A dual-constrained image reconstruction algorithm based on Kalman filtering is proposed to solve the problem of reconstructing the two-dimensional shock wave fringe image from the compressed image obtained by the Velocity Interferometer System for Any Reflector (VISAR) based on Compressed Ultrafast Photography (CUP). Based on the sparsity and smoothness of fringed images, the algorithm firstly transforms the problem into an optimization problem based on wavelet and total variational double prior constraints, and then, considering the noise of actual imaging, the weighted Kalman filter is used to predict and adjust the existing information of the image, and finally the Kalman filter is introduced into the iterative process of the two-step iterative threshold algorithm, and then the double-constraint optimization problem is solved to realize the accurate reconstruction of the compressed image. In the large-noise simulation experiment, the peak signal-to-noise ratio and structural similarity of the reconstructed images of the algorithm are increased by 4.8 dB and 14.81%, respectively, which significantly improves the image reconstruction quality. In actual experiments, the algorithm reconstructs a clear shock wave fringe image and reduces the maximum relative error of shock wave velocity by 9.57% and the average relative error of shock wave velocity by 2.2%, which verifies the feasibility of the algorithm.