A compressed ultrafast imaging system based on compressed sensing and streak camera was simulated. The original 3D image, denoted as I (x-y-t), was encoded and modulated by using digital micromirror devices (DMD), and subsequently transmitted to a slit full-open streak image converter. By means of deflection via a deflecting electric field, the multiple images at various time points were superimposed, resulting in the generation of the final integral image on the CCD. To reconstruct multiple original images I (x-y-t) from the CCD integral images, a total variational restoration algorithm was employed. The process of image acquisition and the restoration algorithm within the compressed ultrafast imaging system was simulated, and the eight dynamic 2D images depicting laser transmission through an air medium were obtained. Each image is exposed for a duration of 12.5 ps, and the reconstructed signal demonstrates a similarity of 0.92 when compared to the original signal.