图像引导放疗中的锥束CT灌注成像方法

为了实现图像引导放疗与功能成像结合的功能图像引导放疗,研究运用图像引导放疗中的锥束CT影像设备进行CT灌注成像的可能性。为了解决锥束CT不能快速成像,进而不能获取准确的体素时间-密度曲线(IDC)的问题,提出了一种基于投影数据的体素密度建模方法。首先,运用计算机仿真技术模拟出锥束CT投影数据;然后,对各体素密度值进行数学建模;最后,利用计算机最优化值求解技术,编程实现模型具体参数的计算。实验证明,该模型得到的TDC和DCE-CT实测获得的TDC有很高的吻合度。该模型实现图像引导放疗中的锥束CT灌注成像是可行的。     

理想材料零件的锥束CT投影仿真

针对锥束CT在理想材料零件研制中的应用需求,给出了基于拓展体素模型的CT仿真零件材料信息表示方法.在体素模型的投影图像仿真计算中,提出了一种三维射束与体素模型的快速遍历与求交算法,并结合Simpson积分公式实现了投影直线积分的高效高精度计算.实验结果验证了该算法的有效性.     

三维锥束CT投影数据的模拟

三维锥束CT是目前研究的热点,也是医学CT和工业CT的发展方向。三维重建算法的可靠性和准确性的研究过程中,模型的设计以及投影数据的模拟是必不可少的一部分。本文详细介绍了3DShepp-Logan头部模型的设计思路、推导了等距锥束射线投影仿真公式,基于3DShepp-Logan头部模型进行了投影数据模拟,并利用FDK算法的重建结果验证了思路的可行性和模型计算的准确性。     

螺旋轨迹Shepp-logan模型的投影仿真

锥束螺旋CT是现代CT 领域内一个活跃的研究方向.为了验证三维CT 重建算法的有效性和准确性,研究仿真模型的投影数据是十分必要的.本文首先利用解析几何和求解二次方程的方法推导了螺旋轨迹扫描下的锥束射线投影仿真公式,给出3D Shepp-Logan头部模型在不同螺距下的投影仿真结果.其次,采用Katsevich方法实现了...     

三维锥束CT中几何参数的校正研究

计算机断层成像技术在工业和医学中的应用,三维锥束CT(Computed Tomography)是显微CT和工业CT目前研究的热点.三维锥束CT系统一般采用FDK重建算法,算法要求锥束中心射线垂直于探测器且投影在探测器中心,然而由于系统机械精度的不足难满足要求,从而给重建结果带来伪影.为解决上述问题,提出了一种投影数据的校正方法:在重建前首先根据几何参数对每幅投影数据进行修正,修正完后再进行重建.实验结果证明:改进后能有效地改善几何参数误差引起的图像失真,对三维锥束CT扫描系统的几何校正具有重要意义.     

锥束CT检测成像仿真系统的研究与实现

设计并实现一个用于CT专业教学和科研的锥束CT检测成像仿真系统.该仿真系统能够模拟对CT设备的控制,生成正投影数据,重建被测物体,并能对重建结果进行三维显示.该系统包括如下关键技术:按真实比例对CT设备建模,实现了锥束CT工作过程的可视化;用场景图方法组织CT场景,简化了场景图形的管理方式;采用GPU加速CT正投影、图像重建和体绘制算法,在一定程度上解决了锥束CT大数据量快速计算问题.实验结果表明,该系统具有较快的运行速度,可满足用户交互操作的需要.     

定步长压缩感知锥束CT重建算法

针对锥束CT成像系统中投影数据不完全的图像重建问题,提出了一种定步长压缩感知锥束CT重建算法。首先将锥束CT重建问题归结为投影数据均方误差作为数据保真项、全变分作为正则项的无约束优化问题,分析目标函数的Lipschitz连续性;然后近似计算Lipschitz常数,求出梯度下降步长,利用梯度下降法进行重建;最后对CT投影数据采用联合代数重建算法更新重建图像。在每次迭代过程中调整梯度下降步长,提高重建算法的收敛速度。Shepp-Logan模型的无噪声实验结果表明,该算法的重建图像信噪比分别比联合代数重建算法、自适应最速下降-凸集投影算法、BB梯度投影算法的重建图像信噪比高出13.7728dB、12.8205dB、7.3580dB。仿真试验表明该重建算法提高了收敛速度,同时减少了重建图像的相对误差,极大提高了用少量投影数据重建的图像质量。     

定步长压缩感知锥束CT重建算法

针对锥束CT成像系统中投影数据不完全的图像重建问题,提出了一种定步长压缩感知锥束CT重建算法。首先将锥束CT重建问题归结为投影数据均方误差作为数据保真项、全变分作为正则项的无约束优化问题,分析目标函数的Lipschitz连续性;然后近似计算Lipschitz常数,求出梯度下降步长,利用梯度下降法进行重建;最后对CT投影数据采用联合代数重建算法更新重建图像。在每次迭代过程中调整梯度下降步长,提高重建算法的收敛速度。Shepp-Logan模型的无噪声实验结果表明,该算法的重建图像信噪比分别比联合代数重建算法、自适应最速下降-凸集投影算法、BB梯度投影算法的重建图像信噪比高出13.7728 dB、12.8205 dB、7.3580 dB。仿真试验表明该重建算法提高了收敛速度,同时减少了重建图像的相对误差,极大提高了用少量投影数据重建的图像质量。     

三维锥束重建中滤波器的设计

设计了几种用于CT三维锥束图像重建的滤波器,并将其对图像质量的影响进行了分析。CT是一种先进的成像技术,现已被应用于多个领域。CT图像重建算法多采用滤波反投影法,滤波是此方法的核心部分。本文介绍了三维锥束近似重建的基本原理,分析并设计了几种用于CT锥束图像重建的滤波器,并且通过投影数据的图像重建结果分析了不同滤波函数对断层图像重建质量的影响。实验结果证明：所设计的几种滤波器能较好的满足实际图像重建的要求。     

锥束CT的图像分块OSEM重建算法

在计算机断层成像（CT）中,有序子集最大期望值算法（OSEM）能够在较短的时间内重建出高质量的图像。对含有噪声的投影数据,投影旋转分度子集划分的不同会影响到图像的重建质量和收敛速度。针对三维锥束CT情况,研究了一种基于图像分块的变子集OSEM重建方法,该方法将图像空间分割成等大小的图像块,然后在迭代过程中,对于不同的图像块用变化的子集进行图像重建。计算机仿真实验表明：该方法在锥束CT图像重建中,能够在抑制噪声的同时提高重建图像的收敛速度。     

A (/spl mu/ + /spl lambda/) evolutionary algorithm for reconstruction of SPECT data

Algorithms used to reconstruct single photon emission computed tomography (SPECT) data are based on one of two principles: filtered back projection or iterative methods. In this paper, an evolution strategy (ES) was applied to reconstruct transaxial slices of SPECT data. Evolutionary algorithms are stochastic global search methods that have been used successfully for many kinds of optimization problems. The newly developed reconstruction algorithm consisting of /spl mu/ parents and /spl lambda/ children uses a random principle to readjust the voxel values, whereas other iterative reconstruction methods use the difference between measured and simulated projection data. The (/spl mu/ + /spl lambda/)-ES was validated against a test image, a heart, and a Jaszczak phantom. The resulting transaxial slices show an improvement in image quality, in comparison to both the filtered back projection method and a standard iterative reconstruction algorithm.     

基于平面区域跟踪的目标位姿参数自动测量

提出一种从序列图像中自动跟踪测量目标位置和姿态参数的方法。利用单应性原理和上一帧图像中目标位姿参数的测量结果,将目标上的典型平面区域重建为同时含有几何信息和亮度信息的平面区域模板;然后根据投影方程,将该模板在一定的位置姿态参数下进行投影仿真成像,当模板的仿真成像结果与当前帧图像中的该平面区域达到最佳匹配时,认为此时仿真成像的位置姿态参数即为当前帧图像的测量结果。通过对该匹配问题进行最优化建模和求解,实现了序列图像中目标位姿参数的自动测量。实验结果表明,本文方法能够在序列图像中对含有典型平面区域的目标实现较高精度的自动跟踪测量。     

Maximum Evidence Method for classification of brain tissues in MRI

Within the family of statistical image segmentation methods, those based on Bayesian inference have been commonly applied to classify brain tissues as obtained with Magnetic Resonance Imaging (MRI). In this framework we present an unsupervised algorithm to account for the main tissue classes that constitute MR brain volumes. Two models are examined: the Discrete Model (DM), in which every voxel belongs to a single tissue class, and the Partial Volume Model (PVM), where two classes may be present in a single voxel with a certain probability. We make use of the Maximum Evidence (ME) criterion to estimate the most probable parameters describing each model in a separate fashion. Since an exact image inference would be computationally very expensive, we propose an approximate algorithm for model optimization. Such method was tested on a simulated MRI-T1 brain phantom in 3D, as well as on clinical MR images. As a result, we found that the PVM slightly outperforms the DM, both in terms of Evidence and Mean Absolute Error (MAE). We also show that the Evidence is a very useful figure of merit for error prediction as well as a convenient tool to determine the most probable model from measured data.     

