锥束工业CT扫描方式与近似重建算法的改进
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摘要
计算机断层成像(简称为CT)无论在医学诊断,还是在工业领域都有着广泛的应用,它被认为是当前最佳的无损检测技术。工业CT和医学CT的基本原理相同,都是以Radon数学变换为基础。但是由于被扫描工件的材质、尺寸和结构等千差万别,所以在射线能量、成像指标和后期处理等方面,工业CT与医学CT有较大的差别。因此,工业CT的扫描方式和重建算法应根据其特点作相应的改进。在三十多年的时间里,CT的扫描方式已由最初的平行束扫描发展到今天的锥束扫描。锥束CT也叫三维CT,与二维扇束CT相比,它具有射线利用率高、轴向分布均匀、扫描时间短等优点。锥束工业CT目前已成为无损检测领域的研究热点。锥束CT的重建算法大致分为迭代法和解析法两大类。迭代重建需要迭代运算,计算比较耗时。解析法又分为精确重建和近似重建,两者比较而言,精确重建需要射线源的扫描轨迹满足Smith提出的充分必要条件,而且算法的执行效率较低。近似算法重建图像的质量虽然没有精确重建的好,但是它具有执行效率高,机械运动简单等优点。Feldkamp、David和Kress提出了基于圆形扫描轨迹的实用近似重建算法(简称为FDK算法),目前该算法是商用锥束CT机上通用的算法。
本文仔细分析了锥束CT扫描的FDK算法及其扫描轨迹,讨论了在探测器尺寸和探测器中心到转台中心的距离都固定的前提下,物体内任一点能够被射线束扫描的条件;物体完全扫描的高度及其与锥角的关系;并在此基础上分析了多层圆形扫描的层间距,为实际多层圆形扫描参数的选择提供依据。仿真结果证实,用FDK算法对锥束CT圆形扫描轨迹得到的投影数据重建,重建图像的质量随锥角的增大而变差,而且完全扫描的高度也随锥角的增大而变小。
在工业CT中,经常会遇到待检测物体的直径大于探测器宽度的情况,此时,基于圆形扫描轨迹的Ⅲ代锥束CT扫描方式和FDK算法的应用受到限制。解决此问题的传统方法是用Ⅱ代锥束CT扫描方式,但是Ⅱ代锥束CT扫描非常耗时,得到的投影数据也有很多冗余,并且它的扫描时间不会因增加探测器的密度而减少。本文结合Ⅱ代和Ⅲ代锥束CT的扫描方式研究了一种Ⅱ+Ⅲ代锥束CT扫描,并且对传统的FDK算法进行改进,得到了一种适合于Ⅱ+Ⅲ代锥束CT重建的水平偏心FDK算法和拼接重建区域的方法,利用这种改进的扫描方式和重建方法不但可以实现大尺寸物体的检测,而且不需要对投影数据重排和插值。在本文的仿真实验中,Ⅱ+Ⅲ代锥束CT的采样时间比Ⅱ代锥束CT大幅度减少,投影数据的相对冗余率也比Ⅱ代锥束CT少得多。
另外,在锥束CT中,一般使用高密度的面阵探测器,相邻探测单元之间的间距约为0.1mm。因此,相邻探测单元之间存在射线散射(或二次散射)引起的串扰。本文讨论了一种在探测器上加隔离网,然后利用探测器四次平移采样再重建的方法来减少射线串扰。通过计算机仿真,证实该方法能够减少相邻探测单元之间的射线串扰以及串扰带来的伪影。
Computed tomography (CT) is regarded as the perfect non-destructive test technology (NDT) in medical diagnosis and engeneering. The principle of industrial computed tomography (ICT) is similar to medical computed tomography. Both are based on Radon transform. In ICT, the size, structure and material of the scanned object vary widely. Thus, the mechanical construction, ray energy, imaging precision and image processing in ICT are partially different from that in medical CT. So, the scan way and the reconstruction algorithm should be modified according to the characteristic of ICT. In about fouty years, the scan mode of CT has changed from parallel-beam to cone-beam. Compared with 2D CT, 3D cone-beam CT, in which cone-beam rays are used to scan the object, has much shorter scan time and higher axis resolution because it can make use of the rays more efficiently. So it has attracted increasing attention, and is gradually being used in medical diagnosis and engineering. The image of the object is reconstructed from cone-beam projection data by use of algebraic or analytic algorithms. The algebraic algorithms need iteration, so the implementary time is longer. There are two types of analytic algorithms: exact and approximate algorithm. The loci of exact algorithms must satisfy the Smith’s necessary and sufficient condition, and the implemenary efficiency is lower. Although the images quality reconstructed by the approximate algorithms is not as good as that reconstructed by exact algorithm, the efficiency is higher than that of the exact algorithms, and scan locus could be incomplete. Feldkamp, Davis and Kress (FDK) proposed the practical approximate cone-beam reconstruction algorithm for the 3D CT with circular ray-source trajectory, which is a generalization of the fan-beam FBP (Filtered Back Projection) algorithm. Now, FDK algorithm is primary reconstruction algorithm in practical cone-beam CT. When detector size and distance between the source and rotary center were both fixed, we analyzed the condition that any point in the object was scanned and the relation between the cone angle and the complete reconstruction height. In addition, we discussed the space-between of multi-cycle locus. The simulations validate reconstruction images qualify is reduced and the complete reconstruction height become lower when the cone angle is larger.
