基于压缩传感和代数重建法的CT图像重建

代数重建法(ART)是一种重要的CT图像重建方法,适合于不完全投影数据的图像重建,其缺点是重建速度慢。为提高图像重建的质量和速度,利用压缩传感理论提出了一种基于ART的高质量图像重建算法。该算法将CT图像的梯度稀疏性结合到ART图像重建中,在每次迭代中的投影操作结束后用梯度下降法调整全变差,减小图像梯度的l1范数。实验结果验证了该算法的有效性。     

Modified adaptive algebraic tomographic reconstruction of gas distribution from incomplete projection by a two-wavelength absorption scheme

A modified adaptive algebraic reconstruction technique (MAART) with an auto-adjustment relaxation parameter and smoothness regularization is developed to reveal the tomographic reconstruction of H 2 O distribution in combustion from incomplete projections. Determinations of relaxation parameter and regularization factor are discussed with regard to the consideration of improvement in reconstruction and reduction of computational burden. A two-wavelength scheme from tunable diode laser absorption measurement, 7444.36 and 7185.59 cm 1 , is used to simplify the nonlinear solution problem for obtaining the tomographic distributions of concentration and temperature simultaneously. Results of calculations demonstrate that MAART can perform the reconstruction results more efficiently with little complex modification and much lower iterations as compared with the traditional algebraic reconstruction technique (ART) or simultaneous iterative reconstruction technique (SIRT) methods. The stability of the algorithm is studied by reconstruction from projections with random noise at different levels to demonstrate the dependence of reconstruction results on precise line-of-sight measurements.     

光谱法分析代数迭代重建算法及改进

采用光谱分析技术,系列研究了已有代数迭代重建算法,并进一步研制了改进算法—简单自相关代数迭代重建算法(SSART)。采用数值模拟的方法模拟重建一个含遮挡物场,研究了SSART模拟效果和重建精度。作为对照,分析了已有的传统代数迭代算法同条件下的重建结果,包括基本代数迭代重建算法(ART)、联合代数迭代重建法(SART)和改进的联合代数迭代重建法(MSART)。重建精度用均方误差(MSE),绝对平均误差(AVE)和峰值相对误差(PE)三种误差指数标定。结果发现,SSART重建结果的三种误差指数都明显减小,其中MSE在10-4数量级上比ART的降低了26.6%,PE在10-2数量级降低了77.6%。因此,SSART重建含遮挡物模型场时,重建精度大幅度提高,重建效果明显改善,对传统代数迭代重建算法显著改进。     

简单自相关代数迭代重建算法

创建了简单自相关代数迭代重建算法(simple self-correlative algebraic reconstruction technique, SSCART),分析了其重建效果。采用数值模拟的方法,对代数迭代法(algebraic reconstruction technique, ART)与SSCART两种算法进行了计算机模拟,分析了模拟效果和重建精度。结果发现,SSCART算法的重建精度均方误差(mean square error, MSE)指标在10-4数量级上比ART的降低了65%[(ART的MSE值-SSCART的MSE)/ART的MSE],峰值相对误差(peak error, PE)指标在10-2数量级上降低了99.9%。计算上仅仅比ART多1个除数因子,所以SSCART具有算法简单、易于实现、重建精度高、稳定性好等优点。就作者检索的文献看是目前最优秀的代数迭代法。     

High-order conservative finite difference GLM–MHD schemes for cell-centered MHD

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities.     

A conservative high order semi-Lagrangian WENO method for the Vlasov equation

In this paper, we propose a novel Vlasov solver based on a semi-Lagrangian method which combines Strang splitting in time with high order WENO (weighted essentially non-oscillatory) reconstruction in space. A key insight in this work is that the spatial interpolation matrices, used in the reconstruction process of a semi-Lagrangian approach to linear hyperbolic equations, can be factored into right and left flux matrices. It is the factoring of the interpolation matrices which makes it possible to apply the WENO methodology in the reconstruction used in the semi-Lagrangian update. The spatial WENO reconstruction developed for this method is conservative and updates point values of the solution. While the third, fifth, seventh and ninth order reconstructions are presented in this paper, the scheme can be extended to arbitrarily high order. WENO reconstruction is able to achieve high order accuracy in smooth parts of the solution while being able to capture sharp interfaces without introducing oscillations. Moreover, the CFL time step restriction of a regular finite difference or finite volume WENO scheme is removed in a semi-Lagrangian framework, allowing for a cheaper and more flexible numerical realization. The quality of the proposed method is demonstrated by applying the approach to basic test problems, such as linear advection and rigid body rotation, and to classical plasma problems, such as Landau damping and the two-stream instability. Even though the method is only second order accurate in time, our numerical results suggest the use of high order reconstruction is advantageous when considering the Vlasov–Poisson system.     

