Background Estimation and Correction for High-Precision Localization Microscopy

Localization
of a single nanosized light emitter has substantial
applications in bioimaging. The accuracy and precision of localization
are limited by the noise and the heterogeneous background superimposed
on the signal. While the effects of noise are well recognized, the
influence of background is less addressed. Proper background correction
not only provides more accurate localization data but also enhances
the sensitivity of detection. Here, we demonstrate a new approach
to background correction by estimating and removing the heterogeneous
but stationary background from a series of images containing a spatially
moving signal. Our approach exploits the correlated signal information
encoded in the neighboring pixels governed by the point-spread function
of the measurement system. This new approach makes it possible to
obtain the background even when the total displacement of the signal
is subdiffraction limited throughout the observation, the scenario
where previous methods become invalid. We characterize our approach
systematically with different types of signal motions at various signal-to-noise
ratios in numerical simulations. We then verify our method experimentally
by recovering the nanoscopic displacements of single gold nanoparticle
moving in a specified pattern and a single virus particle randomly
diffusing on a cell surface. The source code of our algorithm written
in MATLAB is provided together with a sample data set. Our approach
has immediate applications in high-precision optical localization
measurements.