## 1 Introduction  
At present, using three-dimensional (3D) imaging technology to obtain 3D information about the surrounding environment is important in many application fields, particularly in the fields of autonomous driving, 3D printing, machine vision, and virtual reality [1; 2]. Traditional laser 3D imaging is divided into two main types: scanning and non-scanning. Scanning technology performs a point-by-point measurement of the target through a mechanical scanning device. The entire system occupies a large volume and has low measurement efficiency [3; 4]. Non-scanning technology usually uses an area array detector to measure the reflected light at every point in the target area simultaneously. However, imaging using an area array detector has problems, such as a low signal-to-noise ratio, limited imaging resolution, and limited response frequency; these lead to low imaging resolution and accuracy [5; 6; 7].  
Nyquist sampling theory requires that the sampling rate must be more than twice the signal bandwidth to reconstruct the original signal without distortion from the discrete sampling signal, but a large amount of redundant information occupies the resources of the signal sampling system. In 2006, [PERSON], [PERSON], and [PERSON] proposed the theory of compressed sensing [8; 9; 10]. It was proven that for sparse or sparsely expressed signals, the original signal can be reconstructed accurately with a high probability using a small number of measurement times. This resolves the contradiction between measurement resolution and measurement efficiency in traditional 3D imaging signal sampling and makes 3D imaging possible with a single-pixel detector. In 2008, [PERSON] of Rice University developed a single-pixel camera using the theory of compressed sensing; [PERSON] first applied compressed sensing to imaging systems [11]. In 2011, [PERSON] of the University of Rochester used a photon-counting method to achieve 3D compressed sensing imaging [12] using a pulsed laser with a wavelength of 780 nm and achieved a distance resolution of 30 cm. In 2014, [PERSON] of Beijing Institute of Technology proposed a 3D compressed sensing imaging method based on the phase method ranging principle [13] and conducted preliminary simulation verification of the entire system but did not study 3D imaging experiments further. In 2015, [PERSON] of Beihang University used a slicing method and a pulsed laser to realize 3D compressed sensing imaging [14] and accurately reconstructed a target scene with a resolution of \(128\times 128\), achieving an accuracy of 3 mm within a distance of 5 m.  
In this paper, a single-pixel non-scanning 3D imaging system was designed, and the system was investigated in terms of theories, simulations, and experiments. First, the effects of different sampling rates, sparse transform bases, measurement matrices, and reconstruction algorithms on the measurement results were compared through simulation experiments. Second, a non-scanning 3D imaging experimental platform, based on a single-pixel detector, was designed and constructed. Finally, an experiment was performed to compare the effects of different sampling rates and reconstruction algorithms on the reconstruction effect of 3D imaging to obtain a 3D image with a resolution of \(8\times 8\). The results of the experiment showed that the 3D imaging system works, and its reconstruction of the Hadamard measurement matrix and the minimum total variation reconstruction algorithm performed well.