Oil and gas seismic exploration have to adopt irregular seismic acquisition due to the increasingly complex exploration conditions to adapt to complex geological conditions and environments. However, the irregular seismic acquisition is accompanied by the lack of acquisition data, which requires high-precision regularization. The sparse signal feature in the transform domain in compressed sensing theory is used in this paper to recover the missing signal, involving sparse transform base optimization and threshold modeling. First, this paper analyzes and compares the effects of six sparse transformation bases on the reconstruction accuracy and efficiency of irregular seismic data and establishes the quantitative relationship between sparse transformation and reconstruction accuracy and efficiency. Second, an adaptive threshold modeling method based on sparse coefficient is provided to improve the reconstruction accuracy. Test results show that the method has good adaptability to different seismic data and sparse transform bases. The f-x domain reconstruction method of effective frequency samples is studied to address the problem of low computational efficiency. The parallel computing strategy of curvelet transform combined with OpenMP is further proposed, which substantially improves the computational efficiency under the premise of ensuring the reconstruction accuracy. Finally, the actual acquisition data are used to verify the proposed method. The results indicate that the proposed method strategy can solve the regularization problem of irregular seismic data in production and improve the imaging quality of the target layer economically and efficiently.