Image denoising based on the adaptive weighted TVp regularization

Abstract Image denoising problem still remains an active research field in the image processing. To improve the denoising quality, it is very important to describe the local structure of the image in the proposed model. This fact motivates us to introduce an adaptive weighted TVp regularization-based denoising model, where the rotation matrix and the weighted matrix depend on the local structure of the image. Specially, these two matrices can enhance the diffusion of the responding Euler-Lagrangian equation along with the tangential direction of the edge. This procedure offers more control over the regularization and then allows more denoising in smooth regions and less denoising when processing edge regions. In addition, since the proposed model is nonsmooth and non-Lipschitz, we employ the alternating direction method of multipliers (ADMM) to solve it with the help of using the half-quadratic scheme to solve the related l 2 − l p subproblem. In particular, we also provide the convergence analysis of the used numerical methods. Some numerical comparisons show that the proposed model leads to considerable performance gains when tested on several denoising tasks.