Zhang Haibo, Geng Guohua, Wang Xiaodong, Qu Xuan, Hou Yuqing, He Xiaowei
School of Information Sciences and Technology, Northwest University, Xi'an, Shaanxi 710027, China.
Biomed Res Int. 2016;2016:5065217. doi: 10.1155/2016/5065217. Epub 2016 Dec 6.
Sparse reconstruction inspired by compressed sensing has attracted considerable attention in fluorescence molecular tomography (FMT). However, the columns of system matrix used for FMT reconstruction tend to be highly coherent, which means minimization may not produce the sparsest solution. In this paper, we propose a novel reconstruction method by minimization of the difference of and norms. To solve the nonconvex minimization problem, an iterative method based on the difference of convex algorithm (DCA) is presented. In each DCA iteration, the update of solution involves an minimization subproblem, which is solved by the alternating direction method of multipliers with an adaptive penalty. We investigated the performance of the proposed method with both simulated data and experimental data. The results demonstrate that the DCA for minimization outperforms the representative algorithms for , , , and when the system matrix is highly coherent.
受压缩感知启发的稀疏重建在荧光分子断层扫描（FMT）中引起了广泛关注。然而，用于FMT重建的系统矩阵列往往具有高度相关性，这意味着最小化可能不会产生最稀疏的解。在本文中，我们提出了一种通过最小化 范数和 范数之差的新型重建方法。为了解决非凸 最小化问题，提出了一种基于凸差算法（DCA）的迭代方法。在每次DCA迭代中，解的更新涉及一个 最小化子问题，该子问题通过具有自适应惩罚的乘子交替方向法求解。我们用模拟数据和实验数据研究了所提方法的性能。结果表明，当系统矩阵具有高度相关性时，用于 最小化的DCA优于用于 、 、 和 的代表性算法。