一种少投影光学层析新算法及其应用

研究少投影数情况下等离子体温度场重建问题。结合光学层析重建算法及等离子体光谱诊断中的谱线绝对强度法进行自由电弧等离子体温度场重建实验。理论上，详细讨论了一种基于最大熵准则及最优化原理的光学层析图像重建新算法。通过计算机数值模拟，考察了该算法对非对称温度场分布的重建效果。详细分析了投影噪声、投影方向数、场分布性质对重建精度的影响，并与代数迭代重建算法结果进行对比．结果表明，该算法以两个正交方向投影数据重建单峰余弦模拟场平均误差仅为0.3％，而代数迭代重建算法为3．81％；该算法以四个均匀角度间隔投影数据重建三峰随机高斯模拟场平均误差为1．77％，而代数迭代重建算法为2．02％。实验中，运用该算法结合谱线绝对强度法重建了自由电弧等离子体的温度分布。     

用改进的遗传算法和高斯牛顿法联合反演三维地下水流模型参数

遗传算法在处理非线性优化问题时具有较好的全局搜索性能,但在局部搜索时搜索效率不高,解的精度亦不高,高斯牛顿法在处理非线性优化问题时的性质正好和遗传算法相反,利用遗传算法和高斯牛顿法的优点,用改进的遗传算法和高斯牛顿法联合反演地下水数值模型参数.首先用遗传算法求出地下水模型参数的初值,然后利用这组初值用高斯牛顿法进行数值模型参数的反演,并以一非均质各向同性三维承压非稳定流理想模型为例,结合有限元法讨论了用遗传算法和高斯牛顿法联合反演地下水数值模型参数的过程.计算结果表明,联合参数反演方法,具有收敛速度快、解的精度高的特点,在地下水渗流和水资源评价等领域可广泛应用.     

基于代数重建算法的有限角度扫描的光声成像

由于滤波反投影重建算法要求对成像区域进行全方位扫描以获取完全投影数据,它需要较长时间采集大量数据,使其在医学上的应用受到限制。研究了在有限角度下采用代数重建算法进行光声成像的方法,实验用的光源为YAG激光器,波长为1064nm,重复频率20Hz,脉宽为6ns,探测器为针状的磺化聚二氟乙烯(PVDF)膜水听器,接收面积的直径为1mm,从仿真和实验结果表明该方法适用于“非完备投影数据”的光声层析成像。从图像重建效果上与滤波反投影算法相比较,该成像算法提高了重建图像的分辨率和对比度。采用代数重建算法的有限角度的光声成像方法,对临床医学的无损伤检测,具有重要的意义。     

Analysis of algebraic reconstruction technique for accurate imaging of gas temperature and concentration based on tunable diode laser absorption spectroscopy

An improved algebraic reconstruction technique(ART) combined with tunable diode laser absorption spectroscopy(TDLAS) is presented in this paper for determining two-dimensional(2D) distribution of H_2O concentration and temperature in a simulated combustion flame.This work aims to simulate the reconstruction of spectroscopic measurements by a multi-view parallel-beam scanning geometry and analyze the effects of projection rays on reconstruction accuracy.It finally proves that reconstruction quality dramatically increases with the number of projection rays increasing until more than 180 for 20 × 20 grid,and after that point,the number of projection rays has little influence on reconstruction accuracy.It is clear that the temperature reconstruction results are more accurate than the water vapor concentration obtained by the traditional concentration calculation method.In the present study an innovative way to reduce the error of concentration reconstruction and improve the reconstruction quality greatly is also proposed,and the capability of this new method is evaluated by using appropriate assessment parameters.By using this new approach,not only the concentration reconstruction accuracy is greatly improved,but also a suitable parallel-beam arrangement is put forward for high reconstruction accuracy and simplicity of experimental validation.Finally,a bimodal structure of the combustion region is assumed to demonstrate the robustness and universality of the proposed method.Numerical investigation indicates that the proposed TDLAS tomographic algorithm is capable of detecting accurate temperature and concentration profiles.This feasible formula for reconstruction research is expected to resolve several key issues in practical combustion devices.     

