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Abstract The resolution and accuracy of single-molecule localization microscopes (SMLMs) are routinely benchmarked using simulated data, calibration rulers, or comparisons to secondary imaging modalities. However, these methods cannot quantify the nanoscale accuracy of an arbitrary SMLM dataset. Here, we show that by computing localization stability under a well-chosen perturbation with accurate knowledge of the imaging system, we can robustly measure the confidence of individual localizations without ground-truth knowledge of the sample. We demonstrate that our method, termed Wasserstein-induced flux (WIF), measures the accuracy of various reconstruction algorithms directly on experimental 2D and 3D data of microtubules and amyloid fibrils. We further show that WIF confidences can be used to evaluate the mismatch between computational models and imaging data, enhance the accuracy and resolution of reconstructed structures, and discover hidden molecular heterogeneities. As a computational methodology, WIF is broadly applicable to any SMLM dataset, imaging system, and localization algorithm. 

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. 

In single-molecule super-resolution microscopy, engineered point-spread functions (PSFs) are designed to efficiently encode new molecular properties, such as 3D orientation, into complex spatial features captured by a camera. To fully benefit from their optimality, algorithms must estimate multi-dimensional parameters such as molecular position and orientation in the presence of PSF overlap and model-experiment mismatches. Here, we present a novel joint sparse deconvolution algorithm based on the decomposition of fluorescence images into six basis images that characterize molecular orientation. The proposed algorithm exploits a group-sparsity structure across these basis images and applies a pooling strategy on corresponding spatial features for robust simultaneous estimates of the number, brightness, 2D position, and 3D orientation of fluorescent molecules. We demonstrate this method by imaging DNA transiently labeled with the intercalating dye YOYO-1. Imaging the position and orientation of each molecule reveals orientational order and disorder within DNA with nanoscale spatial precision. 

In single-molecule (SM) super-resolution microscopy, the complexity of a biological structure, high molecular density, and a low signal-to-background ratio (SBR) may lead to imaging artifacts without a robust localization algorithm. Moreover, engineered point spread functions (PSFs) for 3D imaging pose difficulties due to their intricate features. We develop a Robust Statistical Estimation algorithm, called RoSE, that enables joint estimation of the 3D location and photon counts of SMs accurately and precisely using various PSFs under conditions of high molecular density and low SBR.