CT图像局部重建算法研究
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摘要
CT (Computed Tomography)是一种先进的无损检测技术,在其很多应用中,经常会遇到感兴趣区域重建、大物体重建、高分辨率重建等实际应用需求,这些往往都会产生局部重建问题。截断投影数据的局部重建是CT重建领域的一个难点,传统的经典重建算法用于局部重建会在重建图像中产生严重的截断伪影。对于实际CT系统的大规模数据量的重建,现有的局部重建算法在重建效率、并行性质、可实现性方面存在诸多的缺陷和不足,很难满足实际CT系统快速准确重建的需求。本文针对不同的具体应用,在保证重建质量的前提下,研究并提出了重建效率高、并行性质好且可方便地用于实际CT系统的局部重建算法。主要研究内容和创新点如下：
1.对于PI线段上没有发生数据截断的局部重建问题,提出了基于数据重排方法的反投影滤波(Backprojection Filtration, BPF)型局部重建算法(T-BPF算法)。该算法先将锥束投影数据重排成帐篷状平行投影数据,然后推导了一种BPF型算法对重排后的帐篷状平行投影数据进行重建。T-BPF算法在保证重建质量的前提下,重建效率比原BPF算法有所提高,而且反投影的运算中各层循环之间没有了相关性,适合使用并行计算进行加速。数字仿真和真实数据重建的实验结果证实了该算法的正确性及其优势。
2.对于投影数据任意截断的一般局部重建问题,提出了基于Radon逆变换的抑制截断伪影的近似局部重建算法。该方法是将2D Radon逆变换推广用于3D锥束CT的局部重建,其滤波过程分为两步：第一步是对投影数据求导,该步骤是局部的,投影数据截断情况下的结果仍然是准确的；第二步是对求导后的投影数据进行Hilbert滤波。该方法具有与ATRACT (Approximate Truncation Resistant Algorithm for Computed Tomography)相当的抑制截断伪影的能力,且其重建效率是ATRACT的两倍以上。数字仿真和真实数据的重建实验证实了该方法的有效性。新提出的基于Radon逆变换的局部重建算法为圆轨迹锥束CT对重建图像精度要求不高的一般局部重建问题提供了一种简单且有效的方法。
3.针对扁平状特殊结构物体的局部重建问题,当PI线段上没有发生数据截断时,提出了一种改进的BPF算法,用于超短扫描的扁平状物体的局部重建。该方法可以大大减少数据采集和成像的时间,提高实际CT系统的使用寿命。该方法是在原BPF算法基础上的一种改进,即固定反投影中的投影角度积分限。通过推导发现如果扁平物体的厚度小于0.0349R(R是圆轨迹的扫描半径),改进算法的误差是可以忽略的。当被重建物体的厚度超出可重建的范围,可以适当增大扫描半径来进行重建。数字仿真和真实数据的实验结果显示该方法是扁平状物体局部重建的一个很好的选择,因为它不仅具有与其它重建算法相当的重建质量,而且可以大大减少成像时间,提高CT系统的使用寿命。
4.针对扁平状特殊结构物体的局部重建问题,当投影数据任意截断时,提出了一种基于FDK算法的扁平状物体的局部重建方法。通过研究发现如果扁平物体的厚度和局部区域在水平方向上的长度满足一定条件,简洁、高效的FDK算法可以处理该局部重建问题。通过数字仿真实验得到了一个可以比较准确重建扁平状物体局部区域的经验性条件,即：局部区域在水平方向上的长度大于该物体在水平方向上的长度的1/8,物体厚度小于该物体在水平方向上的长度的1/13。数字仿真和真实数据的重建结果证实了在这个条件下FDK算法可以很好地实现扁平状物体的局部重建。
5.针对重建物体超出扫描视野的CT图像重建问题,考虑一种视野只覆盖一半物体的扫描结构,对于该扫描方式下任意投影角度都发生截断的投影数据,结合BPF算法和反投影图像可以通过不同投影角度下的投影数据得到这个发现,提出了一种重建半覆盖扫描下截断投影数据的算法。该算法不需要数据重排这个操作,且对于每个点的反投影图像只需要180度范围内投影数据,大大提高了算法的重建效率,重建图像的空间分辨率也有所提高。数字仿真和真实数据的实验验证了算法的正确性及其优点。
最后,对本文工作进行了总结,并对CT图像局部重建算法的发展进行了展望,指出了未来的研究方向和构想。
CT (Computed Tomography) is a kind of advanced nondestructive testing technology. In its many applications, it is common to meet the cases, such as the image reconstruction of region of interest, the image reconstruction of big object, the image reconstruction of high spatical resolution. These all can produce local reconstruction problems. The local reconstruction with truncated projection data is a difficulty in the field of CT reconstruction. Conventional reconstruction algorithms used to deal with the reconstruction of truncated projection data will product severe truncation artifacts. The image reconstruction of practical CT system is a course of complex computing of massive data. The exsiting local reconstruction algorithms have many flaws in reconstruction efficiency and parallel performance, which can't satisfy the requirement of fast and accurate reconstruction for practical CT system. In this paper, aiming at the different concrete applications, we study and design the local reconstruction algorithms with good reconstruction efficiency and parallel performance for practical CT system in the case of the guarantee of reconstruction quality. The main work and innovation of this thesis can be summarized as follows.
