基于轮廓波变换的有限角CT重建理论和方法研究

In some practical application scenarios, the CT system can only scan the object within a limited-angle range, which leads to the acquisited projection data does not meet the requirements of accurate reconstruction, then the CT images present some directional artifacts. Therefore, this project intends to develop an image reconstruction algorithm for the limited-angle CT scanning imaging mode, aims to suppress the directional artifacts and reconstruct some high quality images to meet the non-destructive testing standards or medical diagnostic requirements. Firstly, we propose a non-convex and non-smooth reconstruction model by using the common characteristic of directional artifacts in the limited-angle CT images and the sparseness of image under the contourlet transform. Secondly, we propose a stable limited-angle CT reconstruction algorithm, which based on the idea of alternating direction multiplier method, proximal alternating linear minimization and proximal mapping in a given metric. The convergence, stability and error bounds will be analyzed. Thirdly, we propose a fast and stable limited-angle CT reconstruction algorithm by introducing a preconditioning operator and combining the idea of alternating direction multiplier method and proximal alternating linear minimization, and the convergence, stability, error bound and convergence rate will be analyzed. Finally, the effectiveness of the algorithm is verified by experiments. The model and algorithm proposed in this project can be applied to industrial non-destructive testing or medical clinical diagnosis and other fields.

在有些实际应用场景，CT系统只能够在有限的角度范围内进行扫描，这样导致采集的投影数据不满足精确重建要求，使得CT图像呈现出一定的方向性伪影。为此本项目拟针有限角CT扫描成像模式开发相应的图像重建算法，以期能够抑制方向性伪影并重建出符合无损检测标准或医疗诊断要求的高质量图像。包括：(1)利用有限角CT图像中方向性伪影的共性和图像在轮廓波变换下的稀疏性先验知识，建立非凸非光滑重建模型；(2)结合交替方向乘子法、邻近交替线性最小化以及在给定矩下邻近线性化的思想设计出稳定的有限角CT重建算法，并分析其收敛性、稳定性和误差界等；(3)引入一个预处理子并结合交替方向乘子法和邻近交替线性最小化的思想设计出快速、稳定的有限角CT重建算法，并分析其收敛性、稳定性、误差界以及收敛速度等；(4)通过实验验证算法的有效性。本项目提出的模型和算法可应用于工业无损检测或医学临床诊断等领域。

在有些实际应用场景，CT系统只能够在有限的角度范围内进行扫描，这样导致采集的投影数据不满足精确重建要求，使得CT图像呈现出一定的方向性伪影。为了提高有限角CT重建图像的质量，抑制伪影。本项目提出了一种新的非凸非光滑优化模型和一种在给定矩下的变分临近交替线性化最小化(VPALM)方法，并分析了算法的收敛性。提出了一个结合组结构稀疏性和梯度先验稀疏性的非凸非光滑正则化CT重建模型。提出了一个基于ADMM的深度重建方法。提出了一个结合了l0梯度最小化和GIF的有限角CT图像重建算法。提出了一个基于引导图像滤波和小波框架的有限角CT重建算法。提出了一种基于引导图像滤波(GIF)和小波框架的有限角CT重建算法。提出了一种稀疏诱导动态引导滤波的CT重建技术，并应用到有限角CT中。在国内外期刊上发表标注本项目编号的SCI论文 6 篇。申请发明专利3项。协助培养毕业硕士1人。.