基于改进谱投影梯度算法的X射线发光断层成像

发布时间：2018-10-31 14:07

【摘要】：X射线发光断层成像(XLCT)是一种可同时获得解剖结构和功能信息的新型分子影像技术,在早期肿瘤检测与放疗方面具有重要应用潜力,但由于测量信息少,成像模型复杂等原因,其断层重建一直是挑战性难题。本文采用非单调Barzilai-Borwein梯度(NBBG)算法来求解重建问题目标函数。每次迭代中,谱投影梯度方法近似为L1范数约束的最小二乘问题。Barzilai-Borwein梯度法获得相应的更新方向,提高算法的收敛速度。采用非单调性线性搜索策略构建最优步长,保证全局收敛性。通过将Barzilai-Borwein梯度法和非单调性搜索结合,在保证全局收敛的同时,克服了选取精确步长带来较大计算量的缺点。数值仿真实验和物理实验得到的基于NBBG算法的单光原重建位置误差分别为0.68和0.94mm,与分裂增广拉格朗日收缩算法(SALSA)相比,本文方法在重建精度、鲁棒性和重建效率等方面都获得了较优的结果。
[Abstract]:X-ray emission tomography (XLCT) is a new molecular imaging technology which can obtain anatomical structure and function information simultaneously. It has important application potential in early tumor detection and radiotherapy. Because of the complexity of imaging model, fault reconstruction is always a challenging problem. In this paper, a nonmonotone Barzilai-Borwein gradient (NBBG) algorithm is used to solve the reconstruction problem. In each iteration, the spectral projection gradient method is approximately the least square problem with L1 norm constraint. The Barzilai-Borwein gradient method obtains the corresponding updating direction and improves the convergence speed of the algorithm. The non-monotonic linear search strategy is used to construct the optimal step size to ensure global convergence. By combining the Barzilai-Borwein gradient method with the non-monotonic search, the global convergence is guaranteed, and the shortcoming of choosing the accurate step size is overcome. The position errors of single light reconstruction based on NBBG algorithm obtained by numerical simulation and physical experiments are 0.68 and 0.94mm respectively. Compared with the split augmented Lagrangian shrinkage algorithm (SALSA), the reconstruction accuracy of this method is better than that of the original reconstruction method. Better results are obtained in terms of robustness and reconstruction efficiency.
【作者单位】：西北大学信息科学与技术学院;
【基金】：国家自然科学基金资助项目(No.61372046,No.11571012,No.61640418) 中国博士后科学基金资助项目陕西省科技计划资助项目(No.2015KW-002) 陕西省自然科学研究计划资助项目(No.2015JM6322) 陕西省教育厅基金资助项目(No.15JK1726);陕西省教育厅专项科研计划资助项目(No.14JK1578,No.16JK1772) 西北大学自然科学基金资助项目(No.338020006,No.338050003);西北大学研究生创新项目(No.YZZ15096)
【分类号】：TP391.41;O434.1

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