中文摘要：

不完全角度重建问题一直是CT图像重建领域研究的重点和难点。目前,通常的不完全角度重建方法是基于空域的迭代方法,但由于正反投影的高计算复杂度,空域迭代方法存在计算耗时,对硬件资源需求大等问题。本文提出了一种基于外推的邻近网格迭代算法（INNG-TV）。首先,平行束采样的数据通过傅里叶变换和样条插值到频域空间,然后在迭代的过程中,傅立叶空间投影已知部分的数据始终不变,缺失部分数据通过对重建图像进行INNG外推得到,同时在图像空间对重建图像做非负、最小化总变分等先验及优化约束。

英文摘要：

In CT reconstruction, challenge of few-view projections is always the focus and difficulty. At present, the method based on spatial iterative reconstruction is primary solution. However, due to high computational complexity of projection and back projection, spatial iterative reconstruction has some problems, such as time-consuming, great demand for hardware resources and other issues. In this paper, a CT reconstruction algorithm which is named INNG-TV based on extrapolation in frequency is proposed to improve the performance. We first convert data, which is sampled from parallel beam, into frequency-domain by Fourier transform and spline interpolation. In the following process of iteration, the known data of projection in Fourier space keep constant, whereas the unknown data are estimated by INNG extrapolation. At the same time, prior knowledge and constrained optimization, such as non-negativity constraint and minimum total variation, are introduced to image reconstruction in image space.