On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics

It has been claimed that the particular numerical flux used in Runge–Kutta Discontinuous Galerkin (RKDG) methods does not have a significant effect on the results of high-order simulations. We investigate this claim for the case of compressible ideal magnetohydrodynamics (MHD). We also address the role of limiting in RKDG methods.For smooth nonlinear solutions, we find that the use of a more accurate Riemann solver in third-order simulations results in lower errors and more rapid convergence. However, in the corresponding fourth-order simulations we find that varying the Riemann solver has a negligible effect on the solutions.In the vicinity of discontinuities, we find that high-order RKDG methods behave in a similar manner to the second-order method due to the use of a piecewise linear limiter. Thus, for solutions dominated by discontinuities, the choice of Riemann solver in a high-order method has similar significance to that in a second-order method. Our analysis of second-order methods indicates that the choice of Riemann solver is highly significant, with the more accurate Riemann solvers having the lowest computational effort required to obtain a given accuracy. This allows the error in fourth-order simulations of a discontinuous solution to be mitigated through the use of a more accurate Riemann solver.We demonstrate the minmod limiter is unsuitable for use in a high-order RKDG method. It tends to restrict the polynomial order of the trial space, and hence the order of accuracy of the method, even when this is not needed to maintain the TVD property of the scheme.     

结合透射CT的康普顿背散射图像重建

在康普顿散射成像(CST)技术中可以结合透射成像重建出衰减系数来消除散射重建的非线性,但这样得到的投影矩阵带有误差。而CST重建问题的不适定性对噪声和投影矩阵的误差非常敏感,重建结果会有较大误差。针对此问题,基于压缩感知理论提出了一种新的CST重建算法。新方法将图像重建问题归结为一个图像的全变分(TV)最小化问题,并使用收敛速度较快的基于交替方向法的Split-Bregman方法进行求解。在仿真实验中,通过与代数重建技术(ART)进行比较,在测量数据充足和测量数据不足两种情况下,本文算法都具有更好的重建质量,证明了所提算法在重建精度和抗噪性能方面的优势。     

Compact third-order limiter functions for finite volume methods

We consider finite volume methods for the numerical solution of conservation laws. In order to achieve high-order accurate numerical approximation to non-linear smooth functions, we introduce a new class of limiter functions for the spatial reconstruction of hyperbolic equations. We therefore employ and generalize the idea of double-logarithmic reconstruction of Artebrant and Schroll [R. Artebrant, H.J. Schroll, Limiter-free third order logarithmic reconstruction, SIAM J. Sci. Comput. 28 (2006) 359-381].     

Abilities of nonlinear acoustic methods in locating gas bubbles in biological tissues

On the basis of a numerical solution to the equation of radial oscillations of a gas bubble in a liquid, the abilities of nonlinear acoustic methods in detecting gas bubbles in biological tissues with the use of pulsed acoustic location are analyzed. It is demonstrated that, with moderate amplitudes of the probing signal, it is possible to detect bubbles whose size is close to resonance. An improved version of the method of paired pulses is proposed, along with a method for detecting the bubbles and measuring their dimensions on the basis of a nonlinear excitation of their natural oscillations.     

基于最小区域的锥束ART算法快速图像重建

针对锥束ART算法重建速度慢的问题,考虑到工业CT重建目标尺寸差异较大的特点,提出了一种基于最小重建区域的快速三维图像重建方法。由不同视角下的锥束投影构建最小区域包络,对最小区域包络进行膨胀处理,以消除重建目标边界附近所出现的伪影,在此基础上,给出了射线穿过最小重建区域的体素索引及权因子的计算。该方法能够根据重建目标的尺寸自适应地确定最小重建区域,从而最大限度地减少了计算量。实验结果表明,该方法不仅大幅度提高了锥束ART算法的重建速度,而且有效地提高了重建质量。     

