Structured illumination microscopy with uncertainty quantification

Deep learning shows great potential for super-resolution microscopy, offering biological structures visualization with unprecedented details and high flexibility. An effective pathway toward this goal is structured illumination microscopy (SIM) augmented by deep learning because of its ability to double the resolution beyond the light diffraction limit in real-time. Although the deep-learning-based SIM technique works effectively, it is generally a black box that is difficult to explain the latent principle. Thus, the generated super-resolution biological structures contain unconvinced information for clinical diagnosis. This limitation impedes its further applications in safety-critical fields like medical imaging. In this paper, we report a reliable deep-learning-based SIM technique with uncertainty maps. These uncertainty maps characterize imperfections in various disturbances, such as measurement noise, model error, incomplete training data, and out-of-distribution testing data. Specifically, we employ a Bayesian convolutional neural network to quantify uncertainty and explore its application in SIM. The backbone of the reported neural network is the combination of U-net and Res-net with three low-resolution images from different structured illumination angles as inputs. The outputs are high-resolution images with double resolution beyond the numerical aperture and the pixel-wise confidence intervals quantification of reconstruction images. A series of simulations and experiments validate that the reported uncertainty quantification framework offers reliable uncertainty maps and high-fidelity super resolution images. Our work may promote practical applications of deep-learning-based super-resolution microscopy.