Due to limited acquisition conditions in the field, the seismic data is usually incomplete, which affects the following seismic data processing and seismic interpretation. To solve this problem, the seismic data needs reconstruction. The projection onto convex sets (POCS) method utilizes the sparse characteristics of seismic waveforms in the Curvet domain to reconstruct high signal-to-noise ratio seismic data. This iterative algorithm is stable and has a fast convergence speed. However, during the recovery of seismic data, because the influence of direct waves and the blank area in the upper part of the shot gathers as the iteration progresses, the noise interference in the reconstructed data becomes increasingly severe, resulting in a low signal-to-noise ratio of the final recovered seismic data. Based on the implementation of the POCS iterative threshold algorithm, this article introduces the idea of Prior information constraints to optimize the original algorithm. By first performing coordinate mapping for shot gathers interpolation and then using it as a prior information constraint for interpolation, the impact of noise attenuation is dramatic. Finally, the synthesized seismic shot records were tested with actual shot gathers, and the results illustrated that the new method proposed in this paper can significantly improve the signal-to-noise ratio of reconstructed seismic data and enhance the continuity of seismic wave field events.