Centre for Mathematical Imaging Techniques, Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK.
IEEE Trans Image Process. 2010 Jun;19(6):1518-27. doi: 10.1109/TIP.2010.2042655. Epub 2010 Feb 17.
Variational techniques for gray-scale image denoising have been deeply investigated for many years; however, little research has been done for the vector-valued denoising case and the very few existent works are all based on total-variation regularization. It is known that total-variation models for denoising gray-scaled images suffer from staircasing effect and there is no reason to suggest this effect is not transported into the vector-valued models. High-order models, on the contrary, do not present staircasing. In this paper, we introduce three high-order and curvature-based denoising models for vector-valued images. Their properties are analyzed and a fast multigrid algorithm for the numerical solution is provided. AMS subject classifications: 68U10, 65F10, 65K10.
多年来，人们对灰度图像降噪的变分技术进行了深入研究；然而，针对向量值去噪情况的研究却很少，并且现有的极少数工作都是基于全变差正则化的。众所周知，用于去噪灰度图像的全变差模型会出现阶梯效应，而且没有理由表明这种效应不会传递到向量值模型中。相反，高阶模型不会出现阶梯效应。在本文中，我们引入了三种基于高阶和曲率的向量值图像去噪模型。分析了它们的性质，并提供了一种用于数值求解的快速多重网格算法。AMS 主题分类：68U10, 65F10, 65K10。
