  The tracking and imaging of high-speed moving objects hold significant
promise for application in various fields. Single-pixel imaging enables the
progressive capture of a fast-moving translational object through motion
compensation. However, achieving a balance between a short reconstruction time
and a good image quality is challenging. In this study, we present a approach
that simultaneously incorporates position encoding and spatial information
encoding through the Fourier patterns. The utilization of Fourier patterns with
specific spatial frequencies ensures robust and accurate object localization.
By exploiting the properties of the Fourier transform, our method achieves a
remarkable reduction in time complexity and memory consumption while
significantly enhancing image quality. Furthermore, we introduce an optimized
sampling strategy specifically tailored for small moving objects, significantly
reducing the required dwell time for imaging. The proposed method provides a
practical solution for the real-time tracking, imaging and edge detection of
translational objects, underscoring its considerable potential for diverse
applications.