遗传算法在柱状高温气冷堆换料优化问题中的应用

堆芯换料方案的优化是一个典型的组合优化问题,其搜索空间异常庞大。传统的优化算法很难在如此巨大的搜索空间中寻找出全局最优解。遗传算法以其优良的自适应能力和优化能力,为组合优化问题提供了一个非常有效的解决途径。采用遗传算法对柱状高温气冷堆堆芯装料方案进行了优化,并编写了相应程序。为了提高堆物理的计算精度,堆芯临界计算采用26群输运计算。由于多群输运计算需要大量计算时间,为此对遗传算法进行了并行优化。为了验证遗传算法对柱状高温气冷堆换料的优化能力,构造了一个8组件的小型柱状高温气冷堆换料优化基准题。结果表明,遗传算法在柱状高温气冷堆换料优化问题中具有良好的优化能力和计算稳定性。     

Modeling the problem of low-orbital satellite UV-tomography of the ionosphere

The results of modeling the direct and inverse problems of low-orbital satellite ultraviolet (UV) tomography of the ionospheric 135.6 OI volume emission rate are presented. The direct problem was solved with the orbital geometry of DMSP block 5D3 satellites with SSUSI and SSULI UV spectrographs among the other payloads, the real operating parameters of these instruments (the scan rate and the interval of scan angles), and the set of the model distributions of the volume emission rate that contain irregularities on various scales. The solution of the direct problem yields the radiation intensities in the 135.6 nm line, which is used as the input data for reconstructing the initial (prototype) model distributions of the volume emission rates. The obtained system of linear equations (SLE) was solved using the Algebraic Reconstruction Technique (ART) and Simultaneous Iterative Reconstructive Technique (SIRT) algorithms, which are highly efficient in problems of the low-orbit radio tomography of the ionosphere. It is shown that the initial model distribution can be successively reconstructed if one takes the non-negativity condition of the solution into account, uses weighting functions to decrease the solution in the regions where it is known to be a priori small, and applies inter-iteration smoothing to eliminate the effects of the approximation errors. Here, the averaging parameters should decrease in the course of the iterations. With these constraints fulfilled, the computational costs of the ART- and SIRT-based solutions are similar, while the reconstruction error is approximately 6%. The influence of random errors and bias in the data on the results of the reconstruction is explored. It is shown that with a given error level of the initial data the parameters of the reconstruction algorithms can be adjusted in such a way as to efficiently suppress the influence of the noise with a relative amplitude of 2–3% on the solution.     

Reconstruction of emission coefficients for a non-axisymmetric coupling arc by algebraic reconstruction technique

A preliminary investigation of tomographic reconstruction of an asymmetric arc plasma has been carried out. The objective of this work aims at reconstructing emission coefficients of a non-axisymmetric coupling arc from measured intensities by means of an algebraic reconstruction technique (ART). In order to define the optimal experimental scheme for good quality with limited views, the dependence of the reconstruction quality on three configurations (four, eight, ten projection angles) are presented and discussed via a displaced Gaussian model. Then, the emission coefficients of a free burning arc are reconstructed by the ART with the ten-view configuration and an Abel inversion, respectively, and good agreement is obtained. Finally, the emission coefficient profiles of the coupling arc are successfully achieved with the ten-view configuration. The results show that the distribution of emission coefficient for the coupling arc is different from centrosymmetric shape. The ART is perfectly suitable for reconstructing emission coefficients of the coupling arc with the ten-view configuration, proving the feasibility and utility of the ART to characterize an asymmetric arc.     

An ART iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging

X-ray diffraction enhanced imaging (DEI) has extremely high sensitivity for weakly absorbing low-Z samples in medical and biological fields. In this paper, we propose an Algebra Reconstruction Technique (ART) iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging (DEI-CT). An Ordered Subsets (OS) technique is used to accelerate the ART reconstruction. Few-view reconstruction is also studied, and a partial differential equation (PDE) type filter which has the ability of edge-preserving and denoising is used to improve the image quality and eliminate the artifacts. The proposed algorithm is validated with both the numerical simulations and the experiment at the Beijing synchrotron radiation facility (BSRF).     

基于自适应准则的闪光照相图像重建

 针对闪光照相图像低信噪比的特点,提出了一种自适应的图像重建算法。该算法以代数法(ART)迭代重建为基础,在迭代重建过程中引入了两个权重矩阵,其中一个矩阵用来控制重建过程中的高频分量以保持重建结果的边界;另一个矩阵控制重建结果的平坦区域以提高重建结果的信噪比。通过在迭代过程中更新这两个矩阵来实现图像的自适应重建。数值模拟结果表明,相对于传统的单准则ART重建算法,该方法具有更好的抗噪能力和边界保持能力。