Here we have introduced Hessian structured illumination microscopy, which uses the continuity of the biological structures as a prior knowledge to guide iterative deconvolution of raw images from fluorescent samples undergone sub-ms exposures. The combination of optics, controlling system and deconvolution algorithm enables us to reduce the photon dose by ten folds as compared to normal structured illumination microscopy, and lead to the appreciation of mitochondrial cristae structures and enlarged vesicle fusion pore structures.

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