A fourth order dual method for staircase reduction in texture extraction and image restoration problems

We propose a novel fourth order dual method for the minimization of the non-smooth semi-norm ∥Δ·∥₁ when in amalgamation with a new staircase reducing texture decomposition model of image processing. The proposed model incorporating this high order energy is a variant of the Chambolle Lions denoising model that additionally utilizes a negative Sobolev norm. We claim that the dual method is faster and more stable than the current gradient descent time marching algorithms often used to minimize such energies. Moreover, a proof of convergence of the proposed method, in conjunction with the new model, will be provided. Lastly, we provide guidelines on how the new energy and proposed framework can be naturally incorporated into many popular texture extraction and restoration models of image processing.