正交像散高密度三维单分子定位显微的数值模拟

单分子定位显微(single molecule localization microscopy, SMLM)成像技术利用荧光分子的稀疏发光、探测及定位,实现了纳米级空间分辨率的超分辨成像.为了提高其时间分辨率,需要提高同时发光的荧光分子密度.但随着分子密度的提高,不同分子的点扩散函数(point spread function, PSF)在探测器上将发生严重的重叠现象,导致空间分辨率降低,尤其是在进行三维SMLM成像时.为了解决这一问题,本文提出了一种基于正交像散的高密度三维单分子定位超分辨成像方法,并对该方法进行分析和数值模拟研究.该方法的核心是在单分子定位显微镜中将采集的荧光分成两束成像在同一个探测器的两个区域,并在两个通道中各引入一个光学参数相同但取向相互正交的柱透镜,实现对同一个荧光分子正负两个像散PSF图像的同时探测,然后建立该成像过程的线性投影模型,利用压缩感知算法求解出荧光分子的三维定位信息.结果表明,由于两个正交柱透镜产生的一组正交像散PSF对作为一个分子的系统响应时具有较低的相关性,该方法的高密度三维定位准确性可显著优于采用单个柱透镜的传统像散方法,且离焦程度越大两个...     

时域荧光分子层析图像重建的线性特征数据法

通过扩展用于时域扩散光成像(Diffuse Optical Tomography, DOT)的广义脉冲谱技术,提出了一种用于时域荧光分子层析成像(Fluorescence Molecular Tomography, FMT)的线性特征数据图像重建算法.此算法能够同时重建荧光产率和荧光寿命,并且利用模拟数据对此方法进行验证,证明了算法的有效性.     

含系统模糊的闪光照相正向成像技术研究及应用

<正>向成像技术是正向计算与反演相结合的密度重建技术的基础。为了正确获取闪光照相面光源下复杂客体的正向计算数值图像,提出了面光源点源化的思想,并用窗口化的探测系统模糊、径迹法等技术得到了更加准确的、含系统模糊的正向投影矩阵以及方程。利用含系统模糊的正向投影方程计算实验客体的正向投影,获得了与实验结果一致的边界信息。含系统模糊的正向投影方程和逆问题求解的约束共轭梯度法合成了整体密度重建方法。整体密度重建方法应用于FTO客体的模拟图像和实验图像,都能够将模糊控制在1~2个像素。     

荧光单分子的频率域纳米级快速定位算法及其在超分辨荧光成像中的应用

为了解决现有单分子定位算法中定位速度慢和对噪声有评估依赖性的问题,基于补零快速傅里叶变换和相位梯度算子提出一种新型的噪声自由的频率域非迭代荧光单分子定位算法。计算机模拟结果表明该算法定位精度可达纳米量级,而定位速度与解线性方程组法在同一个数量级。进而在传统实验参数条件下,对不同间隔分子带模型进行了模拟超分辨成像。模拟结果表明,可以区分中心相隔30nm的两个分子带。此外,将该算法用于HeLa细胞突起中微丝束结构的荧光超分辨成像,从重构获得的图像中可以看到微丝束的直径为75～200nm,验证了该算法的实用性。     

流动和传热问题的分区并行计算

针对交错网格下的SIMPLE数值算法实施了分区并行计算方法,在小型局域网下实现了流动和传热问题的并行数值计算.对两个经典的流动和传热问题的数值模拟实验表明,所建立的并行计算环境和分区并行算法能够得到正确的和收敛的数值结果.但与串行计算结果相比,并行计算误差明显大于串行计算误差.对并行算法做出的性能分析表明,所给出的并行算法得到了明显的加速效率.随着计算规模的增大,加速比和并行效率提高更显著.     

基于Boltzmann模型方程的气体运动论HPF并行算法

从修正的BGK-Blotzmann模型方程出发，引入离散速度坐标技术对气体分子速度分量进行离散降维，基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式，发展直接求解气体分子速度分布函数的气体运动论有限差分数值格式，提出了一套能有效模拟各流域三维绕流问题的气体运动论统一算法，在分析研究气体运动论数值算法内在并行度的基础上，开展各流域三维绕流问题统一算法的HPF（高性能FORTRAN）并行化程度设计，建立一套能有效模拟各流域复杂外形体绕流的HPF并行算法软件，并进行了不同Knudsen(克努森）数下三维球体绕流及类“神舟号”返回舱外形体绕流的初步数值实验，将计算结果与过渡区有关实验数据及各流域气体绕流现象进行比较分析，证实了发展的气体运动论HPF并行算法在求解稀薄流到连续流不同流域复杂绕流问题方面的可行性。     

