基于稀疏变量统计分布积分的低剂量CT重建研究

Low dose CT reconstruction is a key problem that needs urgent resolution in the CT application fields. According to the difference of constrains, the low dose iteration reconstruction can be divided into two categories, which are based on statistical constrains and sparse constrains. In this project, combining the statistical constrains and the sparse constrains, the low dose CT reconstruction with the statistical distribution integral constrain of the sparse variations is proposed. The major research contents of this project is as follows: (1) low dose CT reconstruction based on the statistical distribution integral constrain of the local sparse variations; (2) low dose CT reconstruction based on the multivariate statistical distribution integral constrain of the non-local sparse variations; (3) low dose CT reconstruction based on the matrix statistical distribution integral constrain of the non-local image block sparse variations; (4) low dose CT reconstruction based on the mixture, mixture multivariate and mixture matrix statistical distribution integral constrain of the local, non-local, image block sparse variations. Under the same condition (the same sampling views, the same transmitting tube voltage or current), through solving the reconstructed models, the project is to reconstruct images which are better than that reconstructed based on statistical constrains or the sparse constrains only. The project achieves the goal that reduces the radiation and meanwhile not influences the clinic diagnosis practice.

低剂量CT重建是目前CT应用领域亟待解决的重要问题。根据约束的不同,低剂量CT重建分为基于统计约束与基于稀疏约束两类。本项目结合统计约束与稀疏约束，提出了基于稀疏变量统计分布积分约束的低剂量CT重建。项目主要研究内容为：(1)研究基于局部稀疏变量统计分布积分约束的低剂量CT重建；(2)研究基于非局部稀疏变量多变量统计分布积分约束的低剂量CT重建；(3)研究基于图像块稀疏变量矩阵统计分布积分约束的低剂量CT重建；(4)研究基于局部、非局部、非局部图像块稀疏变量的混合、混合多变量、混合矩阵统计分布积分约束的低剂量CT重建。本项目通过对所建模型的优化求解重建出在同等条件下(相同的采样角度，相同的发射管电压或电流)，较采用单一统计约束或稀疏约束更好的CT图像，最终达到在减少患者辐射的同时又不影响临床诊断的应用目的。

低剂量CT重建是目前CT应用领域重要的研究内容之一，它可以降级辐射剂量，确保患者和医务人员的健康。本项目包含如下研究： (1)研究基于局部稀疏变量统计分布积分约束的低剂量CT重建；(2)研究基于非局部稀疏多变量统计分布积分约束的低剂量CT重建；(3)研究基于图像块稀疏变量矩阵统计分布积分约束的低剂量CT重建；(4)研究基于局部、非局部、非局部图像块稀疏变量的混合统计分布积分约束的低剂量CT重建。(5) 对以上模型建立了统一的非凸优化数学模型，并对其收敛性进行了分析。(6)为其它医学图像重建提供了新思路。. 本项目研究取得了一定得研究成果。在随后的研究中会进一步改进重建模型，降低辐射剂量，得到更好低剂量CT图像。