Cosmic ray muon radiography which has a good penetrability and sensitivity to high-Z materials is an effective way for
detecting shielded nuclear materials. Reconstruction algorithm is the key point of this technique. Currently, there are two
main algorithms about this technique. One is the Point of Closest Approach (POCA) reconstruction algorithm which
uses the track information to reconstruct; the other is the Maximum Likelihood estimation, such as the Maximum
Likelihood Scattering (MLS) and the Maximum Likelihood Scattering and Displacement (MLSD) reconstruction
algorithms which are proposed by the Los Alamos National Laboratory (LANL). The performance of MLSD is better
than MLS. Since MLSD reconstruction algorithm includes scattering and displacement information while MLS reconstruction algorithm only includes scattering information. In order to get this Maximum Likelihood estimation, in this paper, we propose to use EM method to get the estimation (MLS-EM and MLSD-EM). Then, in order to saving reconstruction time we use the OS technique to accelerate MLS and MLSD reconstruction algorithm with the initial value set to be the result of the POCA reconstruction algorithm. That is, the Maximum Likelihood Scattering-OSEM (MLS-OSEM) and the Maximum Likelihood Scattering and Displacement-OSEM (MLSD-OSEM). Numerical simulations show that the MLSD-OSEM is an effective algorithm and the performance of MLSD-OSEM is better than MLS-OSEM.