Fast tracking and imaging of translational moving objects via single-pixel imaging leveraging Fourier conjugate symmetry

In single-pixel imaging (SPI), the need to sequentially project numerous encoded patterns leads to low frame rates and pronounced motion blur when capturing moving targets, which severely limits its practical applications. Most existing approaches address this by inserting additional reference frames for motion estimation, but this inevitably reduces imaging efficiency and degrades the signal-to-noise ratio(SNR). To overcome these limitations, we propose a method that enables simultaneous high-precision motion tracking and image reconstruction for arbitrary translational motion without requiring any additional reference frames. Our approach utilizes the property of Fourier phase-conjugate pairs to estimate incremental displacements, which are integrated to form a motion trajectory and further refined using a genetic algorithm guided by total variation minimization. Both simulations and experimental results validate the method's robustness against noise and its capability to achieve clear reconstructions of fast-moving targets. This work opens up new possibilities for dynamic target imaging and offers a promising direction for future extensions to more complex motion models.