1. For some local reconstruction problem (no truncation along PI-line direction), the BPF-type local reconstruction algorithm based on data rebinning method is developed. It is performed by firstly rearranging the cone-beam data to tent-like parallel-beam data, and then applying a proposed BPF-type algorithm to reconstruct images from the rearranged data. In case of the guarantee of reconstruction quality, the reconstruction efficiency of the proposed method has an improvement over the original BPF algorithm. Moreover, there are no relativities in the implementation of the proposed method, so it is fit for parallel computing algorithm. The experiments of numerical simulation and real data reconstruction have demonstrated the correctness and advantages of the proposed algorithm.
2. For the general local reconstruction problem, an approximate truncation resistant algorithm based on Radon inversion transform is developed. The algorithm extends the2D Radon inversion transform to the3D local reconstruction in the circular geometry. It achieves data filtering in two steps. The first step is the derivative of projections which acts locally on the data and can thus be carried out accurately even in presence of data truncation. The second step is the nonlocal Hilbert filtering. Not only the reconstruction efficiency of the proposed method is considerable like FDK algorithm, but also it has comparable ability to restrain truncation artifacts like the approximate truncation resistant algorithm for computed tomography (ATRACT). The numerical simulations and real data reconstructions have been conducted to validate the new reconstruction algorithm. The presented local reconstruction algorithm based on Radon inversion transform provides a simple and efficient approach for the approximate reconstruction from truncated projections in circular cone-beam CT.
3. Aiming at the local reconstruction of special structural specimens which is plate-like, an improved BPF algorithm is presented to reconstruct the plate-like specimens in a super-short scan, thus reducing imaging time and increasing practical CT system throughput. The algorithm of the proposed method is an improved backprojection-filtration (BPF) algorithm using an integral operator with fixed integral interval. It is found that if the thickness of the reconstructed plate-like specimen is less than0.0349R (R is the scanning radius), the uncertainty of the proposed method can be ignored. When the thickness of the reconstructed plate-like specimen is a little large, it can be reconstructed by increasing the scanning radius befittingly. The results of numerical simulation and real data reconstructions show that the proposed method is a good choice for the reconstructions of plate-like specimens, because it can not only yield images with quality comparable to that obtained with existing algorithms, but also reduce imaging time and; increase CT system throughput.
4. Aiming at the local reconstruction of special structural flat object, a method based on FDK algorithm is developed. It is found that if the thickness and the horizontal length of local area satisfy some conditions, accurate reconstruction can be carried out using efficient FDK algorithm. From the results of numerical experiments, an experimental condition is obtained. That is to say when the horizontal length of local region is bigger than the1/8horizontal length of the reconstructed object and the thickness of local region is less than the1/13horizontal length of the reconstructed object. The reconstruction results of numerical simulation and real data confirm FDK algorithm can reconstruct the local area of flat object well under the condition.
5. For the image reconstruction problem that the reconstructed object is big and can not be covered by the field of view, we consider a scanning configuration in which X-ray beams only cover half of the object and the cone-beam projection data are acquired from an asymmetrically positioned half-sized detector. The acquired cone-beam projection data are truncated at every view angle, which does not satisfy the conventional reconstruction condition that the projection data can not be transversely truncated. If an explicit data rebinning process is not invoked, this data acquisition configuration will play havoc with many known cone-beam image reconstruction algorithms. To reconstruct images from the truncated projection data at any view, we apply a recently developed backprojection filtration (BPF) algorithm in circular cone-beam CT and an observation that a correct backprojection image can be formed by combining the projection data from different view angles, and then develop an algorithm to reconstruct3D images for the half-covered scanning configuration. Not only the proposed algorithm does not need the data rebinning process, but also the implementation of backprojection image just needs the projection data in the range of180degree for every reconstruction point. These mean that the proposed algorithm has good reconstruction efficiency and high spatial resolution. Numerical simulations and real data reconstruction experiments are conducted to validate the proposed reconstruction algorithm.
