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A major challenge in many modern superresolution fluorescence microscopytechniques at the nanoscale lies in the correct alignment of long sequences ofsparse but spatially and temporally highly resolved images. This is caused bythe temporal drift of the protein structure, e.g. due to temporal thermalinhomogeneity of the object of interest or its supporting area during theobservation process. We develop a simple semiparametric model for driftcorrection in SMS microscopy. Then we propose an M-estimator for the drift andshow its asymptotic normality. This is used to correct the final image and itis shown that this purely statistical method is competitive with state of theart calibration techniques which require to incorporate fiducial markers intothe specimen. Moreover, a simple bootstrap algorithm allows to quantify theprecision of the drift estimate and its effect on the final image estimation.We argue that purely statistical drift correction is even more robust thanfiducial tracking rendering the latter superfluous in many applications. Thepracticability of our method is demonstrated by a simulation study and by anSMS application. This serves as a prototype for many other typical imagingtechniques where sparse observations with highly temporal resolution areblurred by motion of the object to be reconstructed.

Drift Estimation in Sparse Sequential Dynamic Imaging: with Application to Nanoscale Fluorescence Microscopy