2020/06/18 by Ikram Jumakulyyev, Jumakulyyev, Ikram, Thomas Schultz +1
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #Model Reduction and Neural Networks #Tensor decomposition and applications #cs.CV
paper · pdf · doi:10.48550/arxiv.2006.10406
Accepted for publication in Springer book "Anisotropy Across Fields and Scales"
arxiv created 2020/06/18 · arxiv updated 2020/06/19
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.