Impulse noise corrupts digital images, and hinders the extraction process of information and features in computer vision applications. To restore digital images, total variation (TV) based methods using different data fidelity have been proposed. However, the restored images by using these TV models are always blocky and smeared because of staircase artifacts. Besides, using the \(\ell _2\) -norm as the data fidelity term for impulse noise removal produces unsatisfactory restoration results. Meanwhile, the \(\ell _1\) -norm data fidelity which is normally used for impulse noise produces over-penalized solutions and is not robust to outlier characteristics of impulse noise. To address this, in this paper, we present a new model which uses the non-convex \(\ell _0\) -norm as the data fidelity norm and the total generalized variation (TGV) for the regularizer. The non-convex \(\ell _0\) -norm is more suitable for impulse noise, while the TGV regularization has the ability to preserve edges and reduce the staircase effect better than the TV regularizer. In terms of objective and subjective evaluations, experimental results show that the proposed method is more highly effective and competitive than the latest state-of-the-art algorithms such as the \(\ell _0\) total variation, the \(\ell _1\) total generalized variation, the \(\ell _1\) overlapping group sparse total variation, and the nonconvex-nonconvex TV. Specifically, at noise level corruption of 70% and 90%, the experimental results show that the PSNR and SSIM values achieved by the proposed method are the highest, with noticeable gaps compared to other methods. This highlights a significant improvement in denoising performance at high noise levels.
