Fourth-order anisotropic diffusion equations for noise removal

A class of fourth-order PDEs are proposed to optimize the trade-of between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the directional curvature magnitude of the image intensity function. These PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. So the proposed PDEs are able to avoid the blocky effects and false edges, while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion.