低剂量CT的加权总变差重建算法

针对稀疏投影角度的CT图像重建问题,结合压缩感知理论,提出基于加权迭代支持检测的分块代数重建算法,以较少的投影角度重建出理想的CT图像。首先,针对传统的代数重建技术计算量大、收敛速度慢的问题,提出分块代数重建算法;其次,传统的最小总变差模型会引起图像过度平滑及纹理细节模糊等问题,对此提出一种最小加权总变差算法,即加权迭代支持检测算法,并建立加权迭代支持检测模型;最后,分块代数重建技术与加权迭代支持检测模型交替迭代,使重建结果趋于收敛。本文采用经典的Shepp-Logan体模及实际的脑部CT切片进行重建,以均方根误差作为重建图像的质量评判标准,并与其他重建算法的重建结果进行对比。在经过一定次数的迭代后,基于本文算法的重建图像更贴近原始图像,而且比其他算法更早收敛。实验结果表明,本文算法在重建质量及收敛速度上都优于其他对比算法。     

一种基于反投影滤波的精确心脏重建算法

在分析心脏重建算法存在问题的基础上,结合反投影滤波重建算法及心脏重建的特性.提出一种基于反投影滤波的精确心脏重建算法。该算法通过M平面选取、心脏投影数据处理、M平面重建及重建图像重组等步骤,将滤波反投影重建算法应用于心脏重建中,避免原始非精确心脏重建算法中的锥角伪影、螺旋伪影,提高重建时间分辨率。以一患者的临床图像进行重建。结果对比表明,所提出的重建算法在冠脉血管CT均值上提高8%,最大值上提高4.4%,有效地减少心脏重建所需的投影数据范围,并为实现心脏低剂量超短扫描提供算法支持。     

基于全变分模型的CT不完全角度重建算法研究进展

在计算机断层扫描成像领域,不完全角度重建算法可以在不完备的投影数据中重建出质量较好的图像,而其中比较突出的一类算法是基于全变分模型的重建算法。研究者们在此模型的基础上提出了许多相关的算法,重建出了质量更好的图像。本文首先简要介绍了全变分模型重建算法,然后在模型改进和求解算法两个方面对此模型的重建算法进行研究。在模型改进方面主要介绍了根据全变分模型的局限性以及图像的内涵信息引入相关的先验（方向信息、非局部信息、高阶梯度信息等）来改善图像的重建性能。在求解算法方面主要介绍了经典的梯度下降算法以及基于稀疏优化理论的交替方向最小化算法。最后分析总结了目前存在的问题以及提出模型改进和求解算法两方面相结合依旧是未来发展的趋势。     

基于双平面正交投影X线成像系统的血管图像重建技术

基于双平面正交投影X线成像系统的血管图像的重建技术是一个典型而又有重要应用价值的极少数投影重建图像问题。本在介绍了由双平面正交投影重建出血管图像的基本原理的基础上，重点分析了通过在两个相互正交方向上的投影重建出血管的三维骨架(中轴线)和截面形状的研究方法与进展，并对有待解决的主要问题和今后的发展方向进行了讨论。     

CT图像重建的快速卷积反投影算法的优化

卷积反投影是最重要的一种CT图像重建算法，此算法简单，重建精度高，重建速度较快，应用最广泛。但是CT投影数据量巨大，重建时间比较长。根据卷积反投影算法的特点，提出了此算法的快速实现方法，在PC机上实现时，重建速度约提高20倍。     

基于通用GPU技术的三维TV算法的快速实现

TV算法是一种很好的有限角度投影数据图像重建算法,但在应用于三维的有限角度投影数据重建时,该算法存在的高耗时问题就更为突出并成为其应用瓶颈。本文提出了一套基于通用GPU技术在图形处理器上快速实现的三维TV算法。实验结果表明,与运行在CPU上的三维TV算法相比,该算法在获得可比的重建结果的前提下,有效地提高了重建速度。     