快速多极边界元法用于扩散光学断层成像研究

在求解扩散光学断层成像中的正向问题时, 目前普遍采用有限元法, 但是随着实际模型规模的增大, 有限元法的计算量问题日益显著, 而边界元法则由于可以降低计算维度使计算量减少而备受关注. 本文以均匀的高散射介质为模型, 研究了将快速多极边界元法用于扩散光学断层成像的正向问题. 快速多极边界元法利用核函数的多极展开, 将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归, 再结合广义最小残量法进行迭代求解. 将计算结果和蒙特卡罗法的模拟结果进行了比较, 表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性. 研究结果验证了快速多极边界元法可以用于扩散光学断层成像, 为其大规模和实时成像带来可观的前景. 关键词： 扩散光学断层成像 边界元法 快速多极边界元法     

ICF内爆压缩X光成像过程数值模拟

 基于定态局域热动平衡辐射输运方程求解和光线追踪方法，编制了X光成像后处理程序，能够数值再现ICF内爆压缩X光成像过程。将该程序用于神光Ⅱ装置间接驱动内爆物理的理论设计和实验数据分析。模拟结果表明：燃料区压缩后的尺寸、燃料区掺Ar和内壳层涂S两元素特征谱线发光时序及发光持续时间等过程，后处理方法结果与诊断测量数据基本符合。     

基于Boltzmann输运方程的SPECT系统解析建模方法

在单光子发射断层成像(SPECT)中, 为了校正劣化因素的影响, 提高图像质量, 需要对SPECT成像的物理过程进行准确建模. 本文提出了基于Boltzmann输运方程及其Neumann级数解理论的SPECT系统解析建模方法, 并采用数论高维数值积分算法对解析建模公式进行数值求解. 分别对点源、均匀圆柱体模型和NCAT模型进行SPECT投影过程计算, 将其结果与传统的Monte Carlo建模方法进行比较. 结果表明解析建模方法的计算速度和精度综合性能优于Monte Carlo建模方法, 且具有不受统计噪声影响的优点, 因而更适于进行SPECT成像过程的建模.     

用改进的Fienup迭代算法进行数字全息重建

数字全息成像中往往包括再现像、共轭像和零级项,再现像的分离是常见而又难以彻底解决的问题。提出一种新的全息图重建算法,即利用相干衍射成像（CDI）中的迭代方法处理数字全息图,实现仅有一个实像的再现结果,从而彻底解决该问题。该方法包括两个步骤：首先通过CCD分别测量样品单独存在、样品和参考光同时存在以及参考光的远场衍射分布;然后通过计算机进行迭代运算。由于干涉光的存在,该算法比传统的CDI算法有更快的收敛速度和重建质量。同时进行了数值模拟验证并对生物切片进行了物像重建。     

荧光分子层析中的全时间分辨图像重建法

在荧光分子层析(Fluorescence molecular tomography,FMT)中.全时间分辨(Time Resolved.TR)测量包含了最多的光子传输信息.基于有限元一有限差分扩散方程的正向模型和Newtown-Raphson的逆向模型,将全时间分辨方法用于时域荧光分子层析中.用模拟数据对算法在空间分辨率、定量性、重建尺寸和灰度的保真度以及噪声稳健性等方面进行了验证.结果表明,此方法能够实时重建荧光产率和荧光寿命图像.与以前发展的基于广义脉冲谱技术(Generalized pulse spectrum technique,GPST)的特征数据法进行图像重建相比较.整体上优于广义脉冲谱技术.     

一种改进的光学层析图像重建方法

Alexander D．Klose将联合差分方法用于光学层析图像重建的梯度计算中,但给出的对光学参量的求导算法有局限,他的算法只能实现对边界点光学参量的导数计算,而无法实现对内部点光学参量导数的计算,会导致图像重建失败。在联合差分算法的基础上,研究了针对内部点光学参量的求导方法,给出了一种基于树形结构的对内部点光学参量求导的策略。具体实现时,为了降低计算复杂度,采用近似梯度计算方法。算法的仿真实验结果表明：该方法可以有效地实现对内部点光学参量的导数计算,提出的近似计算方法可降低梯度计算复杂度,提高运算速度,并可得到良好的图像重建质量。     

