Lidar, with its advantages of high measurement accuracy, fine angular resolution, and strong anti-interference capability, plays a pivotal role in the field of scene depth information acquisition. Traditional approaches to achieving lateral spatial resolution in imaging include raster scanning and array detectors. The former necessitates frequent scanning to acquire depth maps, resulting in time consumption and instability. The latter encounters challenges such as high dark count rates, pixel crosstalk, and excessive costs for obtaining high-resolution images using array detectors. The introduction of compressed sensing (CS) offers a novel perspective on realizing non-scanning three-dimensional imaging. In this context, we propose a novel three-dimensional imaging system that combines CS with coherent dual-frequency continuous-wave lidar and utilizes the all-phase fast Fourier transform to extract both amplitude and phase information. This system requires only M measurements, and through a reconstruction algorithm, it achieves the inversion of depth information for N-pixel scenes (M << N). Integrating cost-effective components such as digital micromirrors and single-point detectors, this affordable system accomplishes three-dimensional imaging of a single target. Notably, it significantly reduces the required number of measurements while concurrently ensuring enhanced eye safety and signal-to-noise ratio.