Untrained, physics-informed neural networks for structured illumination microscopy

In recent years there has been great interest in using deep neural networks (DNN) for super-resolution image reconstruction including for structured illumination microscopy (SIM). While these methods have shown very promising results, they all rely on data-driven, supervised training strategies that need a large number of ground truth images, which is experimentally difficult to realize. For SIM imaging, there exists a need for a flexible, general, and open-source reconstruction method that can be readily adapted to different forms of structured illumination. We demonstrate that we can combine a deep neural network with the forward model of the structured illumination process to reconstruct sub-diffraction images without training data. The resulting physics-informed neural network (PINN) can be optimized on a single set of diffraction limited sub-images and thus doesn't require any training set. We show with simulated and experimental data that this PINN can be applied to a wide variety of SIM methods by simply changing the known illumination patterns used in the loss function and can achieve resolution improvements that match well with theoretical expectations.