In ICT, it is common that the diameter of the object is larger than the width of the detector. The conventional 3rd generation circular trajectory and FDK algorithm are limited. In this dissertation, a new“2nd+ 3rd”generation scan mode and an off-center reconstruction algorithm were presented for solving this problem. This“2nd+ 3rd”generation scan mode shares similarities with the conventional 2nd generation cone-beam CT, which is traditionary scan way of inspecting the large object. But the“2nd+ 3rd”generation cone-beam CT needs the source and the detector are only translated a few times at each graduation, and the rotary graduation equals that of the 3rd generation cone-beam CT. The object is reconstructed by joining the pieces of the reconstruction area and using an off-center FDK algorithm that is an extension of the standard FDK algorithm. According to the reconstruction method, the projections do not need rebinning and interpolating, so the implementary efficiency is higher. Futhermore, the view of field and translated times are adjustable according to the size of the oject and horizontal flare angle of cone-beam. In simulation experiments, compared with the 2nd generation cone-beam CT, sampling time of this new scan mode is much shorter than that of the 2nd cone-beam CT, relatively redundant ratio is also reduced greatly. The results of simulations show that the images reconstructed by this method are of good quality.
In cone-beam CT, because of the cross talk between detector units caused by X-ray’s scatter (especially high energy X-ray’s scatter in industrial CT), the Signal-to-Noise of detector and the space resolution of reconstructed image are decreased, and the artifact near the edges of reconstructed image is also generated. We discussed a sample method. The heavy metal partitions are fixed on the detector horizontally and vertically between the adjacent detector units, or are fixed in front of the detector. The object is scanned four times, and the projections are accordingly sampled four times. This sample way could decrease the cross talk of X-ray, and projections are complemented. After each scan, cone-beam projections are backprojected using FDK algorithm respectively. From the results of simulation experiments, we see the presented sample method can efficiently reduce the artifact caused by cross talk of X-ray’s scatter, and keep the space resolution of reconstructed images.
本文仔细分析了锥束CT扫描的FDK算法及其扫描轨迹,讨论了在探测器尺寸和探测器中心到转台中心的距离都固定的前提下,物体内任一点能够被射线束扫描的条件;物体完全扫描的高度及其与锥角的关系;并在此基础上分析了多层圆形扫描的层间距,为实际多层圆形扫描参数的选择提供依据。仿真结果证实,用FDK算法对锥束CT圆形扫描轨迹得到的投影数据重建,重建图像的质量随锥角的增大而变差,而且完全扫描的高度也随锥角的增大而变小。
在工业CT中,经常会遇到待检测物体的直径大于探测器宽度的情况,此时,基于圆形扫描轨迹的Ⅲ代锥束CT扫描方式和FDK算法的应用受到限制。解决此问题的传统方法是用Ⅱ代锥束CT扫描方式,但是Ⅱ代锥束CT扫描非常耗时,得到的投影数据也有很多冗余,并且它的扫描时间不会因增加探测器的密度而减少。本文结合Ⅱ代和Ⅲ代锥束CT的扫描方式研究了一种Ⅱ+Ⅲ代锥束CT扫描,并且对传统的FDK算法进行改进,得到了一种适合于Ⅱ+Ⅲ代锥束CT重建的水平偏心FDK算法和拼接重建区域的方法,利用这种改进的扫描方式和重建方法不但可以实现大尺寸物体的检测,而且不需要对投影数据重排和插值。在本文的仿真实验中,Ⅱ+Ⅲ代锥束CT的采样时间比Ⅱ代锥束CT大幅度减少,投影数据的相对冗余率也比Ⅱ代锥束CT少得多。
另外,在锥束CT中,一般使用高密度的面阵探测器,相邻探测单元之间的间距约为0.1mm。因此,相邻探测单元之间存在射线散射(或二次散射)引起的串扰。本文讨论了一种在探测器上加隔离网,然后利用探测器四次平移采样再重建的方法来减少射线串扰。通过计算机仿真,证实该方法能够减少相邻探测单元之间的射线串扰以及串扰带来的伪影。
Computed tomography (CT) is regarded as the perfect non-destructive test technology (NDT) in medical diagnosis and engeneering. The principle of industrial computed tomography (ICT) is similar to medical computed tomography. Both are based on Radon transform. In ICT, the size, structure and material of the scanned object vary widely. Thus, the mechanical construction, ray energy, imaging precision and image processing in ICT are partially different from that in medical CT. So, the scan way and the reconstruction algorithm should be modified according to the characteristic of ICT. In about fouty years, the scan mode of CT has changed from parallel-beam to cone-beam. Compared with 2D CT, 3D cone-beam CT, in which cone-beam rays are used to scan the object, has much shorter scan time and higher axis resolution because it can make use of the rays more efficiently. So it has attracted increasing attention, and is gradually being used in medical diagnosis and engineering. The image of the object is reconstructed from cone-beam projection data by use of algebraic or analytic algorithms. The algebraic algorithms need iteration, so the implementary time is longer. There are two types of analytic algorithms: exact and approximate algorithm. The loci of exact algorithms must satisfy the Smith’s necessary and sufficient condition, and the implemenary efficiency is lower. Although the images quality reconstructed by the approximate algorithms is not as good as that reconstructed by exact algorithm, the efficiency is higher than that of the exact algorithms, and scan locus could be incomplete. Feldkamp, Davis and Kress (FDK) proposed the practical approximate cone-beam reconstruction algorithm for the 3D CT with circular ray-source trajectory, which is a generalization of the fan-beam FBP (Filtered Back Projection) algorithm. Now, FDK algorithm is primary reconstruction algorithm in practical cone-beam CT. When detector size and distance between the source and rotary center were both fixed, we analyzed the condition that any point in the object was scanned and the relation between the cone angle and the complete reconstruction height. In addition, we discussed the space-between of multi-cycle locus. The simulations validate reconstruction images qualify is reduced and the complete reconstruction height become lower when the cone angle is larger.
In ICT, it is common that the diameter of the object is larger than the width of the detector. The conventional 3rd generation circular trajectory and FDK algorithm are limited. In this dissertation, a new“2nd+ 3rd”generation scan mode and an off-center reconstruction algorithm were presented for solving this problem. This“2nd+ 3rd”generation scan mode shares similarities with the conventional 2nd generation cone-beam CT, which is traditionary scan way of inspecting the large object. But the“2nd+ 3rd”generation cone-beam CT needs the source and the detector are only translated a few times at each graduation, and the rotary graduation equals that of the 3rd generation cone-beam CT. The object is reconstructed by joining the pieces of the reconstruction area and using an off-center FDK algorithm that is an extension of the standard FDK algorithm. According to the reconstruction method, the projections do not need rebinning and interpolating, so the implementary efficiency is higher. Futhermore, the view of field and translated times are adjustable according to the size of the oject and horizontal flare angle of cone-beam. In simulation experiments, compared with the 2nd generation cone-beam CT, sampling time of this new scan mode is much shorter than that of the 2nd cone-beam CT, relatively redundant ratio is also reduced greatly. The results of simulations show that the images reconstructed by this method are of good quality.
In cone-beam CT, because of the cross talk between detector units caused by X-ray’s scatter (especially high energy X-ray’s scatter in industrial CT), the Signal-to-Noise of detector and the space resolution of reconstructed image are decreased, and the artifact near the edges of reconstructed image is also generated. We discussed a sample method. The heavy metal partitions are fixed on the detector horizontally and vertically between the adjacent detector units, or are fixed in front of the detector. The object is scanned four times, and the projections are accordingly sampled four times. This sample way could decrease the cross talk of X-ray, and projections are complemented. After each scan, cone-beam projections are backprojected using FDK algorithm respectively. From the results of simulation experiments, we see the presented sample method can efficiently reduce the artifact caused by cross talk of X-ray’s scatter, and keep the space resolution of reconstructed images.
引文
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