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Neutron penumbral imaging is a significant diagnostic technique in laser-driven inertial confinement fusion experiment. It is very important to develop a new reconstruction method to improve the resolution of neutron penumbral imaging. A new nonlinear reconstruction method based on total variation (TV) regularization is proposed in this paper. A TV-norm is used as regularized term to construct a smoothing functional for penumbral image reconstruction in the new method, in this way, the problem of penumbral image reconstruction is transformed to the problem of a functional minimization. In addition, a fixed point iteration scheme is introduced to solve the problem of functional minimization. The numerical experimental results show that, compared to linear reconstruction method based on Wiener filter, the TV regularized nonlinear reconstruction method is beneficial to improve the quality of reconstructed image with better performance of noise smoothing and edge preserving. Meanwhile, it can also obtain the spatial resolution with 5 μm which is higher than the Wiener method. [ABSTRACT FROM AUTHOR]