(eng): Structured illumination microscopy is a widely popular super-resolution technique for live cell imaging capable of surpassing the diffraction limit. Its temporal resolution is limited by the need to capture multiple low-resolution images to reconstruct a single high-resolution image. When observing rapid biological processes, the local movement between frames leads to the formation of reconstruction artifacts, which subsequently impair the data interpretation. We propose to include this type of movement in the definition of the image formation forward problem. The motion can then be estimated from the original data using optical flow, and the optimization problem is solved using the alternating direction method of multipliers. Our approach is tested against other reconstruction techniques on both synthetic and real biological data.