Overpressure tomography is a typical incomplete data reconstruction problem, which uses the shock wave signal collected by the sensor to invert the overpressure distribution in the test area. In order to improve the solution accuracy, a shock wave overpressure tomography reconstruction method based on Gauss-Newton iterative combined superlaplace regularization is proposed in this paper. Because the collected shock wave signal is usually aliased with the interference signal, which will affect the measurement accuracy of the overpressure value, this paper firstly adopts the improved wavelet threshold algorithm to denoise the shock wave signal. Secondly, the image edges and the two-dimensional chromatographic model are constrained by the superlaplace prior. Then Gauss-Newton iterative algorithm and alternating direction multiplier algorithm are used to solve the problem of large ill-conditioned sparse matrix. The experimental results show that compared with the traditional total variational regularization and total generalized variational regularization, the reconstruction accuracy of the proposed method can be maintained at about 15%, which has certain application value in practical scenarios.