An adaptive fourth-order partial differential equation for image denoising

To overcome the weakness of second order methods such as Perona-Malik model for image denoising, various high order models have been proposed and studied. However, there is not too much analysis of these equations to be found in the literature. In this paper, we propose an adaptive fourth-order partial differential equation, which joints a fourth-order term and a second-order term. The model takes advantage of the fourth-order model's better image avoiding staircase effect and the second-order model's better edge preserving effect. By introducing a functional framework and k-bounded partial variation (BPVk) space, we prove the existence of a weak solution of the proposed model. Experimental results show that the proposed model can alleviate the staircase effect and preserve edges accurately.