Multi-resolution single-pixel imaging via active sub-pixel shift scanning and geometric moment-based motion estimation

To reduce the reliance of super-resolution reconstruction in dynamic single-pixel imaging on the object’s natural motion, and to alleviate the trade-off between temporal and spatial resolution, this paper proposes a multi-resolution single-pixel imaging method based on active sub-pixel shift scanning and geometric-moment-based motion estimation. The system utilizes low-resolution Hadamard patterns to perform active sub-pixel shift scanning and estimates the object’s centroid displacement via geometric moment patterns. The relative displacement between the pattern and the object is jointly determined by the active scanning displacement and the object’s own motion displacement. It is then mapped onto reconstruction grids at different resolutions and incorporated into the corresponding physical forward models, which are used for TV-regularized reconstruction. By applying sliding windows of different lengths to a single continuous sequence of acquired measurements, the proposed method reconstructs images at the base spatial resolution and at 2 × and 4 × the base spatial resolution, with temporal resolution decreasing as the window length and spatial resolution increase, thereby enabling a tunable trade-off between temporal and spatial resolution. Simulation and experimental results demonstrate that the proposed method consistently achieves robust reconstruction performance across various motion states. Furthermore, this paper reveals the mechanism by which sub-pixel displacement generates super-resolution constraints within the Hadamard domain: the low-resolution Hadamard pattern under sub-pixel relative displacement is equivalent to the superposition of multiple high-resolution Hadamard patterns with different weights, thereby providing additional constraints for the recovery of high-resolution Hadamard coefficients.