基于累积量标准差的超分辨光学涨落成像解卷积优化∗

摘要

The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by evaluating the independent stochastic intensity fluctuations of emitters. In principle, it eliminates any noise uncorrelated temporally, and provides unlimited spatial resolution since the calculation of the nth-order cumulant followed by a deconvolution results in an image with n-fold resolution improvement in three dimensions. But in practice, due to limited data length, the statistical uncertainty of cumulants will affect the continuity and homogeneity of SOFI image, which results in the fact that the high order SOFI (typically over 3rd order) cannot improve spatial resolution significantly. Since the variance characterizes the statistical uncertainty of cumulant, we deduce its theoretical expression based on a single dataset. In traditional SOFI techniques, due to lack of statistical analysis of cumulant, there is no noise constraint condition of cumulant in the Lucy-Richardson deconvolution to prevent the algorithm from causing noise amplification. In this paper, based on the cumulant variance formula, we calculate the cumulant standard deviation in each pixel of SOFI image and introduce the results into the Lucy-Richardson algorithm as a DAMPAR to suppress the noise generation in such pixels. The simulation and experimental results show that under the same data length, the deconvolution optimization based on cumulant standard deviation significantly improves the uniformity and continuity of SOFI image. On the other hand, under the premise of identical image quality, this optimization technique can also greatly shorten the image frames to less than half the original, thus promoting the development of super-resolution imaging of living cells.%超分辨光学涨落成像方法通过计算一组随机闪烁图像序列的累积量来提高空间分辨率。在实际实验中，由于计算的图像序列帧数有限，每个像素上累积量估计的误差将显著影响重构图像的均匀性和连续性。传统超分辨光学涨落成像技术由于缺乏对累积量估计的误差分析，在其后续的Lucy-Richardson解卷积算法中，没有对累积量重构图像的噪声添加约束条件。本文利用基于单组有限长数据的累积量标准差公式，计算了超分辨光学涨落显微图像每个像素上的累积量标准差，并将结果引入Lucy-Richardson解卷积算法中作为迭代优化的偏差阈值。模拟和实验结果表明，在相同图像序列长度下，该优化方法显著提高了超分辨重构图像的均匀性和连续性；在同等图像质量下，该方法可缩短图像序列帧数至原来的一半以下，有望用于活细胞动态超分辨成像。