  Single-molecule localization fluorescence microscopy constructs
super-resolution images by sequential imaging and computational localization of
sparsely activated fluorophores. Accurate and efficient fluorophore
localization algorithms are key to the success of this computational microscopy
method. We present a novel localization algorithm based on deep learning which
significantly improves upon the state of the art. Our contributions are a novel
network architecture for simultaneous detection and localization, and new loss
function which phrases detection and localization as a Bayesian inference
problem, and thus allows the network to provide uncertainty-estimates. In
contrast to standard methods which independently process imaging frames, our
network architecture uses temporal context from multiple sequentially imaged
frames to detect and localize molecules. We demonstrate the power of our method
across a variety of datasets, imaging modalities, signal to noise ratios, and
fluorophore densities. While existing localization algorithms can achieve
optimal localization accuracy at low fluorophore densities, they are confounded
by high densities. Our method is the first deep-learning based approach which
achieves state-of-the-art on the SMLM2016 challenge. It achieves the best
scores on 12 out of 12 data-sets when comparing both detection accuracy and
precision, and excels at high densities. Finally, we investigate how
unsupervised learning can be used to make the network robust against mismatch
between simulated and real data. The lessons learned here are more generally
relevant for the training of deep networks to solve challenging Bayesian
inverse problems on spatially extended domains in biology and physics.
