In this paper, we propose a nonlocal adaptive biharmonic regularization term for image denoising and restoration, combining the advantages of fourth order models (without staircase effects and preserving slops) and nonlocal methods (preserving textures). The theoretical analysis of the proposed model is briefly discussed. For its numerical solution, we employ $L^2$ gradient descent and finite difference schemes and design explicit, semi-implicit, and implicit schemes. Numerical results for denoising and restoration are shown on synthetic images, real images, and texture images.