Measuring localization confidence for quantifying accuracy and heterogeneity in single-molecule super-resolution microscopy

We present a computational method, termed Wasserstein-induced flux (WIF), to robustly quantify the accuracy of individual localizations within a single-molecule localization microscopy (SMLM) dataset without ground-truth knowledge of the sample. WIF relies on the observation that accurate localizations are stable with respect to an arbitrary computational perturbation. Inspired by optimal transport theory, we measure the stability of individual localizations and develop an efficient optimization algorithm to compute WIF. We demonstrate the advantage of WIF in accurately quantifying imaging artifacts in high-density reconstruction of a tubulin network. WIF represents an advance in quantifying systematic errors with unknown and complex distributions, which could improve a variety of downstream quantitative analyses that rely upon accurate and precise imaging. Furthermore, thanks to its formulation as layers of simple analytical operations, WIF can be used as a loss function for optimizing various computational imaging models and algorithms even without training data.