基于r-ADMM算法的轴向超分辨荧光显微技术研究

Axial Super-Resolution Fluorescence Microscopy Imaging Technology Based on r-ADMM Algorithm

多角度全内反射荧光显微镜层析成像技术是实现轴向超分辨的主要技术之一,其关键算法是基于交替方向乘子算法对逆问题模型求解。为进一步提高交替方向乘子算法的迭代速度及收敛性,提出将一种基于松弛因子的改进型交替方向乘子算法应用于逆问题的求解中,其核心思想是对拉格朗日函数的分解迭代过程进行过松弛求解。基于该算法,搭建了多角度全内反射荧光显微镜成像系统,采集不同照明角度对应的不同穿透深度的图像堆栈,利用改进型算法重构细胞微管的深度信息,给出了系统的轴向分辨率,并与传统交替方向乘子算法进行了收敛速度的对比,给出了改进型算法达到最优收敛的松弛因子的取值范围,最后通过对线粒体样品进行长时程拍摄,重构了其三维信息,并观测了其融合和裂变的连续过程。实验结果表明,改进型交替方向乘子算法可以实现40 nm的轴向分辨率,并能在保证图像重构质量的同时,使迭代过程的收敛速度提升20%以上。

The multi-angle total internal reflection fluorescence microscopy tomography imaging technology is one of the main techniques for achieving the axial super resolution. The key algorithm is to solve the inverse problem based on the alternating direction multiplier algorithm. In order to further improve the iterative speed and convergence of the alternating direction multiplier algorithm, we propose an improved alternating direction multiplier algorithm based on relaxation factors, which is used for the solution of the inverse problems and whose core idea is to solve the relaxation process of the Lagrangian function decomposition iterative process. Based on the proposed algorithm, the multi-angle total internal reflection fluorescence microscopy imaging system is built. The image stacks with different penetration depths corresponding to different illumination angles are acquired. Then the depth information of cell microtubules is reconstructed using the improved algorithm, and the axial resolution of the system is also given. Moreover, the convergence speed comparison of the improved algorithm with the traditional alternating direction multiplier algorithm is accomplished and the range of relaxation factors for the improved algorithm to achieve the optimal convergence is also given. Finally, the three-dimensional information of mitochondrial samples is reconstructed by long time photographing, and the consecutive processes of fusion and fission are observed. The experimental results show that the improved alternating direction multiplier algorithm can be used to achieve an axial resolution of 40 nm. Moreover, the convergence speed of the iterative process is improved by more than 20% when the image reconstruction quality is ensured.