To solve the problem of reconstructing two-dimensional shock wave fringe from compressed image obtained from Compressed Ultrafast Photography (CUP) and two-dimensional Velocity Interferometer System for Any Reflector (VISAR), a compressed image reconstruction algorithm based on low-rank constraint and total-variation regularization is proposed. The algorithm uses the similarity and smoothness of the spatial structure of the fringe image to transform the reconstruction problem into an optimization problem of kernel norm minimization and total-variation regularization, and splits the optimization problem into multiple sub-problems using the plug-and-play alternate direction multiplier method to solve the optimization problem, thus realizing accurate reconstruction of the CUP-VISAR compressed image. The simulation results show that under the condition of high noise, the peak signal-to-noise ratio of the reconstructed image is increased by 8.45 dB, and the structural similarity is increased by 8.52%. The reconstruction effect is better than that of the mainstream reconstruction algorithm. The experimental results show that the relative error of the maximum velocity of the shock wave fringe is reduced from 13.5% to 3.46% (reduced by nearly 10%), which verifies the effectiveness of the algorithm.