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Image reconstruction in magnetic induction tomography (MIT) aims to reconstruct the internal conductivity distribution in target object according to phase deviation data of detecting coil inducting eddy current in imaging region. Newton-one-step Error reconstructor (NOSER) is a common reconstruction algorithm in MIT, and Hessian matrix is an important part of NOSER, but Hessian matrix is ill-posed for little data changes greatly affecting reconstructed images. In order to obtain stable images, it's necessary to modify Hessian matrix. In this paper, two-dimensional forward problem of MIT was performed by Galerkin finite element method and the regularized NOSER based on eigenvalue threshold method by setting an ideal conduction number to recompose diagonal matrix was presented to reduce the ill-pose. Imaging models was reconstructed with different regularization algorithms using the simulated data, compared with Tikhonov and truncated singular value decomposition, eigenvalue threshold algorithm could obtain a better image quality with higher resolution. The results demonstrate that the eigenvalue threshold regularization algorithm improves image accuracy and anti-noise characteristic; the algorithm has no iterative procedure, it also enhances imaging speed. The algorithm provides foundation for clinical application of MIT technology.