With the rapid development of three-dimensional imaging technology, single-photon LiDAR has become a key technology in high-sensitivity remote sensing and precision imaging. However, under long-distance scanning conditions, traditional imaging techniques often fail to provide high-quality 3D images owing to limitations in sampling rate and resolution. To accurately simulate the detection performance of this system in various scenarios, this paper proposes a method combining a physical model and a binomial sampling process to generate echo photon data, and reconstructs 3D target images under low sampling rates using an improved TVCS algorithm. Simulation and reconstruction results indicate that LiDAR systems integrating compressed sensing theory and single-photon detection technology can effectively reduce photon acquisition and shorten imaging time. Compared with traditional OMP and TVAL3 algorithms, the proposed method maintains a superior peak signal-to-noise ratio and root mean square error, even at significantly reduced sampling rates, demonstrating improved image-recovery performance. This research not only provides new methodological support for the application of single-photon LiDAR under low photon sampling conditions but also expands the application range of compressed sensing theory in practical imaging systems. By linking the measurements of SPAD detectors with optical system parameters, the method describes the imaging process using the probability distribution of photon arrivals, thereby simulating the histogram constructed from single-photon data. Based on the generated data, time-of-flight information is obtained using a time-correlated single-photon counter on single-pixel imaging, enhancing the lateral resolution of single-point detection and providing in-depth information on the situation.