Image denoising based on the adaptive weighted TVp regularization

•This paper propose a new image denoising model by coupling the rotation matrix and the weighted matrix into the TVp quasinorm regularization.•Since the proposed model is nonconvex and non-Lipschitz, we employe the ADMM to solve it with the help of the half-quadratic scheme.•The convergence of the proposed numerical methods is also discussed.•Numerical comparisons show that the proposed model leaded to considerable performance gains when testing on several denoising tasks.