【作者】 于庆坤；

【导师】 杨冬梅；

【作者基本信息】 东北大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 CT(Computed Tomography X射线计算机断层摄影术)自问世以来得到了越来越广泛的应用。CT的广泛应用反过来又推动了对它的研究,使它得到进一步的发展。在过去30年的发展过程中,它基本上经历了五次大的变革。CT的这些发展变化主要体现在两个方面,一是提高扫描速度,二是改善图像的质量。Radon于1917年提出了著名的Radon变换,然而,直到计算机出现以后才实现了傅里叶变换及卷积的快速计算,这一成果才引起人们足够的注意。Radon变换理论现在已经成为CT重建技术的重要基础,这一技术不仅可以应用于医学成像,也同样适用于远程成像等许多图象处理学科。迄今为止,人们已经开发出基于Radon变换的多种比较成熟的重建算法。本文首先介绍了反傅里叶变换重建,然后研究了二维平行束滤波反投影和扇束滤波反投影重建,最后介绍了局部凸组合插值重建方法。通过对CT图像的投影进行傅里叶变换,将变换所得到的数据在极坐标网格中按照角度排列在Radon变换域中,进行反傅里叶变换的时候,首先需要对极坐标下的Radon变换域进行插值。由于经过傅里叶变换之后的Radon变换域中的采样是均匀的,在靠近中心的区域出现过采样,而在远离中心的地方出现欠采样。因此本文提出了一种新的方法进行插值处理,即局部凸组合插值法,并且采用了内插和外插相结合的方法进行插值。插值的权重是由一距离的倒数的函数决定的。通过分别在投影空间和经过傅里叶变换的Radon变换域中进行插值,然后比较插值效果的方法。得出结论,在投影空间进行数据的内插和外插的效果要好于在傅里叶变换之后的Radon变换域中进行内插和外插,其原因主要是因为投影空间所得到的数据要比傅里叶变换空间中所得到的数据更均匀连续,图像仿真的结果也证明了这一点。最后,通过Matlab程序验证了各种插值方法的可行性和正确性。更多还原

【Abstract】 Since the birth of the first CT (Computed Tomography) scanner in 1972, CT has been widely used in the world. The wide uses of CT also generate great impetus for CT research. Several big changes have taken placed during the past 30 years. The changes mainly involve in two aspects-speed and image quality.The Radon transform was introduced by J. Radon in 1917. Little computation attention was given to it until the advent of computers enabled the fast evaluation of Fourier transform and their convolutions. The Radon transform is now a mainstay of computerized tomography in medical imaging as well as many other remote-imaging sciences. So far, many reliable reconstruction methods based on Radon transform have been developed.Firstly we introduce the reverse discrete Fourier transform reconstruction, and then we study the two dimensions filtered back projected, at last we propose the method of local convex combination interpolation. Radon domain can be filled by the Fourier transforms for projection images in a polar gridding format (radial lines for parallel projections, radon arcs for fan-beam projections). The Radon-based tomographic reconstruction requires regridding a polar radon domain into a rectilinear lattice before inverse Fourier transform. Since the radon domain is irregularly sampled by Fourier-transformed projections, i.e, oversampled around the central regions and undersampled at the peripheral regions, the polar-to-Cartesian coordinate grid conversion involves rebinning for oversampled central region, interpolation for undersampled peripheral region, and extrapolation for extending the peripheral boundary. In this paper, we propose a general data interpolation or extrapolation scheme to deal with the radon domain regridding, which is a local convex combination with weights determined by a function of inverse distances. For filling the unavailable entries at peripheral regions, we propose to calculate the corresponding entries in the projection domain, rather than in the radon domain, by interpolations and extrapolations. The interpolation for peripheral region allows us investigate the angular sampling for computed tomography scanning. The extrapolation leads to super-resolution tomographic reconstruction. We find that data interpolation in projection domain may produce better results than in radon domain. This finding may be justified by the fact that the data distribution is more continuous in projection domain than in Fourier domain.Finally the feasibility and correctness of the interpolation are validated by using Matlab programs.更多还原