圆轨道锥束计算机断层成像（Cone-Beam Computed Tomography，CBCT）在医疗和工业领域中广泛应用。大尺寸2D探测器阵列可以极大地减少CBCT设备的扫描时间，提供高的空间分辨率，减少曝光量和获得更高的图像质量，同时也增加了圆轨道锥束CT成像的锥角。FDK（Feldkamp-David-Kress）算法作为目前最常用的锥束CT算法，因其算法结构简单，使用方便，并且对小锥角的图像重建效果较为可观，所以在实际应用中一直保持着主流地位。然而，圆轨道锥束FDK算法不满足精确重建的Tuy-Smith充分条件，因此FDK算法只能进行近似重建，重建图像包含锥束伪影，并且随着锥角的增加而变得愈加严重，主要表现为重建图像沿纵向方向的强度衰减。由于锥束伪影在一定程度上会降低临床诊断性能，所以适当的校正方法是非常有必要的。

本文围绕如何有效地消除大锥角CBCT成像产生的锥束伪影展开研究，具体工作总结如下：

针对如何消除锥束伪影问题，首先对比了几种消除锥束伪影的传统方法，并进行了仿真实验。传统算法包括三种重排算法（P-FDK、T-FDK和C-FDK）、三维加权算法和联合代数迭代重建算法（Simultaneous Algebraic Reconstruction Techniques，SART）。通过使用低对比度Shepp-Logan体模和修正的Defrise仿体进行仿真实验以及实测实验，并将这几种传统校正方法重建结果与FDK算法重建结果作比较。实验得出在进行高对比度物体成像时，传统的T-FDK、C-FDK和三维加权算法无法有效地抑制重建图像的纵向强度衰减及校正图像的失真。SART算法作为一种迭代重建算法，虽然可以有效地校正锥束伪影，但重建时间过长，无法满足临床需求。

针对上述传统算法的出现的问题，本文提出了一种基于FDK的迭代重建算法（IR-FDK），IR-FDK算法不需要额外的修正项，也不需要添加任何额外的轨迹来补充圆形轨迹，并进行了仿真实验和实测实验。利用Defrise、头模型仿真实验和猴子下肢扫描实测数据对IR-FDK算法进行了性能测试，将IR-FDK算法与FDK、三维加权算法、SART算法作比较，利用均方误差（Mean Square Error，MSE）、结构相似性指标（Structure Similarity Index Measure，SSIM）和结构相异性指标（Structure Dissimilarity Index Measure，DSSIM）三个指标得出本文提出的IR-FDK算法可以有效地补偿重建图像的纵向强度衰减及校正图像失真，特别是在大锥角情况下。在锥束伪影校正方面，IR-FDK算法是明显优于FDK算法、加权算法和C-FDK等重排算法。在重建时间方面，IR-FDK算法通过较少的迭代次数可以获得与SART算法相当的效果。

基于CUDA技术对IR-FDK算法进行加速。详细介绍了CUDA的基本理论知识以及CUDA的编程模型，并描述了IR-FDK算法的加速过程。对加速前后的IR-FDK算法进行评估，得出加速后的IR-FDK算法单次迭代的平均计算速度可提升160倍左右。

Cone-Beam Computed Tomography (CBCT) is widely used in medical and industrial applications. The FDK (Feldkamp-David-Kress) algorithm is the most commonly used cone-beam CT algorithm, because of its simple structure, easy to use, and its effectiveness in reconstructing images with small cone angles. The FDK algorithm, as the most commonly used cone-beam CT algorithm, has maintained its mainstream position in practical applications because of its simple structure, ease of use, and relatively impressive image reconstruction results for small cone angles. However, the cone-beam FDK algorithm does not satisfy the Tuy-Smith sufficient condition for accurate reconstruction, so the FDK algorithm can only perform approximate reconstruction, and the reconstructed image contains cone-beam artifacts, which become more serious with the increase of cone angle, mainly in the form of intensity decay along the longitudinal direction of the reconstructed image. Since the cone-beam artifacts degrade the clinical diagnostic performance to a certain extent, appropriate correction methods are necessary.

 

In this thesis,we focus on how to effectively eliminate the cone beam artifacts generated by CBCT imaging with large cone angles, and the specific work is summarized as follows

 

1. To address the problem of how to eliminate cone-beam artifacts, several traditional methods for eliminating cone-beam artifacts are first compared and simulated are conducted. The conventional algorithms include three rearrangement algorithms (P-FDK, T-FDK and C-FDK), 3D weighting algorithm and Simultaneous Algebraic Reconstruction Techniques (SART). Simulation experiments are conducted using low-contrast Shepp-Logan volume models and modified Defrise affine bodies, and the reconstruction results of these traditional correction methods are compared with those of the FDK algorithm. It was concluded that the conventional T-FDK, C-FDK and 3D weighting algorithms could not effectively suppress the longitudinal intensity attenuation of the reconstructed images and correct the image distortion when performing high-contrast object imaging, and the SART algorithm, as an iterative reconstruction algorithm, could effectively correct the cone beam artifacts, but the reconstruction time was too long to meet the clinical needs.

 

To address the problems arising from the above traditional algorithms, an iterative reconstruction algorithm based on FDK (IR-FDK) is proposed in this paper. The IR-FDK algorithm does not require additional correction terms or add any additional trajectories to complement the circular trajectories, and simulation experiments and real measurement experiments are conducted. The performance of the IR-FDK algorithm was tested using Defrise, head model simulation experiments and monkey lower limb scan real measurement data, and the IR-FDK algorithm was compared with FDK, 3D weighting algorithm and SART algorithm, and the three indexes of MSE, SSIM and DSSIM were used to conclude that the IR-FDK algorithm proposed in this paper can effectively compensate the longitudinal intensity attenuation of the reconstructed image and The proposed IR-FDK algorithm can effectively compensate the longitudinal intensity attenuation of the reconstructed image and correct the image distortion, especially in the case of large cone angle. The simulation and measurement experiments show that the IR-FDK algorithm is significantly better than the FDK algorithm, the weighted algorithm and the C-FDK rearrangement algorithm in terms of cone beam artifact correction. In terms of reconstruction time, the IR-FDK algorithm can obtain comparable results with the SART algorithm by a smaller number of iterations.

 

3. The acceleration of IR-FDK algorithm based on CUDA technology. The basic theoretical knowledge of CUDA and the programming model of CUDA are introduced in detail, and the acceleration process of the IR-FDK algorithm is described. The IR-FDK algorithm before and after the acceleration is evaluated, and it is concluded that the average computational speed of the accelerated IR-FDK algorithm can be improved by about 160 times for a single iteration.

 

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