Fourth-order anisotropic diffusion equations for noise removal

A class of fourth-order PDEs are proposed to optimize the trade-off 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 PDE's are able to avoid the blocky effects and edge, while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion.