基于变螺距螺旋FDK重建算法的研究

目前广泛应用的锥束螺旋CT主要采用螺旋FDK算法进行图像重建,但为了使算法能更应用于实际,许多学者对标准的螺旋轨迹进行了拓展.本文主要研究了变螺距螺旋扫描轨迹.变螺距螺旋扫描可以提高扫描速度,有更高的时间、空间分辨率.本文详细介绍了变螺距螺旋扫描轨迹,给出了具体的变螺距螺旋扫描轨迹方程.针对图像重建,本文主要从FDK重...     

The radon-split method for helical cone-beam CT and its application to nongated reconstruction

The mathematical analysis of exact filtered back-projection algorithms is strictly related to Radon inversion. We show how filter-lines can be defined for the helical trajectory, which serve for the extraction of contributions of particular kinds of Radon-planes. Due to the Fourier-slice theorem, Radon-planes with few intersections with the helix are associated with low-frequency contributions to transversal slices. This insight leads to different applications of the new method. The application presented here enables the incorporation of an arbitrary amount of redundant data in an approximate way. This means that the back-projection is not restricted to an n-Pi interval. A detailed mathematical analysis, in which we demonstrate how the defined filter-lines work, concludes this paper.     

Exact radon rebinning algorithm for the long object problem in helical cone-beam CT

This paper addresses the long object problem in helical cone-beam computed tomography. We present the PHI-method, a new algorithm for the exact reconstruction of a region-of-interest (ROI) of a long object from axially truncated data extending only slightly beyond the ROI. The PHI-method is an extension of the Radon-method, published by Kudo, Noo, and Defrise in issue 43 of journal Physics in Medicine and Biology. The key novelty of the PHI-method is the introduction of a virtual object fpsi(x) for each value of the azimuthal angle psi in the image space, with each virtual object having the property of being equal to the true object f(x) in some ROI omegam. We show that, for each psi, one can calculate exact Radon data corresponding to the two-dimensional (2-D) parallel-beam projection of fpsi(x) onto the meridian plane of angle psi. Given an angular range of length pi of such parallel-beam projections, the ROI omegam can be exactly reconstructed because f(x) is identical to fpsi(x) in Omegam. Simulation results are given for both the Radon-method and the PHI-method indicating that 1) for the case of short objects, the Radon- and PHI-methods produce comparable image quality, 2) for the case of long objects, the PHI-method delivers the same image quality as in the short object case, while the Radon-method fails, and 3) the image quality produced by the PHI-method is similar for a large range of pitch values.     

Handling of long objects in iterative improvement of nonexact reconstruction in helical cone-beam CT

In medical helical cone-beam CT, it is common that the region-of-interest (ROI) is contained inside the helix cylinder, while the complete object is long and extends outside the top and the bottom of the cylinder. This is the Long Object Problem. Analytical reconstruction methods for helical cone-beam CT have been designed to handle this problem. It has been shown that a moderate amount of over-scanning is sufficient for reconstruction of a certain ROI. The over-scanning projection rays travel both through the ROI, as well as outside the ROI. This is unfortunate for iterative methods since it seems impossible to compute accurate values for the projection rays which travel partly inside and partly outside the ROI. Therefore, it seems that the useful ROI will diminish for every iteration step. We propose the following solution to the problem. First, we reconstruct volume regions also outside the ROI. These volume regions will certainly be incompletely reconstructed, but our experimental results show that they serve well for projection generation. This is rather counter-intuitive and contradictory to our initial assumptions. Second, we use careful extrapolation and masking of projection data. This is not a general necessity, but needed for the chosen iterative algorithm, which includes rebinning and iterative filtered backprojection. Our idea here was to use an approximate reconstruction method which gives cone-beam artifacts and then improve the reconstructed result by iterative filtered backprojection. The experimental results seem very encouraging. The cone-beam artifacts can indeed be removed. Even voxels close to the boundary of the ROI are as well enhanced by the iterative loop as those in the middle of the ROI.     

Quasi-exact filtered backprojection algorithm for long-object problem in helical cone-beam tomography

Exact reconstruction from axially truncated cone-beam projections acquired with a helical vertex path is a challenging problem for which solutions are currently under investigation by some researchers. This paper deals with a difficult class of this problem called the long-object problem. Its purpose is to reconstruct a central region of interest (ROI) of a long object when the helical path extends only a little bit above and below the ROI. By extending the authors' recent approach based on the triangular decomposition of the Grangeat formula, we derive quasi-exact reconstruction algorithms whose overall structure is of filtered backprojection (FBP) style. Unlike the previous similar approaches to the long-object problem, the proposed FBP algorithms do not require additional two circular scans at the ends of the helical path. Furthermore, the algorithms require a significantly smaller detector area and achieve improved image quality even for a large pitch compared with the approximate Feldkamp algorithms. One drawback of the proposed algorithms is the computational time, which is much longer than for the Feldkamp algorithms. We show some simulation results to demonstrate the performances of the proposed algorithms.     

A general exact reconstruction for cone-beam CT via backprojection-filtration

In this paper, we prove a generalized backprojection-filtration formula for exact cone-beam image reconstruction with an arbitrary scanning locus. Our proof is independent of the shape of the scanning locus, as long as the object is contained in a region where there is a chord through any interior point. As special cases, this generalized formula can be applied with cone-beam scanning along nonstandard spiral and saddle curves, as well as in an n-PI window setting. The algorithmic implementation and numerical results are described to support the correctness of our general claim.     

圆弧轨迹Katsevich类型的锥束CT重建

基于Katsevich重建理论,提出了一种适合圆弧轨迹且具有移不变滤波反投影结构的锥束重建算法.分析了Radon平面绕投影射线连续转动过程中与轨迹平面相交的运动关系,并依据投影数据存储方式确定Radon平面的法线矢量方向.在此基础上,将检测器区域进行划分,进而探讨了与圆弧端点关联的结构因子在检测器阵列单元上的分布规律.同时,根据滤波线在检测器上的分布特点,推导了满足投影数据重采样精度并适合平板检测器的锥束重建公式.利用Forbild模型进行数值模拟,实验结果表明提出的算法有效地抑制了FDK类型重建算法所存在的锥束伪像并且适合长物体重建.     

Anti-aliasing weighting functions for single-slice helical CT

Spatially variant longitudinal aliasing plagues most volumes reconstructed from single-slice helical computed tomography data, and its presence can degrade resolution and distort image structures. We have recently developed a Fourier-based approach to longitudinal interpolation in helical computed tomography that can, for scans performed at pitch 1 or lower, essentially eliminate this longitudinal aliasing by exploiting a generalization of the Whittaker-Shannon sampling theorem whose conditions are satisfied by the interlaced pairs of direct and complementary longitudinal samples. However, the algorithm is computationally intensive and cannot be pipelined. In this paper, we address this shortcoming by deriving two spatial-domain, projection-data weighting functions that approximate the application of the Fourier-based approach, and preserve its aliasing suppression properties to some degree, while allowing for a pipelined implementation. The first approach, which we call simply 180AA, for anti-aliasing, is a direct spatial-domain approximation of the 180FT approach. The second approach, which we call 180BSP, is based on an approximate generalized interpolation approach making use of B-splines. Studies of aliasing and resolution properties in reconstructions from simulated data indicate that while the 180AA and 180BSP approaches do not perfectly replicate the favorable aliasing suppression and resolution properties of the 180FT approach, they do represent an improvement over the clinically standard 180LI approach on these fronts.     

Tomographic reconstruction for tilted helical multislice CT

One of the most recent technical advancements in computed tomography (CT) is the introduction of multislice CT (MCT). Because multiple detector rows are used for data acquisition, MCT offers higher volume coverage, faster scan speed, and reduced X-ray tube loading. Recognizing its unique data-sampling pattern, several image reconstruction algorithms were developed. These algorithms have been shown to be adequate in producing clinically acceptable images. Recent studies, however, have revealed that the image quality of MCT can be significantly degraded when helical data are acquired with a tilted gantry. The degraded image quality has rendered this feature unacceptable for clinical usage. In this paper, we first present a detailed investigation on the cause of the image quality degradation. An analytical model is derived to provide a mathematical basis for correction. Several compensation schemes are subsequently presented, and a detailed performance comparison is provided in terms of spatial resolution, noise, computation efficiency, and image artifacts.     

Moving beam helical CT scanning

Images generated with helical scanning are degraded by partial volume artifacts caused by an increased slice thickness when compared to conventional computed tomography (CT) scanning. The slice thickness for a helical scan is proportional to the sum of the thickness of the fan of radiation and the distance the patient moves during data acquisition. The authors present a method called moving beam helical scanning (MBHS) which significantly reduces the partial volume artifacts caused by helical scanning. The key element of MBHS is a rotatable collimator that is placed between the X-ray source and the patient. As the patient is translated, the collimator is used to aim the fan on a fixed position in the patient. Once sufficient data are obtained to reconstruct a slice, the collimator is quickly reset to scan a target in the next slice. The authors examined the performance of MBHS by scanning wires and phantoms on a modified scanner. The full-width-at-tenth-maximum of the slice profile at iso-center for MBHS is identical to conventional CT versus a 59% increase for conventional helical scanning. It is concluded that MBHS can be used to obtain the scan rate advantages of helical scanning with image quality comparable to conventional scanning.     

锥束CT系统的3D Shepp-Logan体模仿真及其投影数据重建

为了验证锥束CT成像算法的性能,提出了使用Fortran语言编写的3D Shepp-Logan体模作为算法性能验证的参考模型,并详细介绍了3DShepp-Logan体模的参数设置及编程方法。然后,直接加入到正投影程序中得到投影数据。最后,利用得到的投影数据进行了三维医学图像重建的仿真实验。经过实验验证,表明了使用Fortran语言编写的3DSheppLogan体模来验证算法性能是准确可行的。     

Longitudinal aliasing in multislice helical computed tomography: sampling and cone-beam effects

In this study, we examine longitudinal aliasing properties in multislice helical computed tomography (CT) volumes reconstructed under the multiple parallel fanbeam approximation by use of a 180LI-type algorithm. We focus on the differences between the multislice case and the single-slice case, which has been studied previously. Specifically, we examine longitudinal aliasing properties in four-slice scanners for helical pitches 3 and 6, which are sometimes called "preferred" in four-slice helical CT, because it is believed that the effective longitudinal sampling intervals at these pitches are equivalent to those in single-slice helical CT operating at pitches 1 and 2, respectively. While these equivalences have been supported by comparative studies of slice-sensitivity profiles in single- and multislice helical CT, artifacts have been observed in pitch-3 and pitch-6 multislice images that were not evident in their purported single-slice counterparts. We attribute these differences to aliasing arising in the multislice reconstructions that is not present in the single-slice counterparts. We find that the aliasing has two principal origins: sampling effects similar to those in the single-slice case and cone-beam effects. The difference between the multislice, pitch-3 and single-slice, pitch-1 results is attributed to the small cone angle in multislice helical CT, which introduces inconsistencies among the measurements of different detector rows. The difference between multislice, pitch-6 and single-slice, pitch-2 results is attributed to a combination of the cone angle and genuine differences in sampling patterns. It is argued, however, that the lack of strict equivalence with single-slice counterparts does not necessarily undermine the claim that pitches 3 and 6 are "preferred" relative to other pitches in multislice helical CT.     

一种局部CT图像重建算法研究

CT作为一种无创检查设备在医学领域得到广泛的应用,但是受重建方法的限制,它通常只能对相对静止的器官进行扫描断层成像,而对运动物体或器官的成像能力较差,通常会存在运动伪影.克服运动伪影的根本途径就是减少数据采集的时间,这可以通过减少采集范围来实现.中间函数重建算法是一种基于傅里叶空间的重建算法,该算法可以选择感兴趣的部位(ROI)进行局部图像重建,减少数据采集的时间,因此可以使用该算法改善临床上运动物体的扫描成像.     

锥束CT去除环形伪影的方法研究

环状伪影是CT技术人员经常遇到的影响重建图像质量的一种伪影,造成环形伪影的因素很多,其中探测器缺陷引起的环形伪影最为常见。环形伪影表现在原始图像结构上是圆环或者是圆弧,理论认证发现探测器响应效率不一致,会使锥束三维CT重建结果产生环形伪影。环形伪影影响了CT图像的分析和后续处理,因此去除环形伪影显得非常具有使用价值。本...     

