A New Weighted Nuclear Norm Regularization Model for Removing Salt and Pepper Noise With Applications

ABSTRACT The application of weighted kernel norm to image denoising has gained significant research interest in recent years by using the non‐local self‐similarity of images. In this paper, we propose a novel model for removing salt and pepper noise that integrates weighted kernel norm with higher‐order total variation regularization. Subsequently, we use the classical method of alternating direction of multipliers and introduce some auxiliary variables to transform the original problem into saddle point problem. To illustrate the analytical results, a series of numerical simulations are conducted. Finally, experimental comparisons demonstrate the superior performance of the proposed model, which outperforms other competitive methods in terms of both signal‐to‐noise ratio and structural similarity index.