Nonparametric detection of changes over time in image data from fluorescence microscopy of living cells
本文利用自助法构建非参数置信带，检测活细胞荧光显微镜图像中随时间变化的结构是否具有统计显著性，适用于纳米级微小变化分析。
Abstract The question whether structural changes in time‐resolved images are of statistical significance or merely emerge from random noise is of great relevance in many practical applications such as live cell fluorescence microscopy, where intracellular diffusion processes are investigated. Using bootstrap‐methods, we construct nonparametric confidence bands for time‐resolved images from fluorescence microscopy and use these to detect and visualize temporal changes between individual frames in imaging of living cells. We model the images frames as two‐dimensional fields of Poisson random variables and provide a strong approximation result for independent and standardized but not necessarily identically distributed Poisson random variables. The latter result is used to derive a limit result for the maximal difference between the reconstructed and the true image. This provides the theoretical foundation of our method. We apply regularization techniques to cope with the ill‐posedness of the convolution problem induced by the imaging system. Our approach provides a criterion to assess time‐resolved small scale structural changes, for example, in the nanometer range. It can also be adopted for use in other imaging systems. Moreover, a data‐driven selection method for the regularization parameter based on statistical multiscale methods is discussed.