Structured illumination microscopy (SIM) reconstructs a super-resolved image from multiple raw images captured with different illumination patterns; hence, acquisition speed is limited, making it unsuitable for dynamic scenes. We propose a new method, Speckle Flow SIM, that uses static patterned illumination with moving samples and models the sample motion during data capture in order to reconstruct the dynamic scene with super-resolution. Speckle Flow SIM relies on sample motion to capture a sequence of raw images. The spatio-temporal relationship of the dynamic scene is modeled using a neural space-time model with coordinate-based multi-layer perceptrons (MLPs), and the motion dynamics and the super-resolved scene are jointly recovered. We validate Speckle Flow SIM for coherent imaging in simulation and build a simple, inexpensive experimental setup with off-the-shelf components. We demonstrate that Speckle Flow SIM can reconstruct a dynamic scene with deformable motion and 1.88x the diffraction-limited resolution in experiment.
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