Finally, we summarize our research work for the thesis, and discuss some research topics and directions relative to this work in the future.
1.对于PI线段上没有发生数据截断的局部重建问题,提出了基于数据重排方法的反投影滤波(Backprojection Filtration, BPF)型局部重建算法(T-BPF算法)。该算法先将锥束投影数据重排成帐篷状平行投影数据,然后推导了一种BPF型算法对重排后的帐篷状平行投影数据进行重建。T-BPF算法在保证重建质量的前提下,重建效率比原BPF算法有所提高,而且反投影的运算中各层循环之间没有了相关性,适合使用并行计算进行加速。数字仿真和真实数据重建的实验结果证实了该算法的正确性及其优势。
2.对于投影数据任意截断的一般局部重建问题,提出了基于Radon逆变换的抑制截断伪影的近似局部重建算法。该方法是将2D Radon逆变换推广用于3D锥束CT的局部重建,其滤波过程分为两步：第一步是对投影数据求导,该步骤是局部的,投影数据截断情况下的结果仍然是准确的；第二步是对求导后的投影数据进行Hilbert滤波。该方法具有与ATRACT (Approximate Truncation Resistant Algorithm for Computed Tomography)相当的抑制截断伪影的能力,且其重建效率是ATRACT的两倍以上。数字仿真和真实数据的重建实验证实了该方法的有效性。新提出的基于Radon逆变换的局部重建算法为圆轨迹锥束CT对重建图像精度要求不高的一般局部重建问题提供了一种简单且有效的方法。
3.针对扁平状特殊结构物体的局部重建问题,当PI线段上没有发生数据截断时,提出了一种改进的BPF算法,用于超短扫描的扁平状物体的局部重建。该方法可以大大减少数据采集和成像的时间,提高实际CT系统的使用寿命。该方法是在原BPF算法基础上的一种改进,即固定反投影中的投影角度积分限。通过推导发现如果扁平物体的厚度小于0.0349R(R是圆轨迹的扫描半径),改进算法的误差是可以忽略的。当被重建物体的厚度超出可重建的范围,可以适当增大扫描半径来进行重建。数字仿真和真实数据的实验结果显示该方法是扁平状物体局部重建的一个很好的选择,因为它不仅具有与其它重建算法相当的重建质量,而且可以大大减少成像时间,提高CT系统的使用寿命。
4.针对扁平状特殊结构物体的局部重建问题,当投影数据任意截断时,提出了一种基于FDK算法的扁平状物体的局部重建方法。通过研究发现如果扁平物体的厚度和局部区域在水平方向上的长度满足一定条件,简洁、高效的FDK算法可以处理该局部重建问题。通过数字仿真实验得到了一个可以比较准确重建扁平状物体局部区域的经验性条件,即：局部区域在水平方向上的长度大于该物体在水平方向上的长度的1/8,物体厚度小于该物体在水平方向上的长度的1/13。数字仿真和真实数据的重建结果证实了在这个条件下FDK算法可以很好地实现扁平状物体的局部重建。
5.针对重建物体超出扫描视野的CT图像重建问题,考虑一种视野只覆盖一半物体的扫描结构,对于该扫描方式下任意投影角度都发生截断的投影数据,结合BPF算法和反投影图像可以通过不同投影角度下的投影数据得到这个发现,提出了一种重建半覆盖扫描下截断投影数据的算法。该算法不需要数据重排这个操作,且对于每个点的反投影图像只需要180度范围内投影数据,大大提高了算法的重建效率,重建图像的空间分辨率也有所提高。数字仿真和真实数据的实验验证了算法的正确性及其优点。
最后,对本文工作进行了总结,并对CT图像局部重建算法的发展进行了展望,指出了未来的研究方向和构想。
CT (Computed Tomography) is a kind of advanced nondestructive testing technology. In its many applications, it is common to meet the cases, such as the image reconstruction of region of interest, the image reconstruction of big object, the image reconstruction of high spatical resolution. These all can produce local reconstruction problems. The local reconstruction with truncated projection data is a difficulty in the field of CT reconstruction. Conventional reconstruction algorithms used to deal with the reconstruction of truncated projection data will product severe truncation artifacts. The image reconstruction of practical CT system is a course of complex computing of massive data. The exsiting local reconstruction algorithms have many flaws in reconstruction efficiency and parallel performance, which can't satisfy the requirement of fast and accurate reconstruction for practical CT system. In this paper, aiming at the different concrete applications, we study and design the local reconstruction algorithms with good reconstruction efficiency and parallel performance for practical CT system in the case of the guarantee of reconstruction quality. The main work and innovation of this thesis can be summarized as follows.
