Fluorescence photobleaching correction for expectation-maximization algorithm

In 3D fluorescence microscopy, a series of 2D images is collected at different focal settings through the specimen. Each image in this series contains the in-focus plane plus contributions from out-of-focus structures that blur the image. Furthermore, as the series is collected the fluorescent dye in the specimen fades over time in response to the total excitation light dosage which progressively increase as more optical slices are collected. Thus the different optical slices are 2D images of different 3D objects, in the sense that at each time point, the object has a different overall intensity. To date, the approach to compensate for this decay has been to precondition the image by dividing the intensities in each optical slice by a decaying exponential before processing the image by any of a number of existing deblurring algorithms. We have now directly incorporated fluorescent decay into maximum-likelihood estimators for the 3D distribution of fluorescent dye. We derived a generalized expectation-maximization algorithm for the simultaneous estimation of the decay constant, considered homogeneous, and the distribution of fluorescent dye.