论文标题
四阶各向异性扩散，用于注入和图像压缩
Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression
论文作者
论文摘要
边缘增强扩散（EED）可以从其像素的一小部分重建原始图像的近似值。这使其成为基于PDE的图像压缩的有吸引力的基础。在这项工作中，我们将二阶EED推广到四阶对应物。它涉及一个四阶扩散张量，该张量与传统二阶EED相似的方式是从正规图像梯度构造的，允许沿边缘扩散，同时在它们跨越跨越的非线性扩散函数。我们表明，我们的四阶扩散张量形式主义为所有以前的各向异性四阶扩散方法提供了一个统一的框架，并提供了额外的灵活性。我们使用快速的半数方案实现了有效的实施。自然图像和医学图像的实验结果表明，与现有的二阶EED相比，我们的新型四阶方法会产生更准确的重建。
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.
