  Particle tracking is a fundamental task in digital microscopy. Recently,
machine-learning approaches have made great strides in overcoming the
limitations of more classical approaches. The training of state-of-the-art
machine-learning methods almost universally relies on either vast amounts of
labeled experimental data or the ability to numerically simulate realistic
datasets. However, the data produced by experiments are often challenging to
label and cannot be easily reproduced numerically. Here, we propose a novel
deep-learning method, named LodeSTAR (Low-shot deep Symmetric Tracking And
Regression), that learns to tracks objects with sub-pixel accuracy from a
single unlabeled experimental image. This is made possible by exploiting the
inherent roto-translational symmetries of the data. We demonstrate that
LodeSTAR outperforms traditional methods in terms of accuracy. Furthermore, we
analyze challenging experimental data containing densely packed cells or noisy
backgrounds. We also exploit additional symmetries to extend the measurable
particle properties to the particle's vertical position by propagating the
signal in Fourier space and its polarizability by scaling the signal strength.
Thanks to the ability to train deep-learning models with a single unlabeled
image, LodeSTAR can accelerate the development of high-quality microscopic
analysis pipelines for engineering, biology, and medicine.