1. For some local reconstruction problem (no truncation along PI-line direction), the BPF-type local reconstruction algorithm based on data rebinning method is developed. It is performed by firstly rearranging the cone-beam data to tent-like parallel-beam data, and then applying a proposed BPF-type algorithm to reconstruct images from the rearranged data. In case of the guarantee of reconstruction quality, the reconstruction efficiency of the proposed method has an improvement over the original BPF algorithm. Moreover, there are no relativities in the implementation of the proposed method, so it is fit for parallel computing algorithm. The experiments of numerical simulation and real data reconstruction have demonstrated the correctness and advantages of the proposed algorithm.
2. For the general local reconstruction problem, an approximate truncation resistant algorithm based on Radon inversion transform is developed. The algorithm extends the2D Radon inversion transform to the3D local reconstruction in the circular geometry. It achieves data filtering in two steps. The first step is the derivative of projections which acts locally on the data and can thus be carried out accurately even in presence of data truncation. The second step is the nonlocal Hilbert filtering. Not only the reconstruction efficiency of the proposed method is considerable like FDK algorithm, but also it has comparable ability to restrain truncation artifacts like the approximate truncation resistant algorithm for computed tomography (ATRACT). The numerical simulations and real data reconstructions have been conducted to validate the new reconstruction algorithm. The presented local reconstruction algorithm based on Radon inversion transform provides a simple and efficient approach for the approximate reconstruction from truncated projections in circular cone-beam CT.
3. Aiming at the local reconstruction of special structural specimens which is plate-like, an improved BPF algorithm is presented to reconstruct the plate-like specimens in a super-short scan, thus reducing imaging time and increasing practical CT system throughput. The algorithm of the proposed method is an improved backprojection-filtration (BPF) algorithm using an integral operator with fixed integral interval. It is found that if the thickness of the reconstructed plate-like specimen is less than0.0349R (R is the scanning radius), the uncertainty of the proposed method can be ignored. When the thickness of the reconstructed plate-like specimen is a little large, it can be reconstructed by increasing the scanning radius befittingly. The results of numerical simulation and real data reconstructions show that the proposed method is a good choice for the reconstructions of plate-like specimens, because it can not only yield images with quality comparable to that obtained with existing algorithms, but also reduce imaging time and; increase CT system throughput.
4. Aiming at the local reconstruction of special structural flat object, a method based on FDK algorithm is developed. It is found that if the thickness and the horizontal length of local area satisfy some conditions, accurate reconstruction can be carried out using efficient FDK algorithm. From the results of numerical experiments, an experimental condition is obtained. That is to say when the horizontal length of local region is bigger than the1/8horizontal length of the reconstructed object and the thickness of local region is less than the1/13horizontal length of the reconstructed object. The reconstruction results of numerical simulation and real data confirm FDK algorithm can reconstruct the local area of flat object well under the condition.
5. For the image reconstruction problem that the reconstructed object is big and can not be covered by the field of view, we consider a scanning configuration in which X-ray beams only cover half of the object and the cone-beam projection data are acquired from an asymmetrically positioned half-sized detector. The acquired cone-beam projection data are truncated at every view angle, which does not satisfy the conventional reconstruction condition that the projection data can not be transversely truncated. If an explicit data rebinning process is not invoked, this data acquisition configuration will play havoc with many known cone-beam image reconstruction algorithms. To reconstruct images from the truncated projection data at any view, we apply a recently developed backprojection filtration (BPF) algorithm in circular cone-beam CT and an observation that a correct backprojection image can be formed by combining the projection data from different view angles, and then develop an algorithm to reconstruct3D images for the half-covered scanning configuration. Not only the proposed algorithm does not need the data rebinning process, but also the implementation of backprojection image just needs the projection data in the range of180degree for every reconstruction point. These mean that the proposed algorithm has good reconstruction efficiency and high spatial resolution. Numerical simulations and real data reconstruction experiments are conducted to validate the proposed reconstruction algorithm.
Finally, we summarize our research work for the thesis, and discuss some research topics and directions relative to this work in the future.
引文
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