Single-pixel imaging uses a single-pixel detector and sequential structured illumination to reconstruct images, offering remarkable flexibility across spectral bands. A longstanding challenge is that object or platform motion during acquisition is traditionally regarded as a source of blurring and degradation. Here, we present a paradigm in which object motion is reinterpreted as a beneficial source of sub-pixel sampling diversity rather than a detriment. By accurately tracking translational motion-accomplished via geometric moment illumination patterns fused with Hadamard patterns-we encode the known motion into the SPI forward model as structured perturbations. This approach converts motion from a blurring nuisance into a valuable imaging resource, effectively increasing the sampling density beyond the native grid. Incorporating the motion information directly into the inverse problem, we demonstrate that an enhanced-resolved reconstruction of the scene becomes achievable. The resulting linear measurement system, solved via total variation minimization, yields finer image details than SPI reconstructions acquired with a stationary target. Our work suggests that motion in SPI, far from being merely something to mitigate, can be harnessed to fundamentally improve SPI resolution and fidelity in dynamic scenes.
Guo et al. (Mon,) studied this question.