光学学报, 2017, 37 (6): 0617001, 网络出版: 2017-06-08   

基于非凸L1-2正则子的锥束X射线发光断层成像

Nonconvex L1-2 Regularization for Fast Cone-Beam X-Ray Luminescence Computed Tomography
作者单位
西北大学信息科学与技术学院, 陕西 西安 710127
摘要
锥束X射线发光断层成像(CB-XLCT)是一种新型分子影像模态, 对疾病的早期检测、靶向治疗以及药物研制等具有重要意义。然而, 通过传统的压缩感知理论反演生物体内纳米目标的三维分布时, 高维系统矩阵的强相关性会直接影响成像质量。基于非凸稀疏L1-2正则子, 将CB-XLCT的成像问题转化为一种新的稀疏重建模型。采用一种凸差分算法来解决非凸泛函最小化问题, 在每一步凸差分子迭代中采用一种带自适应惩罚项的交替方向乘子法进行高效求解。设计了单目标数字鼠仿体、双目标数字鼠仿体以及真实在体老鼠实验验证提出算法的有效性和稳健性, 并与五种常见正则子 (L1/2,L1,L2,TV和L0)进行对比和分析。实验结果表明, L1-2正则子的成像性能最优, 提出方法可以有效解决CB-XLCT的快速成像问题。
Abstract
Cone-beam X-ray luminescence computed tomography (CB-XLCT) is an attractive hybrid imaging modality, and it is important for early detection of diseases, targeted therapy and drug development. However, the columns of system matrix used for CB-XLCT imaging tend to be highly coherent, which means L1 minimization may not produce the sparsest solution. A novel reconstruction method by minimizing the difference between L1 and L2 norms is proposed. To solve the non-convex L1-2 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 L1 minimization subproblem, which is solved by the alternating direction method of multipliers with an adaptive penalty. The performance of the proposed method is investigated with simulated data and in vivo experimental data. The results demonstrate that the DCA for L1-2 minimization outperforms the representative algorithms for L1, L2, L1/2, TV and L0 when the system matrix is highly coherent. The proposed method can solve the rapid imaging problem of CB-XLCT effectively.

张海波, 耿国华, 赵映程, 孙怡, 易黄建, 侯榆青, 贺小伟. 基于非凸L1-2正则子的锥束X射线发光断层成像[J]. 光学学报, 2017, 37(6): 0617001. Zhang Haibo, Geng Guohua, Zhao Yingcheng, Sun Yi, Yi Huangjian, Hou Yuqing, He Xiaowei. Nonconvex L1-2 Regularization for Fast Cone-Beam X-Ray Luminescence Computed Tomography[J]. Acta Optica Sinica, 2017, 37(6): 0617001.

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