【作者】 李欣欣；

【导师】 谭山；

【作者基本信息】 华中科技大学 ， 控制理论与控制工程， 2015， 硕士

【摘要】 计算机断层成像(Computed Tomography,CT)能够在无损情况下获取物体的内部结构信息,当其应用于放射治疗时,根据重建出的表示人体器官和组织结构信息的影像,诊断出病灶的位置和大小。传统CT采用窄束X射线进行扫描,获取足量的投影数据需要进行多次扫描,探测器采集的投影数据是一维的,通过重建算法产生二维的数据图像,再将这些二维数据图像连续堆积起来重组成三维的物体图像。而锥形束(cone-beam)CT(CBCT)采用宽束X射线,扫描一周就能获得重建需要的全部投影数据。相对于传统CT,锥形束CT使X射线的扫描利用率得到明显提高,同时利用面状探测器来采集投影数据,明显提高了投影数据的采集速度。同时锥形束CT能够显著减少产生的X射线电离辐射,对人体正常细胞造成的伤害也相应降低。锥形束CT的这些优势使其被广泛应用于计算机断层成像领域。全变分图像重建算法在抑制图像噪声和保护图像边缘方面已展现出不错的效果。全变分图像重建有一个较大的缺陷就是重建结果会产生阶梯效应。在本文中,我们提出了引入高阶导数惩罚项的重建方法-基于Hessian Schatten范数的惩罚项,来构造目标函数,从而抑制阶梯效应。计算图像的每一个像素点对应的Hessian矩阵,用该Hessian矩阵的Schatten范数来作为目标函数的惩罚项。本文中我们主要采用了Hessian矩阵的1范数、Frobenius范数和无穷范数。通过对目标函数进行原始-对偶的推导,我们采用的基于Hessian Schatten范数的方法能够用于各阶Hessian Schatten范数,同时也可以解决原问题的非光滑性。采用快速迭代阈值(fast iterative shrinkage-thresholding algorithm,FISTA)方法进行本文目标函数的优化。本文采用MATLAB R2012和Visual Studio 2012软件进行计算机仿真,对实验数据分别用FDK方法、全变分方法(TV)和基于Hessian Schatten范数的方法进行图像重建,并对重建出的图像进行性能指标的比较和分析。我们选择的这些性能指标是峰值信噪比(PSNR)、改善信噪比(ISNR)、对比噪声比(CNR)和结构相似度(SSIM)。通过对仿真数据和真实数据的对比实验表明:基于Hessian Schatten范数的图像重建方法在抑制阶梯效应方面比全变分方法有明显优势。更多还原

【Abstract】 Computed Tomography(CT) can obtain the internal structure information without causing damage to the object. Physician can diagnose the size and location of lesions according to the obtained structure information of human organs or tissues in radiotherapy. The conventional CT uses a narrow beam of X-rays and it is necessary to scan several times to get the whole projection data. The projection is one-dimensional and we can get the two-dimensional image through certain reconstruction method, and stack the successive two-dimensional image data to get the three-dimensional image. Cone-beam CT uses a wide beam of X-rays. We can get all the needed projection data after a 360 degree rotation. Compared with the conventional CT, cone-beam CT can significantly improve the utilization rate of X-ray. Meanwhile, the utilization of the surface detector can significantly improve the acquisition speed of the projection data. Moreover, cone-beam CT can reduce the ionizing radiation dose. Consequently, the damage caused to people’s normal cells can been dramatically reduced. All the advantages of cone-beam CT make it get a wide application in clinic applications.The total variation(TV) penalty has shown state-of-the-art performance in suppressing noises and preserving edges. However, it produces the well-known staircase effect. In this study, to avoid the staircase effect, we proposed to use a new penalty—Hessian Schatten penalty—that involves higher order derivatives. We utilized the Schatten norms of the Hessian matrix, computed at every pixel of the image, as the penalty term to form the objective function. We utilized mainly the Hessian Schatten nuclear norm penalty, Hessian Schatten Frobenius norm penalty and Hessian Schatten spectral norm penalty in this paper. By the derivation of a primal-dual formulation, our Hessian Schatten penalty method can solve the corresponding constrained optimization problem under any choice of Schatten norm, and overcome the non-smooth nature of the problem. The fast iterative shrinkage-thresholding algorithm(FISTA) was employed to solve the optimization of the objective function in this study. This method provides state-of-the-art convergence rate by combining two successive iterates.This paper conducts computer simulations with MATLAB 2012 and Visual Studio 2012. We reconstructed the underlying image from the projection data using FDK method, Total Variation(TV) method and the Hessian Schatten method, and compared their performance with given performance indexes. These indexes we utilized are peak signal to noise ratio(PSNR), improvement signal to noise ratio(ISNR), contrast to noise ratio(CNR) and structural similarity index(SSIM). The experiments on two digital phantoms and two physical phantoms demonstrated the outstanding ability of the Hessian Schatten penalty over the TV-based penalty in suppressing the staircase effect.更多还原