基于穿越长度权重迭代重建算法的研究

目的:传统的CT迭代算法中为了简化运算,投影系数的计算选择用成像射线路径是否穿过像素内来确定投影系数矩阵中元素的数值,穿过为1,不穿过为0。有些射线只穿过像素的边缘,也被赋值为1,扩大了该射线对相应像素投影值的贡献。为减小图像重建的误差,提高图像重建质量,提出了基于穿越长度权重的迭代重建算法,通过精确建模,选择用成像射线路径在像素内的穿越长度来确定投影系数矩阵中元素的数值。方法:采用MATLAB7.0仿真工具,对Shepp-Logan模型进行计算机仿真扫描,分别以传统投影系数和穿越长度权重计算的投影系数进行ML-EM迭代重建图像。结果:仿真数据表明基于穿越长度权重投影系数的ML-EM迭代重建算法,相比基于传统投影系数的迭代重建算法,可以提高重建图像的质量。结论:基于穿越长度权重的ML-EM迭代重建算法,通过精确建模达到了控制噪声、减小误差、较为准确重建的目的。通过对成像的几何和物理因素进行精确的建模,能有效地控制其中的非随机部分的影响,减小图像重建误差,一方面对迭代重建算法提供一种新的投影系数的计算方法,另一方面进一步提高迭代算法在CT重建中的图像质量。     

生物组织连续切片图象计算机三维重建(摘要)

生物组织显微切片的计算机三维重建可以将生物组织切片样本的二维图象精确地重建成它们原来的三维构型。本文提出的重建算法是利用画面上象点的明暗程度来表现重构模型可     

心血管双投影下多目标优化截面重建方法

近年来，心血管双平面投影下的三维重建技术作为一个少投影情形下的特例，已日益受到国际上图象重建和临床应用研究工作者的高度重视和深入研究。多目标优化图象重建法由于其在重建图象的质量、稳定性、重建速度以及收敛性等方面超乎寻常图象重建法的独到之处，已被成功地用于少投影图象重建的领域。本文旨在利用多目标优化法重建双平面投影下的心血管３Ｄ截面，得到了相当满意的结果。文中最末给出了重建两个不同类型的血管截面模型的例子。     

多准则图象空间迭代重建

本文研究图象峰值性函数极小化，原始投影数据与重建图象再投影的平方误差极小化所产生的双准则图象重建问题，双准则函数的优化可由其加权和标量化来研究，这是一种多准则正则化方法，新的多准则图象空间迭代重建克服了单准则ＳＩＲＴ算法的迭代收敛慢及重建图象质量差的问题，同时也克服了基于图象峰值性函数极小的ＡＲＴ算法重建图象中存在着胡椒加盐噪声问题，多准则图象空间迭代重建所产生的图象平滑性能好，伪像成份少。而且快     

A Fourier reconstruction algorithm with constant attenuation compensation using 180 degrees acquisition data for SPECT

In this paper, we develop an approximate analytical reconstruction algorithm that compensates for uniform attenuation in 2D parallel-beam SPECT with a 180-degree acquisition. This new algorithm is in the form of a direct Fourier reconstruction. The complex variable central slice theorem is used to derive this algorithm. The image is reconstructed with the following steps: first, the attenuated projection data acquired over 180 degrees are extended to 360 degrees and the value for the uniform attenuator is changed to a negative value. The Fourier transform (FT) of the image in polar coordinates is obtained from the Fourier transform of an analytic function interpolated from an extension of the projection data according to the complex central slice theorem. Finally, the image is obtained by performing a 2D inverse Fourier transform. Computer simulations and comparison studies with a 360-degree full-scan algorithm are provided.     

