title: On high-order denoising models and fast algorithms for vector-valued images.
abstract: 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.
authors.affiliation: Centre for Mathematical Imaging Techniques, Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK.
authors.forename: Carlos
authors.initials: C
authors.lastname: Brito-Loeza
authors.forename: Ke
authors.initials: K
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D016477:Artifacts; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted