With the rapid development of digital image processing technology, image recovery has been widely used in the fields of medicine, military, public defense, and agro-meteorology. This study integrates TVL1, ROF, Squares TVL1 (STVL1), and SHI model, proposes a non-convex and non-smooth model for removing impulse noise, and uses a variable separation technique ADMM to solve the model. In general, gradient-based methods are not suitable for non-smooth optimizations. Half-quadratic and Iterative Reweighted Least Squares (IRLS) algorithms cannot be applied to non-smooth functions when the zero point is non-differentiable. For non-convex non-smooth terms, Graduated NonConvexity (GNC) algorithms track non-smooth and non-convex minimums along the potential energy of a series of approximate non-smooth energy functions and need to consider their computational time. So in order to deal with non-convex non-smooth terms of the model, the multi-step convex relaxation method is used to solve the subproblem of the model. Although this method only leads to the local optimal solution of the original nonconvex problem, the local solution is an improvement over the global solution of the initial convex relaxation. In addition, because each stage is a convex optimization problem, this method is computationally efficient. The genetic algorithm was used to select the parameters of the model. Through a large number of experiments on different pictures and different noises, the robustness, running time, ISNR and PSNR of the model were better than the other three models. And this model can maintain the local information of the image with better visual quality.