  Edge-enhancing diffusion (EED) can reconstruct a close approximation of an
original image from a small subset of its pixels. This makes it an attractive
foundation for PDE based image compression. In this work, we generalize
second-order EED to a fourth-order counterpart. It involves a fourth-order
diffusion tensor that is constructed from the regularized image gradient in a
similar way as in traditional second-order EED, permitting diffusion along
edges, while applying a non-linear diffusivity function across them. We show
that our fourth-order diffusion tensor formalism provides a unifying framework
for all previous anisotropic fourth-order diffusion based methods, and that it
provides additional flexibility. We achieve an efficient implementation using a
fast semi-iterative scheme. Experimental results on natural and medical images
suggest that our novel fourth-order method produces more accurate
reconstructions compared to the existing second-order EED.
