This paper proposes a regularized generalized orthogonal matching pursuit algorithm with dynamic compensation characteristics based on the application context of compressive sensing in shock wave signal testing. We add dynamic compensation denoising as a regularization condition to the reconstruction algorithm. The resonant noise is identified and suppressed according to the signal a priori characteristics, and the denoised signal is reconstructed directly from the original signal downsampling measurements. The signal-to-noise ratio of the output signal is improved while reducing the amount of data transmitted by the signal. The proposed algorithm’s applicability and internal parameter robustness are experimentally analyzed in the paper. We compare the proposed algorithm with similar compression-aware reconstruction and dynamic compensation algorithms under the shock tube test and measured shock wave signals. The results from the reconstruction signal-to-noise ratio and the number of measurements required for reconstruction verify the algorithm’s effectiveness in this paper.