Simultaneous cartoon and texture for nonconvex image inpainting via the balanced approach

This paper describes an image inpainting algorithm based on two tight frame systems that can sparsely represent cartoons and textures respectively. The proposed minimization formulation adopts nonconvex approximation via balanced approach, and an iterative algorithm is derived to find its solution. Numerical simulations demonstrate that the proposed nonconvex algorithm can significantly improve the image inpainting quality over the usual l₁ algorithm.