A well-balanced and adaptive variational model for the removal of mixed noise

•A variational model for denoising mixed noise based on statistical approaches is proposed.•An adaptive balance between the fidelity term and the smooth term is used for removal mixed noise.•The increase in information concerning edges increases the quality of image denoising results. Image denoising is one of the fundamental problems concerning image processing. Over the last decade mathematical models based on partial differential equations and variational techniques have led to superior results related to denoising problems. The additive noise models have been studied extensively, however, the reconstruction of images corrupted by nonadditive noise has not yet been thoroughly studied. In this paper, a novel variational method for the reconstruction of images corrupted by non-uniformly distributed noise is presented. The proposed model includes a balance between the data term and the regularization term in the energy functional, which takes into account the statistical control of the parameters and the position of the noisy points related to the edges presented in the image. The parameters are determined by the given initial noisy image. The obtained results have shown the effectiveness and robustness of the proposed model and in restoring images with multiplicative noise or mixed Gaussian noise, while preserving edges and small structures belonging to the image.