Fast intersections on nested tetrahedrons (FINT): An algorithm for adaptive finite element based distributed parameter estimation

A variety of biomedical imaging techniques such as optical and fluorescence tomography, electrical impedance tomography, and ultrasound imaging can be cast as inverse problems, wherein image reconstruction involves the estimation of spatially distributed parameter(s) of the PDE system describing the physics of the imaging process. Finite element discretization of imaged domain with tetrahedral elements is a popular way of solving the forward and inverse imaging problems on complicated geometries. A dual-adaptive mesh-based approach wherein, one mesh is used for solving the forward imaging problem and the other mesh used for iteratively estimating the unknown distributed parameter, can result in high resolution image reconstruction at minimum computation effort, if both the meshes are allowed to adapt independently. Till date, no efficient method has been reported to identify and resolve intersection between tetrahedrons in independently refined or coarsened dual meshes. Herein, we report a fast and robust algorithm to identify and resolve intersection of tetrahedrons within nested dual meshes generated by 8-similar subtetrahedron subdivision scheme. The algorithm exploits finite element weight functions and gives rise to a set of weight functions on each vertex of disjoint tetrahedron pieces that completely cover up the intersection region of two tetrahedrons. The procedure enables fully adaptive tetrahedral finite elements by supporting independent refinement and coarsening of each individual mesh while preserving fast identification and resolution of intersection. The computational efficiency of the algorithm is demonstrated by diffuse photon density wave solutions obtained from a single- and a dual-mesh, and by reconstructing a fluorescent inclusion in simulated phantom from boundary frequency domain fluorescence measurements.     

Efficient parallel resolution of the simplified transport equations in mixed-dual formulation

A reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time.A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations [1]. In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the Raviart–Thomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization.     

Experimental validation for time-domain fluorescence diffuse optical tomography of linear scheme

We present a full three-dimensional, featured-data algorithm for time-domain fluorescence diffuse optical tomography that inverts the Laplace-transformed time-domain coupled diffusion equations and employs a pair of appropriate transform-factors to effectively separate the fluorescent yield and lifetime parameters. By use of a time-correlation single-photon counting system and the normalized Born formulation, we ex-perimentally validate that the proposed scheme can achieve simultaneous reconstruction of the fluorescent yield and lifetime distributions with a reasonable accuracy.     

在可扩展机群系统上二维分子动力学问题的并行计算

用分子动力学方法可以有效地研究凝聚介质的激波压缩,并在许多领域得到了广泛应用。由于此方法计算量太大,所以研究并行算法和优化计算就显得特别重要。现在,在可扩展机群系统上,实现了分子动力学程序的并行计算。     

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.     

Numerical evaluation of linearized image reconstruction based on finite element method for biomedical photoacoustic imaging

An image reconstruction algorithm for biomedical photoacoustic imaging is discussed. The algorithm solves the inverse problem of the photoacoustic phenomenon in biological media and images the distribution of large optical absorption coefficients, which can indicate diseased tissues such as cancers with angiogenesis and the tissues labeled by exogenous photon absorbers. The linearized forward problem, which relates the absorption coefficients to the detected photoacoustic signals, is formulated by using photon diffusion and photoacoustic wave equations. Both partial differential equations are solved by a finite element method. The inverse problem is solved by truncated singular value decomposition, which reduces the effects of the measurement noise and the errors between forward modeling and actual measurement systems. The spatial resolution and the robustness to various factors affecting the image reconstruction are evaluated by numerical experiments with 2D geometry.     

Forward and Backward Bellman Equations Improve the Efficiency of the EM Algorithm for DEC-POMDP

Decentralized partially observable Markov decision process (DEC-POMDP) models sequential decision making problems by a team of agents. Since the planning of DEC-POMDP can be interpreted as the maximum likelihood estimation for the latent variable model, DEC-POMDP can be solved by the EM algorithm. However, in EM for DEC-POMDP, the forward–backward algorithm needs to be calculated up to the infinite horizon, which impairs the computational efficiency. In this paper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EM algorithm (MBEM) by introducing the forward and backward Bellman equations into EM. BEM can be more efficient than EM because BEM calculates the forward and backward Bellman equations instead of the forward–backward algorithm up to the infinite horizon. However, BEM cannot always be more efficient than EM when the size of problems is large because BEM calculates an inverse matrix. We circumvent this shortcoming in MBEM by calculating the forward and backward Bellman equations without the inverse matrix. Our numerical experiments demonstrate that the convergence of MBEM is faster than that of EM.