Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression
This work addresses image inpainting and compression for applications like medical imaging, but it is incremental as it builds on prior anisotropic diffusion methods.
The authors tackled the problem of image reconstruction from sparse pixel subsets by generalizing second-order edge-enhancing diffusion to a fourth-order method, achieving more accurate reconstructions on natural and medical images compared to the existing second-order approach.
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.