In this paper, the techniques of blast wave field reconstruction based on tomography were studied. Overpressure field was reconstructed by inverting the velocity field in the process of shock wave transmission. Since the reconstruction process is difficult due to insufficient excitation sources and detectors, an EM algorithm was proposed based on priori information. Appropriate models were constructed using the proposed methods, and a simulation example was put forward at last. The result reveals that compared with the traditional methods, this method has higher precision and converges faster. It also shows the validity and practicality of the developed algorithm in solving the problem of incomplete data reconstruction.