C形臂X线投影图像3D建模及其应用

C形臂X线投影图像3D建模是指以C形臂获取的X线2D投影图像为基础,实现骨骼3D模型的术中重建。与单纯的2D切片图像或投影图像相比,3D重建模型不仅含有更为丰富的骨骼外部形状等解剖结构信息,而且还可包含骨密度及强度等骨骼内部多元有用信息。该技术在骨组织活检、椎弓根螺钉植入、髓内钉固定、及手足骨折修复等手术方面具有广阔的应用前景。对C形臂X线投影图像3D建模技术的研究意义、现状及现存问题进行介绍。在此基础上,分析了该技术所涉及的主要研究内容,提出了可分别沿两条主线研究基于普通C形臂2D投影图像的人体骨骼3D解剖模型构建:一、以C形臂按指定角度间隔获取的密集2D投影图像为基础,采用有限角锥束X射线投影合成方法进行3D重建;二、以C形臂在正位、侧位等姿态下获取的少量2D投影图像为基础,采用基于统计可变模型的非刚性配准方法进行3D重建。对每条主线都提出了对应的解决方案。     

A three-dimensional reconstruction algorithm for an inverse-geometry volumetric CT system

An inverse-geometry volumetric computed tomography (IGCT) system has been proposed capable of rapidly acquiring sufficient data to reconstruct a thick volume in one circular scan. The system uses a large-area scanned source opposite a smaller detector. The source and detector have the same extent in the axial, or slice, direction, thus providing sufficient volumetric sampling and avoiding cone-beam artifacts. This paper describes a reconstruction algorithm for the IGCT system. The algorithm first rebins the acquired data into two-dimensional (2D) parallel-ray projections at multiple tilt and azimuthal angles, followed by a 3D filtered backprojection. The rebinning step is performed by gridding the data onto a Cartesian grid in a 4D projection space. We present a new method for correcting the gridding error caused by the finite and asymmetric sampling in the neighborhood of each output grid point in the projection space. The reconstruction algorithm was implemented and tested on simulated IGCT data. Results show that the gridding correction reduces the gridding errors to below one Hounsfield unit. With this correction, the reconstruction algorithm does not introduce significant artifacts or blurring when compared to images reconstructed from simulated 2D parallel-ray projections. We also present an investigation of the noise behavior of the method which verifies that the proposed reconstruction algorithm utilizes cross-plane rays as efficiently as in-plane rays and can provide noise comparable to an in-plane parallel-ray geometry for the same number of photons. Simulations of a resolution test pattern and the modulation transfer function demonstrate that the IGCT system, using the proposed algorithm, is capable of 0.4 mm isotropic resolution. The successful implementation of the reconstruction algorithm is an important step in establishing feasibility of the IGCT system.     

基于正交匹配追踪及加速近端梯度的人体三维重建

为提高人体三维结构的重建精度,针对重建过程中字典中原子的最佳选择和结构矩阵的优化问题,结合稀疏表示和低秩约束,提出一种正交匹配追踪追踪及加速近端梯度(OMP-APG)算法,以此为医学领域提供丰富的信息,以辅助医生快速精确地制定出治疗方案。首先,对特征点观测矩阵进行奇异值分解(SVD)分解,利用列文伯格-马夸尔特(LM)算法得到唯一确定的相机旋转矩阵;其次,利用稀疏表示中“最大化逼近”思想,通过正交匹配追踪算法对轨迹基系数进行求解,结合预定义的轨迹基求解出人体三维结构矩阵;最后,根据结构矩阵是一个低秩矩阵,将其秩优化问题转化为核范数最小化问题,利用加速近端梯度算法对人体结构矩阵进一步优化处理。将该算法与稀疏逼近算法进行比较,对伸懒腰、瑜伽、拾物、喝水和跳舞等5组不同的人体运动模型进行三维重建,通过其三维重建效果图和三维重建误差的结果显示,其重建精度更高且稳定性更好。在该算法下喝水运动的重建效果最佳,其1 102帧图像序列41个特征点的重建误差为0.030 3,而在稀疏算法下的重建误差为0.017 8。因此,该算法可以有效地提高人体三维结构的重建精度,为医学领域辅助治疗提供相应的技术支持。     

