应用代数重建法编程重建数字图像

对已知和未知数字图像分别沿射线作Radon变换(线积分),用同一种布置射线特殊方法布置射线,每条射线积分步长易知皆为常数。从而,得到已知数字图像每条射线的线积分近似值(“观测值”);易建立未知数字图像线性代数方程组。应用“代数重建法”加法修正迭代编制Matlab程序,用此程序处理“观测值”数据,重建未知数字图像,其数值计算结果较好,与已知数字图像相对误差不超过2%。本文是ART加法修正迭代的基础工作,可为有关部门提供研究“代数重建法”实际应用参考。     

Kaczmarz算法收敛解的性态分析

Kaczmarz算法作为一种重要的代数重建技术(ART)在医学成像及诊断研究中起着很重要的作用。随着计算机硬件技术的发展,诸如ART、SIRT等迭代算法由于其良好的抗干扰性能及数据缺失情况下良好的成像能力逐渐受到人们的重视。本文主要基于矩阵广义逆的定义和性质证明,当x⁽⁰⁾∈R(A^T)^⊥时Kaczmarz算法迭代序列的极限为Moore-Penrose广义解的性质。理论表明Kaczmarz方法求解相容性和不相容性问题都是适定方法,本文从数值实验的角度验证了Kaczmarz方法的“适定”性和求解扰动问题时的“半收敛”性。另外,Kaczmarz方法当x⁽⁰⁾∈R(A^T)^⊥时还是一类正则化方法。     

代数重建法物理模型超声波图像重建

用“DC4型超声波检测仪”检测未知纵波速度分布的嵌有石膏的铝板,沿每条射线采集透射直达波“到时”数据。用特殊的布置方法布置射线,使每条射线积分步长均为已知常数,并沿其做Radon变换（线积分）,从而建立此“铝板模型”纵波速度分布线性代数方程组。编制ART加法修正方法R语言程序处理“到时”数据,重建“铝板模型”纵波速度分布,并提出识别石膏洞的充分必要条件、检验条件和“视察法”,通过重建结果识别出“铝板模型”上“石膏洞”的位置。此外,按照对“铝板模型”的相同的处理方式对“三板平面模型”进行实验及分析。本文重建图像的结果对于了解CT成像方法具有参考价值,有助于CT成像技术的推广应用。     

AMG preconditioning for sedimentary basin simulations in Temis calculator

Basin modelling aims at reconstructing the time evolution of a sedimentary basin in order to make quantitative predictions of geological phenomena leading to hydrocarbon accumulations. It accounts for porous medium compaction, heat transfer, hydrocarbon generation and migration. These physical phenomena are modelled by partial differential equations [Schneider, F., Wolf, S., Faille, I., Pot, D. 2000. A 3D basin model for hydrocarbon potential evaluation: application to Congo offshore. Oil and Gas Science Technologie, Rev-IFP 55, 3–13] representing the mass balances of solid, fluids (water and oil) coupled with Darcy's law and a compaction law. These equations are discretized using a cell-centered Finite Volume method in space and an implicit Euler integration in time. At each time step, the resulting nonlinear system is solved using Newton's method ending up at each Newton iteration with the solution of a linear system which represents the most cpu-time-consuming part of the basin simulator.     

Conditional statistical inverse modeling in groundwater flow by multigrid methods

Due to the notorious lack of data, stochastic simulation and conditioning of distributed parameter fields is generally acknowledged as a major task in order to produce realistic prognoses for groundwater flow phenomena, thus honouring the maximum of information available. In this paper, a new conditioning approach is presented which treats the distributed parameters directly without projection onto lower dimensional spaces and preserves certain desired statistical properties by explicitly stating them as constraints for the conditioning optimization problem. Typically, the conditioning task must be performed very often and the conditioning optimization problems are highly dimensional. Therefore, a second main focus of the paper is on the presentation of efficient multigrid methods for the solution of the conditioning problems. Numerical results are given for a practical application problem. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Best-Estimate Approach for Determining Self-potential Parameters Related to Simple Geometric Shaped Structures

A new approach is proposed in order to interpret field self-potential (SP) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on solving a set of algebraic linear equations, and directed towards the best estimate of the three model parameters, e.g., electric dipole moment, depth, and polarization angle. Its utility and validity are demonstrated through studying and analyzing synthetic self-potential anomalies obtained by using simulated data generated from a known model and a statistical distribution with different random errors components. Being theoretically tested and proven, this approach has been consequently applied on two real field self-potential anomalies taken from Colorado and Turkey. A comparable and acceptable agreement is obtained between the results derived by the new proposed method and those deduced by other interpretation methods. Moreover, the depth obtained by such an approach is found to be very close to that obtained by drilling information.     

CT辐射量降低和投影数目研究（英文）

改进CT技术的最终目标是用较低的辐射剂量重建出更高质量的图像以降低患癌症的风险。近年来受压缩感知理论的启发,减少投影角度重建一直是减少辐射量的一个热门课题。但是,当辐射剂量固定,减少投影角度并不总是意味着更好的图像质量。本文研究固定辐射剂量下图像质量和扫描角度数目的关系。数值实验表明对于固定的辐射剂量,起初图像质量随着扫描角度数目的增加而提高,但是当扫描角度数目足够大之后图像质量反而下降了。在等角全扫描模式下,对于我们测试的辐射剂量和图像,产生最佳图像质量的最佳扫描角度数目是300,这对于实际的应用具有借鉴意义。     

大地电磁三维正演聚集多重网格算法

为了加快大地电磁三维正演的求解速度,本文将一种新型的代数多重网格算法——聚集多重网格（aggregation-based algebraic multigrid, AGMG）算法引入大地电磁三维正演模拟中。首先从准静态条件下的麦克斯韦方程出发,利用交错网格有限体积法进行离散,并采用第一类Dirichlet边界条件形成大型稀疏复线性方程组;然后阐述AGMG算法的粗化策略和套迭代技术,并实施3种不同的AGMG求解算法：1）传统的V循环AGMG算法;2）AGMG预处理共轭梯度（AGMG-CG）;3）AGMG预处理广义共轭残差法（AGMG-GCR）。最终实现大地电磁法三维正演模拟。对典型地电模型进行正演模拟,并与已有的大地电磁三维正反演程序（ModEM）进行结果对比,以验证本文算法的准确性。另外,不同剖分网格和极化方式正演模拟结果与准残量最小化（QMR）迭代算法的对比表明,AGMG预处理求解算法（AGMG-CG、AGMG-GCR）不仅能够改善算法的稳定性,而且能够快速有效地求解正演问题;其中AGMG-GCR迭代次数更少,求解速度更快,误差衰减曲线更光滑,在144×152×104网格剖分情况下,相对于现有ModEM程序能够提高十几倍的计算速度,尤其适合大规模大地电磁三维正演问题。     

三个二次代数曲面的低次拼接

用计算机代数方法，研究了三个二次曲面的光滑拼接，给出了二次拼接曲面存在的判别方法，及计算拼接曲面的Matlab程序。     

A dynamical equivalent to the equilateral libration points of the earth-moon system

Consider the Earth-Moon-particle system as a Restricted Three Body Problem. There are two equilateral libration points. In the actual world system, those points are no longer relative equilibrium points mainly due to the effect of the Sun and to the noncircular motion of the Moon around the Earth. In this paper we present the problem as a perturbation of the RTBP and we look for the dynamical equivalent of L _4,5. It turns out to be a quasiperiodic orbit. It is obtained for a simplified model but the procedure to obtain it is general and can be carried out with an additional computational effort.