重建算法是计算机断层成像（CT）技术的核心。在解析法CT重建过程中，结合先验信息和引入优化约束条件较为困难。通过对滤波反投影(FBP)原理及其重建图像与理想CT 图像差值关系的分析，构造了以FBP 为基础的迭代循环，解决了解析重建过程中先验信息的利用和优化约束条件的引入问题。为抑制迭代FBP 产生的图像伪影，将全变分(TV)模型引入重建过程，建立了TV 约束迭代滤波反投影CT 重建方法。在数值模拟中，针对完善投影数据、稀疏投影数据、含金属投影数据和有限角投影数据等不同情况，重建出了与原始模型高度一致的CT 图像，研究表明TV 约束迭代滤波反投影方法是一种精度高、适应性较强的CT重建方法。

Reconstruction algorithm is the core technology in computerized tomography (CT). It is intractable to utilize priori information and constraint condition in analytical CT reconstruction algorithm. To resolve the problem, by analyzing the principle of the filtered backprojection (FBP) reconstruction algorithm, the relationship between the ideal CT image and the reconstructed CT image is proposed, an iterative method based on FBP is put forward. To suppress the spot artifacts induced by the iterative algorithm, a total variation (TV) model is introduced into the procedure and a TV constrained iterative filtered backprojection is built. In numerical simulation, images reconstructed by this method show high consistency with the ideal image, whether the sinograms are ideal, sparse, metal or limited angle. The results indicate that it is an adaptable and high precision CT reconstruction method.