To increase the temporal resolution and maximal imaging time of super-resolution (SR) microscopy, we have developed a deconvolution algorithm for structured illumination microscopy based on Hessian matrixes (Hessian-SIM). It uses the continuity of biological structures in multiple dimensions as a priori knowledge to guide image reconstruction and attains artifact-minimized SR images with less than 10% of the photon dose used by conventional SIM while substantially outperforming current algorithms at low signal intensities. Hessian-SIM enables rapid imaging of moving vesicles or loops in the endoplasmic reticulum without motion artifacts and with a spatiotemporal resolution of 88 nm and 188 Hz. Its high sensitivity allows the use of sub-millisecond excitation pulses followed by dark recovery times to reduce photobleaching of fluorescent proteins, enabling hour-long time-lapse SR imaging of actin filaments in live cells. Finally, we observed the structural dynamics of mitochondrial cristae and structures that, to our knowledge, have not been observed previously, such as enlarged fusion pores during vesicle exocytosis.