This study investigates the reduction in the resolution of the striations from the center to the edge through analysis of the imaging principle and the static experimental test of a streak tube. To improve the edge spatial resolution of the streak, we apply the compressed sensing to the X-ray streak camera imaging system and construct the compressed sensing (CS) reconstruction model for the streak camera and we implement the CS objective function by the orthogonal matching method. The reconstruction performance of the Gauss measurement matrix, Bernoulli measurement matrix, and M series family measurement matrix are compared, and the reconstruction parameters are optimized. A comparison between the original imaging results and the reconstruction results shows that the contrast ratio of the CS reconstruction is 12.2% higher than that of the original, and the limit resolution is 5 lp/mm higher than that of the original image. Furthermore, the improvement effect far from the central area is better than that at the central area. The CS reconstruction on the M series family measurement matrix can improve the image contrast ratio on the edge of the image, and, thus, static and dynamic spatial resolutions of the image are improved.