Neutron penumbral imaging is an important diagnosis technique in laser-driven inertial confinement fusion experiment. In order to refine the resolution of 5 μm, it is necessary to develop nonlinear methods in reconstructing the detected imaging. In this paper, the authors improve the molecular dynamics method by using the Leap-frog format to increase convergence, and adding the edge-preserving regularization to suppress the edge-diffusion. Furthermore, the conjugate gradient method is also studied, and the relationship and differences between these two methods are revealed. Comparing the reconstruction results of the two methods, the advantages and disadvantages are analyzed for detecting images with noise.