High-speed cameras explore more details than normal cameras in the time sequence, while the conventional video sampling suffers from the trade-off between temporal and spatial resolutions due to the sensor’s physical limitation. Compressive sensing overcomes this obstacle by combining the sampling and compression procedures together. A single-pixel-based real-time video acquisition is proposed to record dynamic scenes, and a fast nonconvex algorithm for the nonconvex sorted regularization is applied to reconstruct frame differences using few numbers of measurements. Then, an edge-detection-based denoising method is employed to reduce the error in the frame difference image. The experimental results show that the proposed algorithm together with the single-pixel imaging system makes compressive video cameras available.