Model-free uncertainty estimation in stochastical optical fluctuation imaging (SOFI) leads to a doubled temporal resolution.

Peter Dedecker,Theo Lasser,Marcel Leutenegger,Bartosz Krajnik,Benjamien Moeyaert,Wim Vandenberg,Sam Duwé

doi:10.1364/boe.7.000467

Abstract

Stochastic optical fluctuation imaging (SOFI) is a super-resolution fluorescence imaging technique that makes use of stochastic fluctuations in the emission of the fluorophores. During a SOFI measurement multiple fluorescence images are acquired from the sample, followed by the calculation of the spatiotemporal cumulants of the intensities observed at each position. Compared to other techniques, SOFI works well under conditions of low signal-to-noise, high background, or high emitter densities. However, it can be difficult to unambiguously determine the reliability of images produced by any superresolution imaging technique. In this work we present a strategy that enables the estimation of the variance or uncertainty associated with each pixel in the SOFI image. In addition to estimating the image quality or reliability, we show that this can be used to optimize the signal-to-noise ratio (SNR) of SOFI images by including multiple pixel combinations in the cumulant calculation. We present an algorithm to perform this optimization, which automatically takes all relevant instrumental, sample, and probe parameters into account. Depending on the optical magnification of the system, this strategy can be used to improve the SNR of a SOFI image by 40% to 90%. This gain in information is entirely free, in the sense that it does not require additional efforts or complications. Alternatively our approach can be applied to reduce the number of fluorescence images to meet a particular quality level by about 30% to 50%, strongly improving the temporal resolution of SOFI imaging.

Highlights

Recent developments have proven a strong interest in diffraction-unlimited far-field fluorescence imaging
Based on statistical resampling we develop a strategy for the direct estimation of the spatially-resolved signal-to-noise ratio (SNR) of arbitrary Stochastic optical fluctuation imaging (SOFI) images
In this work we presented a strategy to estimate the uncertainty associated with a particular SOFI measurement, based on statistical resampling

Summary

Introduction

Recent developments have proven a strong interest in diffraction-unlimited far-field fluorescence imaging. One of the complications in super-resolution imaging is that it is difficult to unambiguously verify the reliability or quality of the generated images, especially when a large amount of computer processing is involved Such estimations are required to ensure that only well-supported observations and conclusions are considered. We have suggested performing this quality control by combining more than one super-resolution imaging technique [15], which can be be done if the fluorophore provides the required functionality. This is not possible if only one imaging technique is suited to the measurement conditions in question, in which case the reliability must be estimated using only the imaging data. Our work provides a way for the unbiased estimation of the SOFI imaging quality, and enables higher-quality SOFI images to be obtained while requiring fewer fluorescence images, while not imposing any additional requirements or limitations

SOFI theory

Estimating the uncertainty of SOFI pixels and pixel combinations

Determining the optimal weights of the cross-cumulant combinations

Practical application and results

6: Calculate SOFI signal κip for detector pixel p and pixel combination i

Fast approximation to the exact calculation

Findings

Conclusion