基于Visualization Toolkit的数字化人体骨骼系统的重建与可视化

在人体骨骼系统的三维可视化过程中,将二维CT数据重建生成理想的三维骨骼数据是非常重要的一环.作者应用可视化工具Visualization Toolkit(VTK)和VC++实现了二维数据的三维重建、面片削减、连通性检测、三维平滑等一系列功能.与利用OpenGL等工具重建得到的骨骼数据相比,不但准确度和视觉效果有了显著改善,数据量也大大减小.VTK在人体骨骼系统的重建及处理工作中取得的良好效果表明,它是医学图像重建和处理的有力工具之一,具有使用灵活,功能强大的优点,值得推广.     

Simulation studies on a pseudo-three-dimensional reconstruction algorithm for volume imaging in multi-ring PET

The imaging performance of a pseudo-three-dimensional (3D) reconstruction algorithm has been investigated. The algorithm is based on ID filtering followed by 3D backprojection. High- and low-frequency components of the image are reconstructed separately, and oblique projections are used only for reconstructing the high-frequency component. The cross talk between different slices due to oblique backprojection is eliminated by high-pass filtering. 'Variable filters', the cut-off frequencies of which are proportional to the tilt angles of projections, provide higher signal-to-noise ratio than 'fixed filters' with similar capability for cross-talk rejection. The maximum ring difference used in the reconstruction of each slice is extended as far as possible, while still satisfying the requirement that the total density of backprojection beams deposited in the slice is approximately uniform in the field of view. This allows the use of almost all available projection data to improve signal-to-noise ratio in peripheral slices. The root mean square noise of the reconstructed images evaluated with simulation studies is in good agreement with numerical calculations, and it is shown that the loss in signal-to-noise ratio caused by discarding the low-frequency component of oblique projections is negligibly small as long as suitable variable filters are used.     

A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection

Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter form factor of the investigated object. Reconstruction from coherently scattered x-rays is commonly done using algebraic reconstruction techniques (ART). In this paper, we propose an alternative approach based on filtered back-projection. For the first time, a three-dimensional (3D) filtered back-projection technique using curved 3D back-projection lines is applied to two-dimensional coherent scatter projection data. The proposed algorithm is tested with simulated projection data as well as with projection data acquired with a demonstrator setup similar to a multi-line CT scanner geometry. While yielding comparable image quality as ART reconstruction, the modified 3D filtered back-projection algorithm is about two orders of magnitude faster. In contrast to iterative reconstruction schemes, it has the advantage that subfield-of-view reconstruction becomes feasible. This allows a selective reconstruction of the coherent-scatter form factor for a region of interest. The proposed modified 3D filtered back-projection algorithm is a powerful reconstruction technique to be implemented in a CSCT scanning system. This method gives coherent scatter CT the potential of becoming a competitive modality for medical imaging or nondestructive testing.     

Three-dimensional photon detection kernels and their application to SPECT reconstruction.

In single photon emission computed tomography (SPECT), three-dimensional photon detection kernels characterize the probabilities that photons emitted by radio-isotopes in different parts of the source region will be detected at particular projection pixels of the projection images. Monte Carlo modelling is used to study these kernels for the case of parallel hole collimators. The use of vectorized Monte Carlo computer code speeds the modelling computations. The contributions of direct and scattered photons to projection data in a transverse plane from neighbouring planes are significant for the case of uniform activity within a water-filled cylinder. A reconstruction method using the 3D kernels is proposed in which projection measurements in three adjacent planes are used simultaneously to estimate the source activity of the center plane. This multiple slice method accounts for the fact that photons detected in a given transverse plane may have originated in other transverse planes with different activity distributions. The matrix equations for image reconstruction are solved using generalized matrix inverses. The new method shows compensation for 3D photon detection effects when applied to projection data from a numerical simulation and a cardiac phantom experiment. Quantitation for the numerical study is improved compared with results from a single slice reconstruction method.