  Structured illumination microscopy (SIM) has become an important technique
for optical super-resolution imaging because it allows a doubling of image
resolution at speeds compatible for live-cell imaging. However, the
reconstruction of SIM images is often slow and prone to artefacts. Here we
propose a versatile reconstruction method, ML-SIM, which makes use of machine
learning. The model is an end-to-end deep residual neural network that is
trained on a simulated data set to be free of common SIM artefacts. ML-SIM is
thus robust to noise and irregularities in the illumination patterns of the raw
SIM input frames. The reconstruction method is widely applicable and does not
require the acquisition of experimental training data. Since the training data
are generated from simulations of the SIM process on images from generic
libraries the method can be efficiently adapted to specific experimental SIM
implementations. The reconstruction quality enabled by our method is compared
with traditional SIM reconstruction methods, and we demonstrate advantages in
terms of noise, reconstruction fidelity and contrast for both simulated and
experimental inputs. In addition, reconstruction of one SIM frame typically
only takes ~100ms to perform on PCs with modern Nvidia graphics cards, making
the technique compatible with real-time imaging. The full implementation and
the trained networks are available at http://ML-SIM.com.
