基于改进谱投影梯度算法的X射线发光断层成像

X-ray luminescence computed tomography based on improved spectral projected gradient algorithm

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。

X-ray Luminescence Computed Tomography （XLCT）,a novel imaging technique which can obtain anatomical structure and functional information simultaneously,has an important application prospect in early tumor detection and radiotherapy.But due to the less measurement and complex imaging model,the tomography reconstruction always is a challenging problem.This paper presents a gradient algorithm based on Non-monotone Barzilai-Borwein（NBBG） to obtain the optimal solution of the objective.In each iteration,a spectral gradient-projection method approximately was minimized as a least-squares problem with an explicit L1-regularized constraint.The Barzilai-Borwein was employed to get the appropriate updating direction,further to improve the convergence speed of the proposed method.In addition,anonmonotone line search strategy was applied to build the optimal step length,which guarantees global convergence.The combination of nonmonotone line Barzilai-Borwein step length search strategy with spectral projected gradient method not only can ensure the global convergence,but also can reduce the computational cost of selecting exact step-size.From numerical simulation experiments and the physical experiment,the Location Errors （LE） of single target reconstruction based on NBBG are 0.68 and 0.94 mm respectively.Compared with Split Augmented Lagrangian Shrinkage Algorithm （SALSA）,NBBG can obtain better results in terms of LE,robustness and efficiency.