AREM algorithm in image reconstruction and sensor field estimation.      

Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm

We developed a new image reconstruction algorithm for magnetic resonance electrical impedance tomography (MREIT). MREIT is a new EIT imaging technique integrated into magnetic resonance imaging (MRI) system. Based on the assumption that internal current density distribution is obtained using magnetic resonance imaging (MRI) technique, the new image reconstruction algorithm called J-substitution algorithm produces cross-sectional static images of resistivity (or conductivity) distributions. Computer simulations show that the spatial resolution of resistivity image is comparable to that of MRI. MREIT provides accurate high-resolution cross-sectional resistivity images making resistivity values of various human tissues available for many biomedical applications.     

一种时变三维电离层CT算法

提出了利用GPS观测数据获得时变三维电离层电子密度分布的一种CT反演算法。对GPS地面接收台网的合理布设进行了初步的尝试，在此基础上，利用实际的GPS射线路径和通过IRI90模式计算得到的TEC进行了模拟反演，得到了电子密度在一小时内随时间、空间变化的图像。通过与IRI90模式直接得到的电子密度分布图像进行比较，证明该算法能重现原始模型中的特征，其重建质量较好。     

A multigrid expectation maximization reconstruction algorithm for positron emission tomography

The problem of reconstruction in positron emission tomography (PET) is basically estimating the number of photon pairs emitted from the source. Using the concept of the maximum-likelihood (ML) algorithm, the problem of reconstruction is reduced to determining an estimate of the emitter density that maximizes the probability of observing the actual detector count data over all possible emitter density distributions. A solution using this type of expectation maximization (EM) algorithm with a fixed grid size is severely handicapped by the slow convergence rate, the large computation time, and the nonuniform correction efficiency of each iteration, which makes the algorithm very sensitive to the image pattern. An efficient knowledge-based multigrid reconstruction algorithm based on the ML approach is presented to overcome these problems.     

Reconstruction algorithms: Transform methods

Transform methods for image reconstruction from projections are based on analytic inversion formulas. In this tutorial paper, the inversion formula for the case of two-dimensional (2-D) reconstruction from line integrals is manipulated into a number of different forms, each of which may be discretized to obtain different algorithms for reconstruction from sampled data. For the convolution-backprojection algorithm and the direct Fourier algorithm the emphasis is placed on understanding the relationship between the discrete operations specified by the algorithm and the functional operations expressed by the inversion formula. The performance of the Fourier algorithm may be improved, with negligible extra computation, by interleaving two polar sampling grids in Fourier space. The convolution-backprojection formulas are adapted for the fan-beam geometry, and other reconstruction methods are summarized, including the rho-filtered layergram method, and methods involving expansions in angular harmonics. A standard mathematical process leads to a known formula for iterative reconstruction from projections at a finite number of angles. A new iterative reconstruction algorithm is obtained from this formula by introducing one-dimensional (1-D) and 2-D interpolating functions, applied to sampled projections and images, respectively. These interpolating functions are derived by the same Fourier approach which aids in the development and understanding of the more conventional transform methods.     

Analysis and synthesis of multicomponent signals using positivetime-frequency distributions

A new approach to the analysis and reconstruction of multicomponent nonstationary signals from their time-frequency distribution (TFD) is presented. Specifically, we consider a TFD based on the recently introduced minimum cross entropy principle (MCE). This positive TFD is cross-terms free and, hence, has an advantage over the family of bilinear distributions. Based on the MCE-TFD, a new algorithm for reconstructing the phase and amplitude parameters of each component of the signal is developed. To evaluate the accuracy of the algorithm. Monte Carlo simulations are presented and compared with the corresponding Cramer-Rao bound. It is shown that the new algorithm is superior to presently available methods in both efficiency and performance. It is concluded that together with the MCE-TFD representation, the proposed approach provides a powerful tool for analysis of nonstationary multicomponent signals embedded in additive Gaussian noise     

Microwave imaging-complex permittivity reconstruction with aLevenberg-Marquardt method

This paper refers to quantitative reconstruction of the dielectric and conductive property distributions of biological objects by means of active microwave imaging. An iterative reconstruction algorithm based on the Levenberg-Marquardt method is tested with synthetic data. The influence of the receiver geometry is investigated and two methods for choosing the regularization parameter, an empirical method and generalized cross validation (GCV) method, are examined     

On Bayesian image reconstruction from projections: uniform and nonuniform a priori source information

A method that incorporates a priori uniform or nonuniform source distribution probabilistic information and data fluctuations of a Poisson nature is presented. The source distributions are modeled in terms of a priori source probability density functions. Maximum a posteriori probability solutions, as determined by a system of equations, are given. Interactive Bayesian imaging algorithms for the solutions are derived using an expectation maximization technique. Comparisons of the a priori uniform and nonuniform Bayesian algorithms to the maximum-likelihood algorithm are carried out using computer-generated noise-free and Poisson randomized projections. Improvement in image reconstruction from projections with the Bayesian algorithm is demonstrated. Superior results are obtained using the a priori nonuniform source distribution.     

An algorithm using projection onto subspace of prior distributions for long-wavelength sound wave CT

The stationary long-wavelength sound wave computed tomography is a nonlinear inverse problem that requires the use of prior information of the object. However, the prior assumptions that are usually used in similar inverse problems are more or less inappropriate. In this paper, a new reconstruction algorithm using the prior information is proposed and compared with subspace regularization method and Marquardt reconstruction algorithms. The simulation shows that the proposed algorithm can give a better reconstructed result whether the actual distribution is compatible or incompatible with the prior distributions.     

Density reconstruction using arbitrary ray-sampling schemes

Methods for calculating the distribution of absorption densities in a cross section through an object from density intergrals along rays in the plane of the cross section are well-known, but are restricted to particular geometries of data collection. So-called convolutional-back projection-summation methods, used now for parallelray data, have recently been extended to special cases of the fan-beam reconstruction problem by the addition of pre- and post-multiplication steps. In this paper, a technique for deriving reconstruction algorithms for arbitrary ray-sampling schemes is presented; the resulting algorithms entail the use of a general linear operator, but require little more computation than the convolutional methods, which represent special cases. The key to the derivation is the observation that the contribution of a particular ray sum to a particular point in the reconstruction essentially depends on the negative inverse square of the perpendicular distance from the point to the ray, and that this contribution has to be weighted by the ray-sampling density. The remaining task is the efficient arrangement of this computation, so that the contribution of each ray sum to each point in the reconstruction does not have to be calculated explicitly. The exposition of the new method is informal in order to facilitate the application of this technique to various scanning geometries. The frequency domain is not used, since it is inappropriate for the space-variant operators encountered in the general case. The technique is illustrated by the derivation of an algorithm for parallel-ray sampling with uneven spacing between rays and uneven spacing between projection angles. A reconstruction is shown which attains high spatial resolution in the central region of an object by sampling central rays more finely than those passing through outer portions of the object.