Blockwise conjugate gradient methods for image reconstruction in volumetric CT

Cone beam computed tomography (CBCT) enables volumetric image reconstruction from 2D projection data and plays an important role in image guided radiation therapy (IGRT). Filtered back projection is still the most frequently used algorithm in applications. The algorithm discretizes the scanning process (forward projection) into a system of linear equations, which must then be solved to recover images from measured projection data. The conjugate gradients (CG) algorithm and its variants can be used to solve (possibly regularized) linear systems of equations Ax=b and linear least squares problems minx∥b-Ax∥(2), especially when the matrix A is very large and sparse. Their applications can be found in a general CT context, but in tomography problems (e.g. CBCT reconstruction) they have not widely been used. Hence, CBCT reconstruction using the CG-type algorithm LSQR was implemented and studied in this paper. In CBCT reconstruction, the main computational challenge is that the matrix A usually is very large, and storing it in full requires an amount of memory well beyond the reach of commodity computers. Because of these memory capacity constraints, only a small fraction of the weighting matrix A is typically used, leading to a poor reconstruction. In this paper, to overcome this difficulty, the matrix A is partitioned and stored blockwise, and blockwise matrix-vector multiplications are implemented within LSQR. This implementation allows us to use the full weighting matrix A for CBCT reconstruction without further enhancing computer standards. Tikhonov regularization can also be implemented in this fashion, and can produce significant improvement in the reconstructed images.     

基于近似模型的y轴微机械陀螺系统级优化

提出一种基于近似模型的MEMS系统级优化方法,给出具体实现流程,并结合一个y轴微机械陀螺进行优化。该方法解决了如何得到近似优化目标函数表达式的关键问题。所得的y轴微机械陀螺优化参数,使得陀螺驱动模态谐振频率fx和检测模态谐振频率fz分别为3 074 Hz和2 998 Hz,两者之间相差7 6 Hz,较好的实现了模态匹配,且都在3 000 Hz的设计要求附近,约束条件也得到了满足。该优化方法为在MEMS设计中快速获得系统级优化方案提供较好参考。     

Robust LQR design for systems with probabilistic uncertainty

In this paper, we consider the design of robust quadratic regulators for linear systems with probabilistic uncertainty in system parameters. The synthesis algorithms are presented in a convex optimization framework, which optimize with respect to an integral cost. The optimization problem is formulated as a lower‐bound maximization problem and developed in the polynomial chaos framework. Two approaches are considered here. In the first approach, an exact optimization problem is formulated in the infinite‐dimensional space, which is solved approximately using polynomial‐chaos expansions. In the second approach, an approximate problem is formulated using a reduced‐order model and solved exactly. The robustness of the controllers from these two approaches are compared using a realistic flight control problem based on an F16 aircraft model. Linear and nonlinear simulations reveal that the first approach results in a more robust controller.     

Matlab遗传算法工具箱在非线性优化中的应用

投影寻踪是一种降维处理技术,通过它可以将多维分析问题通过投影方向转化为一维问题分析。应用该法的关键在于寻求最佳投影方向,这可以转化为一个复杂的非线性优化问题来进行解决。选取某地区大气环境质量评价的投影寻踪评价模型,编制相关的目标函数和约束函数,应用基于MATLAB的遗传算法和直接搜索工具箱进行优化求解。结果表明：该工具箱在求解此类非线性优化问题上的有效性和方便性,从而为各领域应用投影寻踪模型提供了强有力的优化工具。     

Reconstruction of linearly parameterized models from single imageswith a camera of unknown focal length

This paper deals with the problem of recovering the dimensions of an object and its pose from a single image acquired with a camera of unknown focal length. It is assumed that the object in question can be modeled as a polyhedron where the coordinates of the vertices can be expressed as a linear function of a dimension vector. The reconstruction program takes as input, a set of correspondences between features in the model and features in the image. From this information, the program determines an appropriate projection model for the camera, the dimensions of the object, its pose relative to the camera and, in the case of perspective projection, the focal length of the camera. This paper describes how the reconstruction problem can be framed as an optimization over a compact set with low dimension (no more than four). This optimization problem can be solved efficiently by coupling standard nonlinear optimization techniques with a multistart method. The result is an efficient, reliable solution system that does not require initial estimates for any of the parameters being estimated     

Simulation based optimization of stochastic systems with integer design variables by sequential multipoint linear approximation

Optimization problems are considered for which objective function and constraints are defined as expected values of stochastic functions that can only be evaluated at integer design variable levels via a computationally expensive computer simulation. Design sensitivities are assumed not to be available. An optimization approach is proposed based on a sequence of linear approximate optimization subproblems. Within each search subregion a linear approximate optimization subproblem is built using response surface model building. To this end, N simulation experiments are carried out in the search subregion according to a D-optimal experimental design. The linear approximate optimization problem is solved by integer linear programming using corrected constraint bounds to account for any uncertainty due to the stochasticity. Each approximate optimum is evaluated on the basis of M simulation replications with respect to objective function change and feasibility of the design. The performance of the optimization approach and the influence of parameters N and M is illustrated via two analytical test problems. A third example shows the application to a production flow line simulation model. Received April 28, 2000