Multislice helical CT: image temporal resolution

A multislice helical computed tomography (CT) halfscan (HS) reconstruction algorithm is proposed for cardiac applications. The imaging performances (in terms of the temporal resolution, z-axis resolution, image noise, and image artifacts) of the HS algorithm are compared to the existing algorithms using theoretical models and clinical data. A theoretical model of the temporal resolution performance (in terms of the temporal sensitivity profile) is established for helical CT, in general, i.e., for any number of detector rows and any reconstruction algorithm used. It is concluded that the HS reconstruction results in improved image temporal resolution than the corresponding 180 degrees LI (linear interpolation) reconstruction and is more immune to the inconsistent data problem induced by cardiac motions. The temporal resolution of multislice helical CT with the HS algorithm is comparable to that of single-slice helical CT with the HS algorithm. In practice, the 180 degrees LI and HS-LI algorithms can be used in parallel to generate two image sets from the same scan acquisition, one (180 degrees LI) for improved z-resolution and noises, and the other (HS-LI) for improved image temporal resolution.     

Reduction of artifacts induced by misaligned geometry in cone-beam CT

The quality of computed tomography (CT) images frequently suffers from artifacts caused by scanner misalignments. In this paper, we discuss the results of our improved approximate cone-beam reconstruction formula, which corrects for the mechanical misalignment of the scanner. Based on the general filtered back-projection (FBP) algorithm proposed by Feldkamp, the new formula reduces the artifacts in reconstructed images. Six parameters are employed to describe the scanner misalignment. Experimental results show that the images reconstructed by using the new formula are clearer than those reconstructed by using the general FBP algorithm in a misaligned system. Through the new formula, we have reduced the artifacts caused by misalignment.     

三维CT变螺距螺旋投影数据模拟方法

为了研究不同扫描方式下的三维CT重建算法,首先必须获取相应扫描方式下的投影数据,投影数据的仿真可以用来验证重建算法的准确性和可靠性.变螺距螺旋扫描可以提高扫描速度,有更高的时间、空间分辨率.本文采用三维Shepp-Logan头部模型,详细介绍了该模型在变螺距螺旋扫描方式下的投影数据的仿真计算,利用解析几何求解二次方程仿...     

Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation

Preliminary evaluation of recently developed large-area flat panel detectors (FPDs) indicates that FPDs have some potential advantages: compactness, absence of geometric distortion and veiling glare with the benefits of high resolution, high detective quantum efficiency (DQE), high frame rate and high dynamic range, small image lag (< 1%), and excellent linearity (approximately 1%). The advantages of the new FPD make it a promising candidate for cone-beam volume computed tomography (CT) angiography (CBVCTA) imaging. The purpose of this study is to characterize a prototype FPD-based imaging system for CBVCTA applications. A prototype FPD-based CBVCTA imaging system has been designed and constructed around a modified GE 8800 CT scanner. This system is evaluated for a CBVCTA imaging task in the head and neck using four phantoms and a frozen rat. The system is first characterized in terms of linearity and dynamic range of the detector. Then, the optimal selection of kVps for CBVCTA is determined and the effect of image lag and scatter on the image quality of the CBVCTA system is evaluated. Next, low-contrast resolution and high-contrast spatial resolution are measured. Finally, the example reconstruction images of a frozen rat are presented. The results indicate that the FPD-based CBVCT can achieve 2.75-lp/mm spatial resolution at 0% modulation transfer function (MTF) and provide more than enough low-contrast resolution for intravenous CBVCTA imaging in the head and neck with clinically acceptable entrance exposure level. The results also suggest that to use an FPD for large cone-angle applications, such as body angiography, further investigations are required.     

基于空间解析几何的锥束CT系统角度偏差测量

针对锥束CT系统中机械结构的几何参数偏差校正 问题,提出一种基于空间解析几何算法的锥 束CT系统角度偏差的测量方法。利用一种校准模板,仅通过采集单一投影角度对应的投 影数据即 可得到锥束CT系统的角度偏差。仿真和实验结果 表明,利 用本文方法可以有效地获得待测锥束CT系统的机械角度偏差,其测量精度可达到分度量级。 与平面 解析几何法测量结果的对比分析可知,本文测量方法可实现角度偏差参数的有效分离。本文 方法具有较高的可靠性和测量效率,无需模板多角度旋转投影,具有较好的实用性。