总变差正则化断层图像重建的解耦Bregman迭代算法

摘要

Recently, there are many practical applications of tomographic reconstruction that consist of minimizing the sum of a residual energy and image total variation (TV). In this paper, we develop an uncoupled iterative algorithm for solving the recent popular TV-regularized CT optimization problem. Using surrogate function, we split the sum minimization scheme to the minimizing weighted least square function and TV denoising with weighted norm iteratively. In order to find the stable solution of this model, we use Chambolle' s scheme to overcome the numerical difficulty due to the non differentiability of the TV norm and use Bregman scheme to accelerate the iteration process. Experimental results show that the proposed approach outperforms some existing TV tomography methods based on the gradient descent algorithms.%在断层重建的很多工程应用中,由于低剂量以及成像硬件等原因,经常需要在测量数据不充分的情况下去重建图像.基于图像分段光滑的假设,提出采用误差的加权范数作为数据保真项,TV(total variation)作为正则项的断层图像重建模型.该模型求解时,首先通过引入代理函数将原问题解耦为残差的加权范数最小化和加权范数TV去噪这两个子问题;然后采用了Chambolle的对偶空间正交投影法的框架对加权范数TV去噪问题进行求解,避免了由于TV项在不可导处所带来的计算不稳定;最后,为了提高收敛速度并且避免由正则化参数选取所引起的数值不稳定,引入Bregman方法,给出该模型的快速迭代算法.在扇形束少角度欠采样的条件下,对理想情况和高斯噪声情况下进行仿真测试,并同多种算法进行了比较.实验结果表明,该算法重建效果好,收敛速度快.