大口径管状物外部CT检测的径向边缘增强图像重建模型与算法研究

CT（computed tomography）image reconstruction from x-ray projections, is a typical inverse problem. To solve it is a challenging task. When the projection data are insufficient, the inverse problem is ill-posed. The limitation of detector size, the restriction of x-ray energy, the interference of liquid for data acquisition, etc. commonly occur in the inspection of large diameter tubular object using CT technique. To solve these problems, detector is placed by an offset, and only the exterior annulus region of large diameter tubular object is scanned and reconstructed. This is referred to as the exterior CT. The edges along the radial direction in reconstructed images are blurred because the projection data of X-rays, which intersect with the interior central region of tubular object, are missed. In order to enhance radial edges and reduce the artifacts, three models are proposed in this item, incluing an exterior CT reconstruction model that is based on radial edge enhanced TV ( total variation ), an exterior CT reconstruction model that is based on the radial edge enhanced gradient and L0 quasi-norm regularization, and an exterior CT reconstruction model that is based on the radial edge enhanced Shearlet transform and L0 quasi-norm regularization. The numerical algorithms are developed to solve the these models. Furthermore, the existence of solution for the reconstruction models, convergence of algorithms, error bound between numerical solution and reference image, and adaptive selection strategy for the regularization parameter are researched in theory, and validated by experiments. The researches of this item, can be applied to aerospace engineering, petroleum pipeline transportation and other fields. They have both mathematical theoretical innovation and important engineering significance for nondestructive testing. They also have reference values to general ill-posed inverse problems caused by insufficient data.

从射线投影重建CT图像，是一种典型的逆问题。当投影数据不足时，该逆问题是不适定的，其求解具有挑战性。在大口径管状物的CT检测中，为解决探测器尺寸不足、射线能量不够、管道内流质干扰射线采集等问题，将探测器偏置，只扫描并重建感兴趣的物体外部环形区域，称为外部CT。由于通过中心区域的射线投影数据缺失，导致重建图像径向边缘模糊。为了加强径向边缘，抑制伪影，提出基于径向边缘增强TV的外部CT图像重建模型、基于径向边缘增强梯度与L0正则化的外部CT图像重建模型、基于径向边缘增强Shearlet变换与L0正则化的外部CT图像重建模型，发展求解上述模型的数值算法，对模型解的存在性、算法的收敛性、模型数值解的误差界、正则化参数的自适应选择策略进行理论研究，并用实验验证。本项目的研究，可应用于航天工业和石油管道传输等领域，具有数学理论创新和重要的无损检测工程意义，对数据不足引起的一般不适定逆问题有参考价值。

在大口径管状物的CT检测中，为解决探测器尺寸不足、射线能量不够、管道内流质干扰射线采集等问题，将探测器偏置，只扫描并重建感兴趣的物体外部环形区域，称为外部CT。本项目重点研究外部CT图像重建算法，包括基于径向边缘增强 TV 的外部 CT 图像重建方法，基于柱坐标加权方向全变分的外部圆周锥束CT图像重建方法，基于极坐标各向异性相对全变分的外部CT图像重建等。提出的方法可有效地增强外部CT的径向边缘，解决了外部CT图像径向边缘模糊这一关键技术难题，为外部CT的应用扫清了障碍。还研究了有限角CT 图像重建方法和低信噪比CT 图像重建方法等。发表论文24篇，其中被SCIE收录20篇，授权中国发明专利6项（其中2项转让使用权），主编1个工业CT相关国家标准。在国际国内多个会议和单位做学术报告。培养博士研究生7名，硕士研究生11名，获国家精品开放课程和国家级一流本科课程，全国和美国数学建模竞赛一等奖。项目成果已应用于重庆真测科技股份有限公司和国家重大仪器专项的产品研发。可应用于航天工业和石油管道传输等领域，具有算法创新和重要的无损检测工程意义。