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