A non-convex and non-smooth weighted image denoising model

Abstract

In order to provide a more effective method to describe the local structure of the degraded image and to enhance the robustness of the denoising, we propose a non-convex total variational image denoising model that combines the non-convex log function with an adaptive weighted matrix within the total variation framework. In the proposed model, the weighted matrix is capable of effectively describing the primary direction of the edge structure, based on the coupling of the gradient operator of the denoising image and the diagonal matrix. As the proposed model is a non-convex and non-smooth optimisation problem, the iterative reweighted ${\ell }^1$ algorithm and alternating direction multiplier method are employed to decompose it into a number of readily solvable sub-problems. The results obtained from numerical experiments demonstrate that the proposed model is capable of effectively suppressing the noise while maintaining the local structure of the image.