中文摘要：

这个工作处于内部问题在区分的 backprojection (DBP ) 的重建方法的申请上集中设计到凸的集合(POCS ) 上。首先，我们在场内部问题的定义和真实截断的 Hilbert 转变，然后构画出 DBP-POCS 的实现步。在那以后，我们为兴趣( ROI )的区域介绍中间部分的已知的条件精确重建和内部问题的唯一的条件，并且验证内部问题的唯一和稳定性通过数字实验的精确重建，然后用过滤 backprojection ( FBP )在重建图象为内部问题比较结果。另外，作者也设计 ROI 重建的申请模型并且处于内部问题做一次起始的尝试到 DBP-POCS 方法的申请。

英文摘要：

This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.